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Journal articles on the topic 'Nonlinear stiffness law'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Karádi, Dániel T., András A. Sipos, Marianna Halász, Viktor Hliva, and Dezső Hegyi. "An elastic phenomenological material law of technical textile with a nonlinear shear behaviour." Journal of Reinforced Plastics and Composites 40, no. 19-20 (March 30, 2021): 759–69. http://dx.doi.org/10.1177/07316844211005842.

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In technical textile engineering, macro-level phenomenological modelling effectively describes the material’s highly nonlinear behaviour. However, existing material laws concentrate on the normal stiffness in the orthotropic yarns and simplify the shear effect because of the two orders of magnitude difference between shear and normal stiffness. This article introduces an improved phenomenological model that includes nonlinear shear behaviour, and it determines the material parameters with a previously applied data fitting method for exponential functions. The nonlinear shear behaviour is valid for the elastic state, that is, at the service level of the loads. Time-dependent, cyclic loading or plastic behaviour is not considered.
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2

Biwa, S., S. Nakajima, and N. Ohno. "On the Acoustic Nonlinearity of Solid-Solid Contact With Pressure-Dependent Interface Stiffness." Journal of Applied Mechanics 71, no. 4 (July 1, 2004): 508–15. http://dx.doi.org/10.1115/1.1767169.

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Nonlinear interaction between elastic wave and contact interface, known to result in the so-called contact acoustic nonlinearity, is examined in a one-dimensional theoretical framework. The present analysis is based on a nonlinear interface stiffness model where the stiffness property of the contact interface is described as a function of the nominal contact pressure. The transmission/reflection coefficients for a normally incident harmonic wave, and the amplitudes of second harmonics as well as DC components arising at the contact interface are derived in terms of the interface stiffness properties and other relevant acoustic parameters. Implications of power-law relations between the linear interface stiffness and the contact pressure are examined in detail regarding the linear and nonlinear acoustic responses of the contact interface. Also, a plausible range of the relevant power-law exponent is provided from considerations based on the rough-surface contact mechanics. The analysis clarifies the qualitative contact-pressure dependence of various nonlinearity parameters based on different definitions. A particular power law is identified from existing experimental data for aluminum-aluminum contact, for which some explicit nonlinear characteristics are demonstrated. The theoretical contact-pressure dependence of the second harmonic generation at the contact interface is found to be in qualitative agreement with previous measurements.
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3

Dean, Edward T. R., and Rich Metters. "Cyclic Stiffness Degradation in Nonlinear Jackup Dynamics." SPE Projects, Facilities & Construction 5, no. 02 (June 1, 2010): 89–96. http://dx.doi.org/10.2118/132170-pa.

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4

Giaccu, Gian Felice, and Luca Caracoglia. "Generalized power-law stiffness model for nonlinear dynamics of in-plane cable networks." Journal of Sound and Vibration 332, no. 8 (April 2013): 1961–81. http://dx.doi.org/10.1016/j.jsv.2012.12.006.

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5

Gu, Jianguo, and Yimin Zhang. "Dynamic analysis of a ball screw feed system with time-varying and piecewise-nonlinear stiffness." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 18 (July 30, 2019): 6503–18. http://dx.doi.org/10.1177/0954406219865923.

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In this study, a single-degree-of-freedom model is established to investigate the dynamic characteristics of a single-nut double-cycle ball screw feed system by considering the contact states of the nonlinear kinematic joints. Based on fully considering the parameters of the ball screw feed system, the axial deformations and forces of the key components are calculated to construct a set of piecewise-nonlinear restoring force functions of the system displacement and worktable position. The variations of the contact stiffnesses of the kinematic joints and transmission stiffness of the system with different boundary conditions are analyzed and the results indicate that they all have abrupt changes when the system displacement reaches a critical value. The changing law of the system transmission stiffness in the whole stoke is discussed. Additionally, the effects of excitation force, worktable position and system mass on the dynamic characteristics of the system and its correlative components are analyzed.
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6

Čečrdle, Jiří, Jaromír Maleček, Václav Hlavatý, and Petr Malínek. "Simulation of Nonlinear Characteristic of Aileron Attachment on Aeroelastic Demonstrator Using Active Electromagnetic Spring Concept." Applied Mechanics and Materials 821 (January 2016): 191–98. http://dx.doi.org/10.4028/www.scientific.net/amm.821.191.

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The paper is focused on the design and development of the system simulating nonlinear attachment of the aileron actuation on the aeroelastic demonstrator. The system is based on the concept of the digitally controlled additional stiffness, activated by the real time control law system, controlling the required ratio of the force and deformation. The solution is based on the electromagnetic exciter. The nonlinear force is simulated by means of the system of the exciter and the deformation sensor. The active control system is independent of the excitation system. It adds the force ensuring the required characteristics and it allows to simulate the additional stiffness, damping or mass. Doing this, it is possible to adjust the selected vibration mode by controlling the force and obtain the required nonlinear characteristics. In the second order, there is also a constant influence of the exciter mass, stiffness and damping. The simulation of the linear, quadratic and cubic additional stiffness were verified.
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7

Elad, D., R. D. Kamm, and A. H. Shapiro. "Tube law for the intrapulmonary airway." Journal of Applied Physiology 65, no. 1 (July 1, 1988): 7–13. http://dx.doi.org/10.1152/jappl.1988.65.1.7.

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A semiempirical model of a pressure-area relationship for the bronchial airways is developed. It is described by a single similarity law consistent in form with the nonlinear elastic behavior of biological tissue. The tethering effect of the parenchyma is lumped into the wall properties of the bronchi and is included in an effective wall stiffness. The model, which is fitted to the experimental data of Takishima and his associates (J. Appl. Physiol. 38: 875-881, 1975), is lung-volume dependent and is therefore suitable for the analyses of airflow at different lung volumes, especially for modeling of forced expiration.
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8

Lei, Gang, Qian Chen, Ying Liu, and Jingjing Jiang. "An Inverse Method to Reconstruct Complete Stiffness Information of Rubber Bushing." Advances in Materials Science and Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/187636.

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A specific rubber bushing, with only radial and axial stiffness data having been acquired, is studied. In terms of the hyperelastic material of this bushing, three-term Ogden law is utilized as the material constitutive model which requires to be characterized. Without the material mechanical tests provided, a parameter identification method is proposed for searching a group of acceptable parameters which are able to model rubber-like material of this rubber bushing. In this case, based on the nonlinear finite element analysis method and optimization technique, the parameters of material law are determined, and the rotational stiffness of this bushing is also evaluated. The complete stiffness information has been established.
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9

Guo, Jishu, and Guohui Tian. "Mechanical design and robust tracking control of a class of antagonistic variable stiffness actuators based on the equivalent nonlinear torsion springs." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 232, no. 10 (June 22, 2018): 1337–55. http://dx.doi.org/10.1177/0959651818781272.

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The novel conceptual model of the antagonistic variable stiffness actuator based on the equivalent nonlinear torsion spring and the friction damper is demonstrated. For the dynamic model of the antagonistic variable stiffness actuator in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance, and input saturation constraints, using the coordinate transformation, the state space model of the antagonistic variable stiffness actuator with composite disturbances and input saturation constraints is transformed into an extended integral chain–type pseudo-linear system with input saturation constraints. Subsequently, a combination of the linear extended state observer, sliding mode control, and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the antagonistic equivalent nonlinear torsion spring-based variable stiffness actuator. Under the proposed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system has been proved via Lyapunov stability analysis. Simulation studies demonstrate the effectiveness and the robustness of the proposed robust adaptive tracking control method for the antagonistic variable stiffness actuator.
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10

Luo, Yue Gang, Song He Zhang, Bin Wu, and Hong Ying Hu. "Stability Analysis of Nonlinear Stiffness Rotor-Bearing System with Pedestal Looseness Fault." Applied Mechanics and Materials 483 (December 2013): 285–88. http://dx.doi.org/10.4028/www.scientific.net/amm.483.285.

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The dynamic model of nonlinear stiffness rotor-bearing system with pedestal looseness fault was set up, taking the linearity and cube item as the physics nonlinear factors. The periodic solution of system was analyzed by continuation-shooting algorithm for periodic solution of nonlinear non-autonomous system, and the stability of system periodic motion and unsteady law are discussed by Floquet theory. The unstable form of it is Hopf bifurcation. In the region of critical rotate speed, the main motion of the system is periodic-4; and it of ultra critical rotate speed, the main motion of the system is periodic-3 and chaotic motion. The conclusions provide theoretic basis reference for the fault diagnosis of the rotor-bearing system.
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11

Zhang, Sheng Dong, Zheng Lin Liu, and Hong Tao Yu. "Operating Performance Study of Ship’s Propulsive Shaft Including Stern Bearing’s Stiffness." Applied Mechanics and Materials 271-272 (December 2012): 1586–91. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.1586.

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In this paper, making ship propulsion shaft as the research object, We do research on characteristics of water-lubricated stern tube bearings and operating performance of ship’s propulsion shaft. Using FEM to discuss the impact law of the geometric properties to water-lubricated rubber bearing stiffness. Combining multiple dynamic and FEM theory, we build propulsion shaft rigid-flexible coupling dynamic model and discuss the influence of stern bearings’ stiffness. Results show that: In a certain scope, water-lubrication stern tube bearing’s stiffness changes in linear rule to the length-diameter ratio, and nonlinear change to radius ratio. Bearings’ stiffness has little influence on reaction force, but has much influence on displacement acceleration.
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12

Labadi, Youcef, and Naceur Eddine Hannachi. "Nonlinear damage behaviour of concrete structures." Canadian Journal of Civil Engineering 32, no. 4 (August 1, 2005): 765–74. http://dx.doi.org/10.1139/l05-018.

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Concrete structures are becoming more and more sophisticated and submitted to severe conditions, for example: high stresses and temperatures, cyclic loadings, earthquakes, etc. It is therefore necessary to simulate correctly the behaviour and damage of such structures. However, the behaviour of this material is among the most complex ones: various phenomena are observed experimentally, such as, loss of stiffness, irreversible strains, stiffness recovery and dissymmetric behaviour to mention a few. If all these effects are taken into consideration, it would lead to models that use numerous parameters. In this paper, a framework for damage mechanics of concrete is presented and used to simulate the nonlinear behaviour of concrete using finite element method (FEM). A relatively simple isotropic damage model, containing essentially no adjustable parameters is shown to produce results in remarkably good agreement with experimental results. Indeed, the damage law requires only the fracture energy to be completely defined. A special form of damage surfaces is constructed to illustrate the application of the model. A new damage criterion, defined as an equivalent strain norm, is proposed to take into consideration the dissymmetric behaviour of concrete. To verify the FEM program including the model, the predicted deformations are compared with experimental results and results from other nonlinear constitutive models.Key words: elasticity, quasi-brittle materials, damage, cracking, nonlinear behaviour, concrete modelling, finite element, simulation.
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13

Chen-Hui, Jia, Du Cai-Feng, and Qiu Ming. "Research on Nonlinear Dynamic Characteristics and Stability of Aerodynamic Bearings." Open Mechanical Engineering Journal 8, no. 1 (September 16, 2014): 243–50. http://dx.doi.org/10.2174/1874155x01408010243.

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In order to research the conical spiral groove aerodynamic bearings, the lubrication mathematical model of the bearings was established. The Reynolds equation of the laminar flow condition is used to calculate the partial differential equation of the perturbation pressure with the local finite difference method. Through calculating the stiffness and damping coefficient, the influence of the speed of law and eccentricity ratio on the dynamic characteristic coefficients has been gained. The mathematical model for the stability of the bearing-rotor system is established to study the influence law of speed influence of the law of speed and eccentricity ratio on the stability. The results show that the influence of the bearing's speed and eccentricity on the dynamic characteristics is significant. A reasonable choice of the bearing's speed and eccentricity contributes to improve the dynamic characteristics and the stability of the bearing-rotor system.
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14

Li, Da Lei, Yue Feng Yin, and Fang Fang Ding. "Function Simulation Analysis for Conical Spring of DANA Axis-Fixed Transmission." Advanced Materials Research 305 (July 2011): 57–60. http://dx.doi.org/10.4028/www.scientific.net/amr.305.57.

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The conical spring is one critical part of DANA MHR-3200 series Transmission, its structure is compact and it has good stability and used for bearing larger load and vibration attenuation. Using SolidWorks Simulation to conduct simulation analysis for the stiffness and modality of conical spring, acquire the deformation law of spring under service load, the stiffness curve with nonlinear characteristics, the first four orders natural frequencies and its modal shape, which will lay a foundation for the RE design of conical spring and provide basis for its reconfiguration and repair after lose efficacy.
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15

Marklund, Erik, Janis Varna, and Lennart Wallström. "Nonlinear Viscoelasticity and Viscoplasticity of Flax/Polypropylene Composites." Journal of Engineering Materials and Technology 128, no. 4 (June 30, 2006): 527–36. http://dx.doi.org/10.1115/1.2345444.

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In tensile tests the flax/polypropylene composites clearly show nonlinear behavior in loading and hysteresis loops in unloading. In creep tests performed at different load levels the response was nonlinear viscoelastic, and after recovery, viscoplastic strains were detected. No degradation in stiffness could be seen and thus nonlinear viscoelasticity and viscoplasticity were assumed to be the main cause for the observed behavior. The fracture surface of a specimen that experienced creep rupture at 24 MPa was investigated using a scanning electron microscope. The viscoplastic response was studied experimentally and described by a power law with respect to time and stress level in the creep test. The nonlinear viscoelasticity was described using Schapery’s model. The application of Prony series and a power law to approximate the viscoelastic compliance was investigated. Both descriptions have accuracy sufficient for practical applications. However, at high stresses the attempts to describe the viscoelastic compliance by a power law with a stress-independent exponent failed and therefore stress dependence of this exponent was included in the data analysis. The accuracy within the considered stress range is good, but the thermodynamic consistency of this procedure has to be proven.
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16

Wang, Jingyue, Haotian Wang, Huan Wang, and Lixin Guo. "Influence of the Random System Parameters on the Nonlinear Dynamic Characteristics of Gear Transmission System." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 7-8 (December 20, 2017): 619–30. http://dx.doi.org/10.1515/ijnsns-2016-0119.

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AbstractIn order to analyze the influence of the random parameters of the system on the nonlinear dynamic characteristics of the gear transmission system, considering the random perturbation of damping ratio, gear backlash, meshing frequency, meshing stiffness and the low frequency excitation caused by torque fluctuation, the random vibration equations of three-degree-of-freedom gear transmission system are established according to the Newton’s law. The motion differential equations are solved by the Runge–Kutta method. The effects of different random parameters such as load ratio, tooth frequency ratio, damping ratio, gear backlash and meshing stiffness on the dynamic response of the gear transmission system are analyzed in light and heavy loads and low and high speeds.
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17

Jiang, Xiu Gen, Yang Yang, Feng Jie Zhang, Jin San Ju, and Xiao Chuan You. "Analysis of the Load-Carrying Capability of the Casing Plug Joint of Steel Tube Structures Considering the Contact Effect." Advanced Materials Research 33-37 (March 2008): 321–26. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.321.

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Nonlinear finite element model analysis of the casing plug joints of steel tubular has been realized by ANSYS software. The law of load-carrying capability and stiffness of joint are separately gained by changing the ratio of length and diameter (R/L) and the ratio of the casing length and the main tube length (l/L). The influence of the casing thickness on the load-carrying capability and stiffness are also discussed. The results indicated that the load-carrying capability and stiffness of the joints both increase with the ratio(R/L) increment and the ratio of the casing length and main tube length (l/L). When the main tube thickness is equal to casing thickness, the load-carrying capacity of joints achieves the most.
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18

Fortin, M., J. Soulhat, A. Shirazi-Adl, E. B. Hunziker, and M. D. Buschmann. "Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison With a Fibril-Reinforced Biphasic Model." Journal of Biomechanical Engineering 122, no. 2 (October 18, 1999): 189–95. http://dx.doi.org/10.1115/1.429641.

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Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample’s radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models. [S0148-0731(00)00702-0]
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19

Guo, Quan Quan, and Jie Ting Hu. "Research on Bearing Capacity of Steel Tube-Reinforced Concrete Column Subjected to Eccentric Compression Load." Advanced Materials Research 163-167 (December 2010): 66–73. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.66.

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Nonlinear constitutive law was used in this paper. On the basis of plain section assumption, through isoparametric element theory, nonlinear secant and tangent stiffness matrices of section were derived. Nonlinear equation was solved by Newton-Raphson method. The bearing mechanism under the eccentric compression was revealed by changing eccentricity and position coefficient. The result is found to be in good agreement with the experimental data, and it shows that large and minor eccentricity failure mode, which are similar to reinforced concrete, are existed in steel tube-reinforced concrete column. In addition, force-moment correlation curve is derived. By calculation and comparison. The ultimate capacity is found to be greatly underestimated in the current technical specification.
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20

Lian, Tan, and Dang Pei. "Study on Rub-Impact Dynamical Behavior of An Asymmetrical Rotor-Bearing with Variable Ratio of Stiffness." Open Mechanical Engineering Journal 9, no. 1 (February 20, 2015): 80–85. http://dx.doi.org/10.2174/1874155x01509010080.

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A rub-impact mathematic model of an Asymmetrical rotor-bearing with nonlinear oil film force is built in the paper. The bifurcation diagrams of the response were given following the changing of ratio of stiffness. We analyzed the bifurcation and the chaos character of an Asymmetrical rotor-bearing with operating rotor stiffness changing, then we get the dynamical character and the law when the rubbing happen. The nonlinear dynamic behaviors of the system were studied by using the numerical value integral and Poincare mapping methods. By analysis the process of rub-impact, it is so complex and many low frequencies with large amplitude are in the range of 0.3~0.6 X. The way of period-chaos-period and the phenomena of diverging backward whirl are discovered when the rubbing happen. These results provide important theoretical references for the safety operation of generating sets and the exact identification of the faults in rotating machinery.
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21

Xu, Bing, Zhi Geng Fan, Shao Rong Yu, and Wei Niu. "Stress Relaxation Analysis of Polyurethane Foam Preloaded Structures." Advanced Materials Research 97-101 (March 2010): 871–74. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.871.

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Based on the nonlinear finite element analysis method, FEA models which describe the viscoelastic friction contact state of the polyurethane foam preloaded structures are created. In the simulations, the general Maxwell viscoelastic constitutive relation is introduced and a seven-parameter general Maxwell viscoelastic model is used to fit the experimental stress relaxation curve of polyurethane foam. During the nonlinear contact analysis, coulomb friction law is adopted, and the effects of the coulomb friction coefficient on the reaction force in the axial direction are analyzed. The FE results show that the change tendencies of relation curves of the structures are similar to which of the polyurethane foams. In the end, the influences of stiffness ratio of polyurethane foam to the outer component on the structural relaxed force are discussed, and the FE results indicate that the stiffness ratios affect the stress (force) relaxation degree remarkably. That is to say a good structure design could optimize the mechanical performance of the complicated structures greatly.
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22

Deshmukh, S. N., and N. K. Chandiramani. "LQR Control of Wind Excited Benchmark Building Using Variable Stiffness Tuned Mass Damper." Shock and Vibration 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/156523.

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LQR control of wind induced motion of a benchmark building is considered. The building is fitted with a semiactive variable stiffness tuned mass damper adapted from the literature. The nominal stiffness of the device corresponds to the fundamental frequency of the building and is included in the system matrix. This results in a linear time-invariant system, for which the desired control force is computed using LQR control. The control force thus computed is then realized by varying the device stiffness around its nominal value by using a simple control law. A nonlinear static analysis is performed in order to establish the range of linearity, in terms of the device (configuration) angle, for which the control law is valid. Results are obtained for the cases of zero and nonzero structural stiffness variation. The performance criteria evaluated show that the present method provides displacement control that is comparable with that of two existing controllers. The acceleration control, while not as good as that obtained with the existing active controller, is comparable or better than that obtained with the existing semiactive controller. By using substantially less power as well as control force, the present control yields comparable displacement control and reasonable acceleration control.
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23

Horowitz, A., I. Sheinman, Y. Lanir, M. Perl, and S. Sideman. "Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part I: Two Dimensional Formulation for Thin Myocardial Strips." Journal of Biomechanical Engineering 110, no. 1 (February 1, 1988): 57–61. http://dx.doi.org/10.1115/1.3108406.

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A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.
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24

Zhou, Le, Xiao Xing Liu, Ying Li, and Dong Yan. "Nonlinear Analysis of FRP SRC Concrete Beams." Advanced Materials Research 393-395 (November 2011): 201–4. http://dx.doi.org/10.4028/www.scientific.net/amr.393-395.201.

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On the basis of the theory of FRP sheet steel reinforcing concrete beams (SRC-beams), in order to better explore the force performance of FRP (Fiber Reinforce Plastic) steel reinforcing concrete beams, this paper analyzes the stress process simulation of the beam using the computer program of nonlinear analysis. In order to validate the program of the beam section the reliability of the simulation analysis, this paper brings beam section size and its material performance parameters into program and gets different parameters on the bearing capacity of beams influence law. Research shows that when working in the stage of FRP elasticity the reinforcement of FRP layers has little influence on bend curvature figure. In the elastic-plastic stage it has larger influence and the cure increases with the increase of FRP reinforcement layer. It shows that with the increase of the section stiffness beam bending flexural capacity is also bigger.
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25

Li, Ying, and Ye Tang. "Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/1393954.

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The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton’s second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff’s fractional material model are much larger than those predicted by Mote’s fractional material model.
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26

Gourc, Etienne, Sébastien Seguy, Guilhem Michon, and Alain Berlioz. "Chatter Control in Turning Process with a Nonlinear Energy Sink." Advanced Materials Research 698 (May 2013): 89–98. http://dx.doi.org/10.4028/www.scientific.net/amr.698.89.

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This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.
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Horowitz, A., I. Sheinman, and Y. Lanir. "Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part II: Three Dimensional Formulation for Thick Ventricular Wall Segments." Journal of Biomechanical Engineering 110, no. 1 (February 1, 1988): 62–68. http://dx.doi.org/10.1115/1.3108407.

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A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness, and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.
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Nematollahi, Mohammad Sadegh, Hossein Mohammadi, Rossana Dimitri, and Francesco Tornabene. "Nonlinear Vibration of Functionally Graded Graphene Nanoplatelets Polymer Nanocomposite Sandwich Beams." Applied Sciences 10, no. 16 (August 15, 2020): 5669. http://dx.doi.org/10.3390/app10165669.

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We provide an analytical investigation of the nonlinear vibration behavior of thick sandwich nanocomposite beams reinforced by functionally graded (FG) graphene nanoplatelet (GPL) sheets, with a power-law-based distribution throughout the thickness. We assume the total amount of the reinforcement phase to remain constant in the beam, while defining a relationship between the GPL maximum weight fraction, the power-law parameter, and the thickness of the face sheets. The shear and rotation effects are here considered using a higher-order laminated beam model. The nonlinear partial differential equations (PDEs) of motion are derived from the Von Kármán strain-displacement relationships, here solved by applying an expansion of free vibration modes. The numerical results demonstrate the key role of the amplitudes on the vibration response of GPL-reinforced sandwich beams, whose nonlinear oscillation behavior is very important in the physical science, mechanical structures and other mathematical analyses. The sensitivity of the response to the total amount of GPLs is explored herein, along with the possible effects related to the power-law parameter, the structural geometry, and the environmental conditions. The results indicate that changing the nanofiller distribution patterns with the proposed model can remarkably increase or decrease the effective stiffness of laminated composite beams.
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29

Qi, Nian, and Ji Hong Ye. "Nonlinear Dynamic Analysis of Space Frame Structures by Discrete Element Method." Applied Mechanics and Materials 638-640 (September 2014): 1716–19. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1716.

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This document explores the possibility of the discrete element method (DEM) being applied in nonlinear dynamic analysis of space frame structures. The method models the analyzed object to be composed by finite particles and the Newton’s second law is applied to describe each particle’s motion. The parallel-bond model is adopted during the calculation of internal force and moment arising from the deformation. The procedure of analysis is vastly simple, accurate and versatile. Numerical examples are given to demonstrate the accuracy and applicability of this method in handling the large deflection and dynamic behaviour of space frame structures. Besides, the method does not need to form stiffness matrix or iterations, so it is more advantageous than traditional nonlinear finite element method.
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30

Hu, Hongyang, Ming Feng, and Tianming Ren. "Effect of roundness error on the performance of novel gas foil conical bearings." Industrial Lubrication and Tribology 72, no. 7 (April 4, 2020): 895–904. http://dx.doi.org/10.1108/ilt-01-2020-0019.

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Purpose The purpose of this paper is to study the effect law of roundness error on the properties of gas foil conical bearing (GFCB), and the performance of bearings with different non-circular sleeve shapes are calculated. Design/methodology/approach For the bump-type GFCB, the nonlinear bump foil stiffness model and 1-D beam top foil stiffness model are built. On this basis, the finite element method and finite difference method are used to solve the Reynolds equation and the film thickness equation coupled, and the static and dynamic properties of GFCB are calculated. The effect law of sleeve roundness error on the static performance under different conditions is obtained. Moreover, the dynamic stiffness and damping characteristics under different errors are also studied. Findings The roundness error will decrease the load capacity and friction torque of GFCB, and increase the attitude angle. The error effect is more dramatic when there is larger eccentric, small nominal clearance, larger error value and more error lobes, and the static performance exhibits a periodic change in the circumferential direction. The roundness error can also decrease the direct stiffness and cross-coupled damping of GFCB, while the cross-coupled stiffness increases largely, which will reduce the bearing stability. Originality/value The roundness error adversely affects the static and dynamic characteristics of GFCB, which should be concerned by bearing designers, researchers and academicians. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2020-0019/
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31

von Boetticher, Albrecht, and Axel Volkwein. "Numerical modelling of chain-link steel wire nets with discrete elements." Canadian Geotechnical Journal 56, no. 3 (March 2019): 398–419. http://dx.doi.org/10.1139/cgj-2017-0540.

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Chain-link mesh is one of several net types used as protection against rockfall, shallow landslides, and debris flows. The dynamic impact and the corresponding nonlinear barrier response require numerical models. Chain-link meshes show a nonlinear anisotropic behaviour caused by the geometry of the wire. Resolving this geometry and its deformation results in a bottleneck of numerical costs. We present a discrete element model that covers the nonlinear and anisotropic behaviour of the chain-link mesh, using results from either small-scale, quasi-static tension tests or from a detailed mechanical model as material-law input. The mesh stiffness, resistance, and failure depend on the inner mesh opening angle and thus on the direction of deformation. This information enters the model through the transformation of the nonlinear, three-dimensional deformation processes into a nonlinear material law, with an interpolated dependency on the inner mesh angle. The model maps the resistance of the mesh against impacting masses and covers the energy absorption and it is capable of predicting the dynamic behaviour of different protection barriers with high accuracy, optimized calculation time, and minimized calibration efforts. This is illustrated by high impact energy tests that follow the ETAG027 standard, and also with a rockfall attenuating system.
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32

Jia, Chenhui, Huanji Pang, Wensuo Ma, and Ming Qiu. "Analysis of dynamic characteristics and stability prediction of gas bearings." Industrial Lubrication and Tribology 69, no. 2 (March 13, 2017): 123–30. http://dx.doi.org/10.1108/ilt-09-2015-0134.

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Purpose The prediction model to estimate the stability of a rotor-bearing system is established, which can predict the stability of gas bearings by applying Routh–Hurwitz stability criterion. This paper aims to provide the theoretical foundation for controlling actively the bearing running stiffness and damping and stemming the instability of a gas film. Design/methodology/approach The nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established. Perturbation control equation is derived by the partial derivative method. The finite difference method is used to discrete the perturbation control equation in generalized coordinate system, and the difference expression of perturbation pressure is derived. The relational expression which involves the relationship between the dynamic characteristic coefficients of HSGHGB systems and perturbation pressure is deduced. So, the transient perturbation pressure distribution of a three-dimensional micro gas film, nonlinear gas film force, dynamic stiffness and dynamic damping coefficients of bearings are numerically computed using VC++6.0 programs. Findings The results show that the influence of supply pressure, speed and eccentricity on the dynamic characteristics of bearings is significant. Originality/value The influence law of supply pressure, speed and eccentricity ratio on the dynamic stiffness and damping coefficients of HSGHGB systems is researched. The prediction model to estimate the stability of rotor-bearing system is established, which can predict the stability of gas bearings by applying the Routh–Hurwitz stability criterion.
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33

Zhang, Xuhui, Wenjuan Yang, Meng Zuo, Houzhi Tan, Hongwei Fan, Qinghua Mao, and Xiang Wan. "An Arc-shaped Piezoelectric Bistable Vibration Energy Harvester: Modeling and Experiments." Sensors 18, no. 12 (December 17, 2018): 4472. http://dx.doi.org/10.3390/s18124472.

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In order to improve vibration energy harvesting, this paper designs an arc-shaped piezoelectric bistable vibration energy harvester (ABEH). The bistable configuration is achieved by using magnetic coupling, and the nonlinear magnetic force is calculated. Based on Lagrangian equation, piezoelectric theory, Kirchhoff’s law, etc., a complete theoretical model of the presented ABEH is built. The influence of the nonlinear stiffness terms, the electromechanical coupling coefficient, the damping, the distance between magnets, and the load resistance on the dynamic response and the energy harvesting performance of the ABEH is numerically explored. More importantly, experiments are designed to verify the energy harvesting enhancement of the ABEH. Compared with the non-magnet energy harvester, the ABEH has much better energy harvesting performance.
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34

Xu, Xing-zhi, Ya-kui Gao, and Wei-guo Zhang. "Iterative Learning Control of a Nonlinear Aeroelastic System despite Gust Load." International Journal of Aerospace Engineering 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/237804.

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The development of a control strategy appropriate for the suppression of aeroelastic vibration of a two-dimensional nonlinear wing section based on iterative learning control (ILC) theory is described. Structural stiffness in pitch degree of freedom is represented by nonlinear polynomials. The uncontrolled aeroelastic model exhibits limit cycle oscillations beyond a critical value of the free-stream velocity. Using a single trailing-edge control surface as the control input, a ILC law under alignment condition is developed to ensure convergence of state tracking error. A novel Barrier Lyapunov Function (BLF) is incorporated in the proposed Barrier Composite Energy Function (BCEF) approach. Numerical simulation results clearly demonstrate the effectiveness of the control strategy toward suppressing aeroelastic vibration in the presence of parameter uncertainties and triangular, sinusoidal, and graded gust loads.
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35

Guo, Li Na. "The Application of an Unsaturated Soil Elastoplasticity Model in Dam-Reservior Coupling System." Advanced Materials Research 261-263 (May 2011): 1239–43. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.1239.

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This paper summarized the research of an unsaturated soil elastoplastic model(BBM), then a revised elastoplastic incremental stiffness matrix for unsaturated soil is deduced,discrete the governing equation in space domain and time domain with Galerkin weighted residual method and Euler method,a nonlinear finite element program is developed for the analysis the water-mechanical coupling system of unsaturated soil.The constitutive model is used for a homogeneous dam’s FSI problem, and the seepage and deformation in dam’s distribution consistent with law.
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36

Alimoradzadeh, Mehdi, Mehdi Salehi, and Sattar Mohammadi Esfarjani. "Nonlinear Dynamic Response of an Axially Functionally Graded (AFG) Beam Resting on Nonlinear Elastic Foundation Subjected to Moving Load." Nonlinear Engineering 8, no. 1 (January 28, 2019): 250–60. http://dx.doi.org/10.1515/nleng-2018-0051.

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Abstract In recent years, structures made of Functionally Graded materials (FGMs) are used in industries due to the continuously compositional variation of the constituents in FGMs along different directions. In order to develop FGMs, nonlinear vibration analysis to study dynamic behavior is needed. This study proposes nonlinear vibration analysis of a simply supported axially functionally graded (AFG) beam subjected to a moving harmonic load as an Euler-Bernoulli beam utilizing Green’s strain tensor. Axial variation of material properties of the beam is based on the power law. The governing equations of motion are derived via Hamilton’s principle. The Galerkin’s method is implemented to reduce the nonlinear partial differential equations of the system to a number of nonlinear ordinary differential equations. He’s variational method is applied to obtain approximate analytical expressions for the nonlinear frequency and the nonlinear dynamic response of the AFG beam. The effect of some parameters such as the power index and stiffness coefficients, among others, on the nonlinear natural frequency has been investigated. The influence of above mentioned parameters as well as the velocity of the moving harmonic load on the nonlinear dynamic response has been studied. The results indicate that these parameters have a considerable effect on both nonlinear natural frequency and response amplitude.
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37

Chiou, B. C., and M. Shahinpoor. "Dynamic Stability Analysis of a Two-Link Force-Controlled Flexible Manipulator." Journal of Dynamic Systems, Measurement, and Control 112, no. 4 (December 1, 1990): 661–66. http://dx.doi.org/10.1115/1.2896192.

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This study investigates the effect of link flexibility on the dynamic stability of a two-link force-controlled robot manipulator. The nonlinear open-loop equations for the compliant motion are derived first. By employing the hybrid force/position control law, the closed-loop dynamic equations are then explicitly derived. The nonlinear closed-loop equations are linearized about some equilibrium configurations. Stability analyses are carried out by computing the eigenvalues of the linearized system equations. Results are verified by the numerical simulations using the complete nonlinear dynamic equations. The effect of the wrist force sensor stiffness on the dynamic stability is also investigated. Results show that the link flexibility is indeed an important source of dynamic instability in the motion of force-controlled manipulators. Moreover, the system stability is dominated by the effect of the distributed flexibility of the first link.
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38

Domscheit, A., H. Rothert, and T. Winkelmann. "Refined Methods for Tire Computation." Tire Science and Technology 17, no. 4 (October 1, 1989): 291–304. http://dx.doi.org/10.2346/1.2141689.

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Abstract Realistic computation of automobile tires is best achieved by modeling the whole tire with finite element methods. A numerical solution of the quasi-static contact problem for the whole tire requires a refined mesh of elements with redundant degrees of freedom when nonlinear material assumptions are considered. Both laminated shell elements and incompressible continuum elements are used here. The stiffness matrix of a shell element is determined by numerically integrating all layers within the thickness of each element. Numerical studies have been made by a finite element technique that includes shell elements and Swanson's material model, which covers large deformations. The major contribution of this paper is implementation of a composite theory that includes effects of large displacements on the stiffness into an existing element. Swanson's material law was also simplified and implemented.
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39

Arefi, Mohammad, Mahmoud Pourjamshidian, Ali Ghorbanpour Arani, and Timon Rabczuk. "Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams." Journal of Low Frequency Noise, Vibration and Active Control 38, no. 1 (December 18, 2018): 122–42. http://dx.doi.org/10.1177/1461348418815410.

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This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.
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40

Pan, Zhi Hong, Ai Qun Li, and Yi Gang Sun. "Nonlinear Static Analysis of RC Shear Wall Structure Based on Opensees." Advanced Materials Research 163-167 (December 2010): 1425–30. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.1425.

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To study the seismic performance of RC shear wall, and to develop its fine nonlinear analysis method, systemic studies on nonlinear static analysis and it’s realization method are carried out. Beginning with rotating-angle softened-truss model for coupled shear and flexural responses, analytical model of solid wall is presented based on the comparative study on four types of constitutive law of concrete for confined concrete of boundary zone. Good agreements between analytical and experimental results of load-displacement relation are found, which indicates that the proposed analytical method can reflect the global mechanical behavior of shear wall well. Studies on coupling beam and global perforated wall modeling are implemented, then modeling approach and nonlinear static analysis method for perforated wall are proposed. Comparing analytical load-displacement curve to experimental, initial stiffness and first turning point agree well and analytical ultimate capacity is close to experimental, which is shown that the load-displacement curve can actually exhibit the general load-displacement trend of perforated wall.
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41

Cai, Jian Jun, Jia Long Sun, and Feng Zhang. "Nondestructive Testing Method of Vertical Prestressed Finishing Twisted Steel Tension." Applied Mechanics and Materials 351-352 (August 2013): 1117–21. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.1117.

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Based on the dynamic, selecting the vibration shape functions for obtaining the structural frequency, without using the differential operation of the conventional Rayleigh law which improved the calculation accuracy, the three-parameter model was built which include the frequency of the exposed segment, the segment length of the exposed steel reinforcements and anchorage segment increased stiffness coefficient. Meanwhile the validity of the three-parameter model was verified using finite element numerical simulation. The vertical pretensioning force of the box girder webs model was designed at laboratory. The natural frequency of vertical prestressing tendons exposed section was obtained through the high-frequency acceleration sensor which was set up at the top of the exposed section. Relying on experimental test data, the model which had the nonlinear relationship between the effective tensile force and anchorage segment increased stiffness coefficient was established.
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42

Zhao, Jie, Yan Wang, Hao Wu, and Miao Ruan. "Coupling mechanism of highly nonlinear solitary waves with damaged composite material plates." Composites and Advanced Materials 30 (January 1, 2021): 2633366X2092808. http://dx.doi.org/10.1177/2633366x20928088.

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The coupling interaction between nonlinear solitary waves in one-dimensional granular chains and damaged composite material plates is considered. Based on Hertz contact law and meso-mechanical model of stiffness reduction of composite material plates when the fiber breakage is the main damage mode, the coupled differential equations of particle chains and damaged composite material plates are derived. By solving the differential equations with Runge–Kutta method to get the velocity and displacement curves of particles and analyzing the delays and amplitude ratios of reflected waves, it is found that the damage quantity, fiber volume fraction, and thickness of damaged composite material plates as well as gravity have an effect on solitary waves. The preliminary research results provide a theoretical basis for nondestructive testing of damaged composite material plates by using solitary waves.
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43

Liu, Yongguang, Xiaohui Gao, and Chunxu Chen. "Research of Jiles-Atherton Dynamic Model in Giant Magnetostrictive Actuator." Mathematical Problems in Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/2609069.

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Due to the existence of multicoupled nonlinear factors in the giant magnetostrictive actuator (GMA), building precise mathematical model is highly important to study GMA’s characteristics and control strategies. Minor hysteresis loops near the bias magnetic field would be often applied because of its relatively good linearity. Load, friction, and disc spring stiffness seriously affect the output characteristics of the GMA in high frequency. Therefore, the current-displacement dynamic minor loops mathematical model coupling of electric-magnetic-machine is established according to Jiles-Atherton (J-A) dynamic model of hysteresis material, GMA structural dynamic equation, Ampere loop circuit law, and nonlinear piezomagnetic equation and demonstrates its correctness and effectiveness in the experiments. Finally, some laws are achieved between key structural parameters and output characteristics of GMA, which provides important theoretical foundation for structural design.
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44

Khoa, Nguyen Minh, and Hoang Van Tung. "Nonlinear thermo-mechanical stability of shear deformable FGM sandwich shallow spherical shells with tangential edge constraints." Vietnam Journal of Mechanics 39, no. 4 (December 27, 2017): 351–64. http://dx.doi.org/10.15625/0866-7136/9810.

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This paper presents an analytical approach to investigate the nonlinear axisymmetric response of moderately thick FGM sandwich shallow spherical shells resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. Material properties are assumed to be temperature independent, and effective properties of FGM layer are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations and various degree of tangential constraint of boundary edge into consideration. Approximate solutions are assumed to satisfy clamped boundary condition and Galerkin method is applied to derive closed-form expressions of critical buckling loads and nonlinear load-deflection relation. Effects of geometrical parameters, thickness of face sheets, foundation stiffness, imperfection, thermal environments and degree of tangential edge constraints on the nonlinear stability of FGM sandwich shallow spherical shells are analyzed and discussed.
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45

Wang, C. Y., R. Z. Wang, C. C. Chuang, and T. Y. Wu. "Nonlinear Dynamic Analysis of Reticulated Space Truss Structures." Journal of Mechanics 22, no. 3 (September 2006): 199–212. http://dx.doi.org/10.1017/s1727719100000848.

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AbstractIn this paper, a simpler formulation for the nonlinear motion analysis of reticulated space truss structures is developed by applying a new concept of computational mechanics, named the vector form intrinsic finite element (VFIFE or V-5) method. The V-5 method models the analyzed domain to be composed by finite particles and the Newton's second law is applied to describe each particle's motion. By tracing the motions of all the mass particles in the space, it can simulate the large geometrical and material nonlinear changes during the motion of structure without using geometrical stiffness matrix and iterations. The analysis procedure is vastly simple, accurate, and versatile. The formulation of VFIFE type space truss element includes a new description of the kinematics that can handle large rotation and large deformation, and includes a set of deformation coordinates for each time increment used to describe the shape functions and internal nodal forces. A convected material frame and an explicit time integration scheme for the solution procedures are also adopted. Numerical examples are presented to demonstrate capabilities and accuracy of the V-5 method on the nonlinear dynamic stability analysis of space truss structures.
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46

Sobota, P. M., and K. A. Seffen. "Bistable polar-orthotropic shallow shells." Royal Society Open Science 6, no. 8 (August 2019): 190888. http://dx.doi.org/10.1098/rsos.190888.

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We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in order to enhance morphing structures. The material law causes stress singularities when the circumferential stiffness is smaller than the radial stiffness ( β < 1), requiring a careful choice of the trial functions in our Ritz approach, which employs a higher-order geometrically nonlinear analytical model. Bistability is found to strongly depend on the orthotropic ratio, β , and the in-plane support conditions. An investigation of their interaction offers a new perspective on the effect of the hoop stiffness on bistability: while usually perceived as promoting, it is shown to be only stabilizing insofar as it prevents radial expansions; however, if in-plane supports are present, it becomes a redundant feature. Closed-form approximations of the bistable threshold are then provided by single-curvature-term approaches. For significantly stiffer values of the radial stiffness, a strong coupling of the orthotropic ratio and the support conditions is revealed: while roller-supported shells are monostable, fixed-pinned ones are most disposed to stable inversions; insight is given by comparing to a simplified beam model. Eventually, we show that cutting a central hole is a suitable method to deal with stress singularities: while fixed-pinned shells are barely affected by a hole, the presence of a hole strongly favours bistable inversions in roller-supported shells.
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47

Moreno-Ahedo, L., and S. Diarte-Acosta. "Stability analysis of linear systems with switchable stiffness using the Floquet theory." Journal of Vibration and Control 25, no. 5 (November 29, 2018): 963–76. http://dx.doi.org/10.1177/1077546318811419.

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In this paper, a novel approach based on the Floquet theory is applied for the stability analysis of a mass–spring system with switchable stiffness. The Reid model is used to describe the dynamics of this semi-active vibration control problem. The semi-active control is achieved by a spring which commutes between a maximum and minimum stiffness according to a prescribed state-dependent rule and its performance is characterized by a system parameter, which relates to the extreme values of the stiffness. In order to apply the Floquet theorem, the Reid model is written as a linear periodic differential equation by converting the state-dependent rule into a time-periodic control law. The application of the theory allows us to obtain the Floquet multipliers and exponents in terms of the system parameter. The multipliers lie inside the unitary circle showing asymptotic stability, while the exponents are used to solve an optimization problem by applying a sensitivity analysis. Our results are validated by analyzing the Reid model using nonlinear analysis techniques. According to our findings, the present approach provides a useful tool to analyze the vibration control of linear systems with switchable stiffness in a natural and straightforward way, which also gives mathematical tractability for optimization purposes. In addition, this approach can be extended to study the cases of multi-degree-of-freedom systems and forced systems.
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48

Jha, Abhishek Kumar, and Sovan Sundar Dasgupta. "Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 19-20 (July 30, 2019): 7101–15. http://dx.doi.org/10.1177/0954406219866467.

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Modeling of fractionally damped nanostructure is extremely important because of its inherent ability to capture the memory and hereditary effect of several viscoelastic materials extensively used in nanotechnology. The nonlinear free vibration characteristics of a simply-supported nanobeam with fractional-order derivative damping via nonlocal continuum theory are studied in this article. Using Newton’s second law, the equation of motion for the nanobeam embedded in a viscoelastic matrix is derived. The Galerkin method is employed to transform the integro-partial differential equation of motion into a Duffing-type nonlinear ordinary differential equation. The fractional-order damping term is replaced by a combination of linear damping and linear stiffness term. The approximate analytical solution obtained via method of averaging is found to be in good agreement with solution obtained through numerical scheme. Detailed study of system parameters reveals that the fractional-order derivative damping has significant influence on the time response and effective natural frequency of the nanobeam.
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49

Han, Bangcheng, Yanpeng Chen, Haitao Li, and Lianhui Yang. "Discrete Model Reference Adaptive Control for Gimbal Servosystem of Control Moment Gyro with Harmonic Drive." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/897579.

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The double-gimbal control moment gyro (DGCMG) demands that the gimbal servosystem should have fast response and small overshoot. But due to the low and nonlinear torsional stiffness of harmonic drive, the gimbal servo-system has poor dynamic performance with large overshoot and low bandwidth. In order to improve the dynamic performance of gimbal servo-system, a model reference adaptive control (MRAC) law is introduced in this paper. The model of DGCMG gimbal servo-system with harmonic drive is established, and the adaptive control law based on POPOV super stable theory is designed. The MATLAB simulation results are provided to verify the effectiveness of the proposed control algorithm. The experimental results indicate that the MRAC could increase the bandwidth of gimbal servo-system to 3 Hz and improve the dynamic performance with small overshoot.
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50

Gaetani d’Aragona, Marco, Maria Polese, and Andrea Prota. "Effect of Masonry Infill Constitutive Law on the Global Response of Infilled RC Buildings." Buildings 11, no. 2 (February 7, 2021): 57. http://dx.doi.org/10.3390/buildings11020057.

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Masonry-infilled reinforced concrete frames represent a very common construction typology across the Mediterranean countries. The presence of infills substantially modifies the global seismic performances of buildings in terms of strength, stiffness, and energy dissipation. Although several research studies focused on the overall performances of infilled reinforced concrete frames, the modeling of infill panels remains an open issue due to the complex interaction between the infill and the frame and the uncertainties involved in the definition of the problem. In the present paper, an existing masonry-infilled RC frame designed according to obsolete seismic codes is chosen as a case study. A refined three-dimensional finite element model is built for performing nonlinear static and time-history analyses in order to investigate some significant aspects related to the modeling of infills. In particular, it is investigated the effect of different infill constitutive models on the seismic performance of infilled RC building expressed in terms of engineering demand parameters such as interstory drift ratios and peak floor accelerations, and on the generation of damage fragility curves.
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