Academic literature on the topic 'Nonlinear stiffness law'
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Journal articles on the topic "Nonlinear stiffness law"
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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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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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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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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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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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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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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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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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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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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.
Dissertations / Theses on the topic "Nonlinear stiffness law"
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Widarda, Dina Rubiana. "Longitudinal forces in continuously welded rails due to nonlinear track-bridge interaction for loading sequences." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1238081328011-05497.
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The use of continuously welded rails (CWR) governs the longitudinal stress caused by seasonal temperature changes, bending of supporting structure and braking/accelerating due to passing trains. Those three loads have been regulated in Eurocode1 and accomplished by the national codes like DIN Fb-101 in Germany. An additional loading case identified and treated in this thesis is the load due to a change of the coupling stiffness in longitudinal direction between the track and bridge. This additional load occurs as a consequence of the employment of a nonlinear stiffness law which increases the restoring force by a factor of 3 when the situation of the track changes from ‘unloaded’ to ‘loaded’ due to a passing train. This particular phenomenon has not been mentioned in the codes so far though it is a natural consequence of fundamental conditions in those codes. For CWR the longitudinal coupling between the rail and bridge plays an important role. This coupling interface is created either by a ballast, for a ballasted track, or by a fastening system in the case of slab track. The deformation state of the coupling interface characterizes the behaviour of the system, whether elastic or plastic. Therefore, the nonlinear behaviour is valid for the system. To accommodate the nonlinear nature, a sequential loading analysis is used, taking into account the loading history. As the change situation due to a passing train happens in a short time, the influence of the mass acceleration should be taken into account in the system’s equilibrium. This aspect is investigated by treating the dynamic load as an impulse-like load. However, a realistic load needs some time to affect the whole bridge, thus the continuous change of stiffness is used to simulate the dynamic analysis. There is a lack of information on determining the value of coupling stiffness in longitudinal direction caused by a passing train. Therefore, it is important to evaluate the coupling stiffness from field measurements in order to find reliable values. The implementation of the load onto several typical bridges shows that the change of the coupling stiffness increases the stresses and it should not be neglected. The evaluation of the load due to a change of the coupling stiffness accompanied by bending of the supporting structure gives satisfactory results by using the static analysis only. Thus, a dynamic analysis can be avoided. Multiple cycles of passing trains occurring after seasonal temperature change indicate a significant increase of elastic parts along the track-bridge coupling interface and a decrease in stresses in the rails. Thus the danger of deterioration is reduced significantlyDie Verwendung von durchgehend geschweißten Schienen auf Brücken führt zu zusätzlichen Längsspannungen infolge der Lastfälle jahreszeitliche Temperaturänderung, Brückendurchbiegung und Bremsen/Anfahren. Diese drei Lasten sind durch den Eurocode 1 vorgegeben und in die nationale deutsche Norm DIN Fb-101 integriert. In dieser Arbeit wird erstmals ein weiterer Lastfall identifiziert und behandelt, der durch den Wechsel der Koppelsteifigkeit in Längsrichtung zwischen Gleis und Tragwerk bei der Zugüberfahrt begründet wird. Dieser Lastfall wird hier mit „Ruck“ bezeichnet und ist eine zwangsläufige Konsequenz des nichtlinearen Längsverschiebewiderstandes, wie er im EC 1 und im DIN Fb-101 vorgegeben ist. Dennoch wurden die Auswirkungen auf das Systemverhalten bisher nicht untersucht. Bei einem Wechsel vom unbelasteten Gleis zum belasteten Gleis während einer Zugüberfahrt erhöht sich zum Beispiel der Längsverschiebewiderstand für ein Schottergleis um den Faktor 3! Die dadurch bedingte Veränderung des Zusammenwirkens zwischen Gleis und Tragwerk führt zu einer Veränderung des Systemzustandes und damit zu veränderten Schienenspannungen. Für durchgehend geschweißte Schienen spielt die Längskopplung zwischen Schiene und Brücke eine wesentliche Rolle. Beim Schottergleis wird sie dargestellt durch die Einbettung des Gleisrostes im Schotterbett im Zusammenwirken mit der Schienenbefestigung. Bei der festen Fahrbahn durch das Befestigungssystem. Für kleine Deformationen ist die Koppelsteifigkeit proportional zur Relativverschiebung zwischen Gleis und Brücke. Darüberhinaus geht das linear elastische Verhalten in ein quasi plastisches Verhalten mit konstanter Koppelkraft über. Folgerichtig ist die Behandlung einer Lastenfolge nur in inkrementeller Weise unter Einbeziehung der Verformungsgeschichte mechanisch korrekt. Die Lastfälle Bremsen/Anfahren, Brückendurchbiegung und Ruck ereignen sich nur während der Zugüberfahrt; also in relativ kurzer Zeit, dann allerdings mit einem erheblichen Lastgradienten. Somit stellt sich die Frage nach dem Einfluss der Massenbeschleunigungen, die in dieser Arbeit geklärt wird. Die im Fachbericht genanntenWerte für den Längsverschiebewiderstand des belasteten Gleises basieren auf einer relativ geringen Datenmenge. Aus diesem Grund werden die Messdaten einer umfangreichen Feldmessung mit Zugüberfahrten zu Aussagen über den Längsverschiebewiederstand herangezogen und die Problematik derartiger Messungen beleuchtet. Die unterschiedlichen Modellierungen des Lastfalls „Ruck“, einmal rein statisch und zum anderen dynamisch, ergeben übereinstimmende Schienenlängsspannungen für die statische und die kontinuierliche dynamische Variante. Somit kann auf die aufwändige dynamische Analyse verzichtet werden. Mehrere Zyklen von Zugüberfahrten im Anschluss an eine jahreszeitliche Temperaturänderung bewirken einen signifikanten Abbau der Durchrutschbereiche, also eine Erhöhung der elastischen Abschnitte in der Koppelfuge zwischen Bauwerk und Gleis verbunden mit einer Abnahme der Schienendruckspannungen. Somit hilft dieser Effekt dem System, der jahreszeitlichen Temperaturänderung zu widerstehen
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Widarda, Dina Rubiana. "Longitudinal forces in continuously welded rails due to nonlinear track-bridge interaction for loading sequences." Doctoral thesis, Technische Universität Dresden, 2008. https://tud.qucosa.de/id/qucosa%3A23616.
Full textAbstract:
The use of continuously welded rails (CWR) governs the longitudinal stress caused by seasonal temperature changes, bending of supporting structure and braking/accelerating due to passing trains. Those three loads have been regulated in Eurocode1 and accomplished by the national codes like DIN Fb-101 in Germany. An additional loading case identified and treated in this thesis is the load due to a change of the coupling stiffness in longitudinal direction between the track and bridge. This additional load occurs as a consequence of the employment of a nonlinear stiffness law which increases the restoring force by a factor of 3 when the situation of the track changes from ‘unloaded’ to ‘loaded’ due to a passing train. This particular phenomenon has not been mentioned in the codes so far though it is a natural consequence of fundamental conditions in those codes. For CWR the longitudinal coupling between the rail and bridge plays an important role. This coupling interface is created either by a ballast, for a ballasted track, or by a fastening system in the case of slab track. The deformation state of the coupling interface characterizes the behaviour of the system, whether elastic or plastic. Therefore, the nonlinear behaviour is valid for the system. To accommodate the nonlinear nature, a sequential loading analysis is used, taking into account the loading history. As the change situation due to a passing train happens in a short time, the influence of the mass acceleration should be taken into account in the system’s equilibrium. This aspect is investigated by treating the dynamic load as an impulse-like load. However, a realistic load needs some time to affect the whole bridge, thus the continuous change of stiffness is used to simulate the dynamic analysis. There is a lack of information on determining the value of coupling stiffness in longitudinal direction caused by a passing train. Therefore, it is important to evaluate the coupling stiffness from field measurements in order to find reliable values. The implementation of the load onto several typical bridges shows that the change of the coupling stiffness increases the stresses and it should not be neglected. The evaluation of the load due to a change of the coupling stiffness accompanied by bending of the supporting structure gives satisfactory results by using the static analysis only. Thus, a dynamic analysis can be avoided. Multiple cycles of passing trains occurring after seasonal temperature change indicate a significant increase of elastic parts along the track-bridge coupling interface and a decrease in stresses in the rails. Thus the danger of deterioration is reduced significantly.Die Verwendung von durchgehend geschweißten Schienen auf Brücken führt zu zusätzlichen Längsspannungen infolge der Lastfälle jahreszeitliche Temperaturänderung, Brückendurchbiegung und Bremsen/Anfahren. Diese drei Lasten sind durch den Eurocode 1 vorgegeben und in die nationale deutsche Norm DIN Fb-101 integriert. In dieser Arbeit wird erstmals ein weiterer Lastfall identifiziert und behandelt, der durch den Wechsel der Koppelsteifigkeit in Längsrichtung zwischen Gleis und Tragwerk bei der Zugüberfahrt begründet wird. Dieser Lastfall wird hier mit „Ruck“ bezeichnet und ist eine zwangsläufige Konsequenz des nichtlinearen Längsverschiebewiderstandes, wie er im EC 1 und im DIN Fb-101 vorgegeben ist. Dennoch wurden die Auswirkungen auf das Systemverhalten bisher nicht untersucht. Bei einem Wechsel vom unbelasteten Gleis zum belasteten Gleis während einer Zugüberfahrt erhöht sich zum Beispiel der Längsverschiebewiderstand für ein Schottergleis um den Faktor 3! Die dadurch bedingte Veränderung des Zusammenwirkens zwischen Gleis und Tragwerk führt zu einer Veränderung des Systemzustandes und damit zu veränderten Schienenspannungen. Für durchgehend geschweißte Schienen spielt die Längskopplung zwischen Schiene und Brücke eine wesentliche Rolle. Beim Schottergleis wird sie dargestellt durch die Einbettung des Gleisrostes im Schotterbett im Zusammenwirken mit der Schienenbefestigung. Bei der festen Fahrbahn durch das Befestigungssystem. Für kleine Deformationen ist die Koppelsteifigkeit proportional zur Relativverschiebung zwischen Gleis und Brücke. Darüberhinaus geht das linear elastische Verhalten in ein quasi plastisches Verhalten mit konstanter Koppelkraft über. Folgerichtig ist die Behandlung einer Lastenfolge nur in inkrementeller Weise unter Einbeziehung der Verformungsgeschichte mechanisch korrekt. Die Lastfälle Bremsen/Anfahren, Brückendurchbiegung und Ruck ereignen sich nur während der Zugüberfahrt; also in relativ kurzer Zeit, dann allerdings mit einem erheblichen Lastgradienten. Somit stellt sich die Frage nach dem Einfluss der Massenbeschleunigungen, die in dieser Arbeit geklärt wird. Die im Fachbericht genanntenWerte für den Längsverschiebewiderstand des belasteten Gleises basieren auf einer relativ geringen Datenmenge. Aus diesem Grund werden die Messdaten einer umfangreichen Feldmessung mit Zugüberfahrten zu Aussagen über den Längsverschiebewiederstand herangezogen und die Problematik derartiger Messungen beleuchtet. Die unterschiedlichen Modellierungen des Lastfalls „Ruck“, einmal rein statisch und zum anderen dynamisch, ergeben übereinstimmende Schienenlängsspannungen für die statische und die kontinuierliche dynamische Variante. Somit kann auf die aufwändige dynamische Analyse verzichtet werden. Mehrere Zyklen von Zugüberfahrten im Anschluss an eine jahreszeitliche Temperaturänderung bewirken einen signifikanten Abbau der Durchrutschbereiche, also eine Erhöhung der elastischen Abschnitte in der Koppelfuge zwischen Bauwerk und Gleis verbunden mit einer Abnahme der Schienendruckspannungen. Somit hilft dieser Effekt dem System, der jahreszeitlichen Temperaturänderung zu widerstehen.
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Nazari, Farshid. "Strongly Stable and Accurate Numerical Integration Schemes for Nonlinear Systems in Atmospheric Models." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32128.
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Nonlinearity accompanied with stiffness in atmospheric boundary layer physical parameterizations is a well-known concern in numerical weather prediction (NWP) models. Nonlinear diffusion equations, furthermore, are a class of equations which are extensively applicable in different fields of science and engineering. Numerical stability and accuracy is a common concern in this class of equation.
In the present research, a comprehensive effort has been made toward the temporal integration of such equations. The main goal is to find highly stable and accurate numerical methods which can be used specifically in atmospheric boundary layer simulations in weather and climate prediction models, and extensively in other models where nonlinear differential equations play an important role, such as magnetohydrodynamics and Navier-Stokes equations.
A modified extended backward differentiation formula (ME BDF) scheme is adapted and proposed at the first stage of this research. Various aspects of this scheme, including stability properties, linear stability analysis, and numerical experiments, are studied with regard to applications for the time integration of commonly used nonlinear damping and diffusive systems in atmospheric boundary layer models. A new temporal filter which leads to significant improvement of numerical results is proposed.
Nonlinear damping and diffusion in the turbulent mixing of the atmospheric boundary layer is dealt with in the next stage by using optimally stable singly-diagonally-implicit Runge-Kutta (SDIRK) methods, which have been proved to be effective and computationally efficient for the challenges mentioned in the literature. Numerical analyses are performed, and two schemes are modified to enhance their numerical features and stability.
Three-stage third-order diagonally-implicit Runge-Kutta (DIRK) scheme is introduced by optimizing the error and linear stability analysis for the aforementioned nonlinear diffusive system. The new scheme is stable for a wide range of time steps and is able to resolve different diffusive systems with diagnostic turbulence closures, or prognostic ones with a diagnostic length scale, with enhanced accuracy and stability compared to current schemes. The procedure implemented in this study is quite general and can be used in other diffusive systems as well.
As an extension of this study, high-order low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes are analyzed and introduced, based on the optimization of amplification and phase errors for wave propagation, and various optimized schemes can be obtained. The new scheme shows no dissipation. It is illustrated mathematically and numerically that the new scheme preserves fourth-order accuracy. The numerical applications contain the wave equation with and without a stiff nonlinear source term. This shows that different optimized schemes can be investigated for the solution of systems where physical terms with different behaviours exist.
Conference papers on the topic "Nonlinear stiffness law"
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Honavara Prasad, Srikanth, and Daejong Kim. "Scaling Laws of Radial Clearance and Bump Stiffness of Radial Foil Bearings." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56704.
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Design and analysis of foil bearings involve consideration to various physical aspects such as fluid pressure, structural deformation and heat generation due to viscous effects within the bearing. These complex physical interactions are mathematically governed by highly nonlinear partial differential equations. Therefore, foil bearing design involves detailed calculations of flow fields (velocities, pressures), bump deflections (structural compliance) and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile etc.). The computational effort in terms of time and hardware requirements make high level engineering analyses tedious which presents an opportunity for development of rule of thumb laws for design guidelines. Scaling laws for bearing clearance and bump stiffness of radial foil bearings of various sizes are presented in this paper. The scaling laws are developed from first principles using the scale invariant Reynolds equation and bump deflection equation. Power law relationships are established between the 1) radial clearance and bearing radius and 2) bump stiffness and bearing radius. Simulation results of static and dynamic performance of various bearing sizes following the proposed scaling laws are presented.
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Jo, Hoonhee, and Hiroshi Yabuno. "Reduction of Primary Resonance Amplitude of Nonlinear Oscillator by a New Type of Nonlinear Dynamic Vibration Absorber." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35286.
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The paper proposes a nonlinear dynamic vibration absorber for primary external resonance of system having cubic nonlinearity. A main system with nonlinear spring stiffness and subjected to harmonic excitation is considered. We calculate nonlinear spring stiffness produced by repulsive force of permanent magnets using Coulomb’s law. A damped pendulum system, whose natural frequency is in the neighborhood of twice that of the main system, is nonlinear coupled to the main system by link as a dynamic vibration absorber. This nonlinear dynamic vibration bsorber does not utilize linear coupling to the main system but utilizes nonlinear coupling. Therefore, the attachment of the nonlinear dynamic vibration absorber does not increase the number of degrees of freedom of the main system. Primary resonance amplitude is decreased in the case when pendulum is unlocked and hysteresis of the frequency response curve is disappeared. This means that attachment of dynamic vibration absorber has the same effect that increases directly the damping coefficent of the main system. Experimental results for this type of device are compared with a numerical results obtained from Runge-Kutta method. Comparison of the frequency response curves with and without nonlinear dynamic vibration absorber show validity of the proposed absorber.
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Wu, Ruiqin, Wei Zhang, and Ming Hui Yao. "Nonlinear Vibration of a Rotor-Active Magnetic Bearing System With 16-Pole Legs." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67103.
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In this paper, the nonlinear dynamics of a rotor-active magnetic bearing system with 16-pole legs and the time varying stiffness is investigated. The magnetic forces are obtained through an electromagnetic theory. The motion governing equation is derived by using Newton law. The resulting dimensionless equation of motion for the rotor-AMB system with 16-pole legs and the time varying stiffness is presented with the two-degree-of-freedom system including parametric excitation, the quadratic and cubic nonlinearities. The averaged equations of the rotor-AMB system are obtained by using the method of multiple scales under the case of the primary parametric resonance and 1/2 sub-harmonic resonance. The numerical results show that there exist the periodic, quasi-periodic and chaotic motions in the rotor-active magnetic bearing system. Since the weight of the rotor effect the system, it is also found that there are the different shapes of motion on the two directions of the rotor-AMB system. The parametric excitation, or the time-varying stiffness produced by the PD controller has great impact on the system. Thus, the complicated dynamical response in the rotor-AMB system can be controlled through adjusting the parametric excitation.
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Bo¨hm, Friedrich. "Nonlinear Dynamics of Pneumatic Tires and Application to Elastic Vehicles." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85030.
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A vehicle is a light weight elastic, hysteretic damped free body only connected with the assumed intertial system by accelerations and mutual contact forces. Tires produce, if in contact with the ground, accelerations at the axles and all mass elements have to be integrated simultanously to get their pathes, according to Newton’s law. The rotational motion of the body-tire system is very sensitive to disturbances in the accelerations and changes the slip conditions of the tires. Nonlinearity is kinematic, compression stiffness, friction and hysteresis. Slip is simulated using the dislocation way of sensor points on the surface. The slip conditions together with the contact conditions produce the nonlinear tire deformations in every computed time step. Relevant time intervals are to be elucidated from frequency measurements and are to be used for defining splitted masses and for connecting with stiffness parameters from material tests. To the resulting central force system a D’Alembert bending force system can be added as a small disturbance. Explicit time integration by predictor-corrector method of third order, controlling acceleration, is used. The computing procedure is therefore an exact central force system only disturbed by a bending force system in equilibrium. No assumption for small nonlinear terms is necesssary, numerical stability is controlled by Shannon and Gershgorin theorems, Lit [1–11].
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Jahani, Kamal, and Parisa Aghazadeh. "Joint Characteristic Effect on the Performance of Nonlinear Piezoelectric Energy Harvesters." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9015.
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In this work, the effects of joint characteristics on the performance of a nonlinear piezoelectric energy harvester are investigated numerically. Large amplitude deflection unimorph beam with a tip mass and a nonlinear piezoelectric layer is considered as an energy harvester. By applying Euler-Lagrange equation and the Gauss’s law, mechanical and electrical equations of motion are obtained respectively, under two scenarios, i.e. with an ideal (rigid) joint and with a flexible one. A numerical approach is followed to investigate the effects of each nonlinear parameter of the harvester (stiffness, damping and piezoelectric coefficient) on harvested power. Results show that considering ideal joint between harvester and base structure leads to overestimating the maximum output power and the range of effective excitation frequency.
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Hinkle, Adam R., Sachin Goyal, and Harish J. Palanthandalam-Madapusi. "An Estimation Method of a Constitutive-Law for the Rod Model of DNA Using Discrete-Structure Simulations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87763.
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The continuum-rod model has emerged as an efficient tool to describe the long-length-scale structural-deformations of DNA which are critical to understanding the nature of many biological processes such as gene expression. However, a significant challenge in continuum-mechanics-based modeling of DNA is to estimate its constitutive law, which follows from its interatomic bond-stiffness. Experiments and all-atom molecular dynamics (MD) simulations have suggested that the constitutive law is nonlinear and non-homogeneous (sequence-dependent) along the length of DNA. In this paper, we present an estimation method and a validation study using discrete-structure simulations. We consider a simple cantilever-rod with an artificially constructed, discrete lattice-structure which gives rise to a constitutive law. Large deformations are then simulated. An effective constitutive-law is estimated from these deformations using inverse methods. Finally, we test the estimated law by employing it in the continuum rod-model and comparing the simulation results with those of discrete-structure simulations under a different cantilever loading-conditions.
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Bo, Shangguan, Zili Xu, Qilin Wu, XianDing Zhou, and ShouHong Cao. "Forced Response Prediction of Blades With Loosely Assembled Dovetail Attachment by HBM." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-59778.
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To understand the mechanism of interfacial damping of axial loosely assembled dovetail to suppress blade vibration, a dry friction force model is presented by the Coulomb friction law and the macroslip model, and the mathematical expression of the friction force is derived. The nonlinear friction force is linearized as an equivalent stiffness and an equivalent damping through the one-term harmonic balance method. The effect of centrifugal force on the equivalent stiffness and the equivalent damping is studied. The forced response of one simplified blade with loosely assembled dovetail attachment is predicted by the harmonic balance method, in which the blade is described by the lumped mass and spring model, and the friction contact joints is simplified as a ideal friction damper. The results show that the equivalent stiffness of loosely assembled dovetail attachment increases with blade centrifugal force, gradually reaches a certain value, and there exists the maximum value for the equivalent stiffness. The equivalent damping increases at the beginning and then decreases with blade centrifugal force increasing, there exists a maximum too. The resonant frequency of blade rises with blade centrifugal force, but it no longer increases when the centrifugal force exceed a certain value. There exists a special centrifugal force on which the effect of dry friction damping is the best.
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Kumar, M. Senthil, and P. M. Jawahar. "Computer Simulation of the Response of a Railway Vehicle Carbody." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39143.
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In this paper, a nonlinear mathematical model has been constructed by deriving the equations of motion of a Rail Vehicle carbody using Newton’s law. The nonlinear formula is used to evaluate the wheel rail contact forces. The nonlinear profile of wheel and rail are taken into account. Also the lateral stiffness of the track is taken into consideration. The equations of motion are derived for (a) Carbody with conventional wheelset (b) Carbody with unconventional wheelset (independently rotating wheels). For lateral vibration, 17 degrees of freedom are considered. The degrees of freedom represent lateral and yaw movements of 4 wheelsets and lateral, yaw and roll movements of the bogie and carbody. These equations of motion are transformed into a form suitable for numerical differential equation by Runge Kutta method. In the interest of computing economy, certain approximations have been introduced for calculating the creep forces. Sample results are given for a model of a typical railway vehicle used by the Indian Railways. The lateral dynamic response of the railway vehicle carbody for both conventional and unconventional wheelset has been analysed.
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Carobino, Evandro Souto, Renato Pavanello, Rodrigo Batista Tommasini, Debora Junqueira Fonseca, and Leonardo de Oliveira Carvalho. "A Non Linear Finite Element Model to Analyse the Dynamics of Subsea Lifting Operation Using Synthetic Cables." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18225.
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Abstract In the context of subsea lifting many equipment and strategies are employed in order to avoid dynamic instabilities and complex mechanical behaviors during the installation procedures. One of those strategies is the use of synthetic cables to reduce the total sustained weight on the crane and to shift the resonance frequency of the system, leading to reductions of fails risks. This work presents a numerical model intended to predict the dynamic behavior of a cable-equipment system under the influence of the sea waves. The cable is discretized in a finite element mesh which accounts for a nonlinear material model for the elasticity of the cable. The nonlinear elastic law uses a polynomial function to represent the force on the cable as a function of the strain, being able to predict the variation of the stiffness for different load conditions. Further, hydrodynamic forces are considered acting on the equipment and are modeled via Morison’s equation, which introduces a quadratic nonlinear forcing term. The equation of motion is then integrated at the time domain through a Newmark-β predictor-corrector method in order to obtain the dynamic response of the system. Furthermore, an Orcaflex model is constructed using an equivalent linear stiffness representation for the synthetic cable. The results obtained are compared, and the differences between them are highlighted for typical subsea lifting scenarios. In this case, the proposed model can predict non trivial dynamic behaviors of the system such as dependence on the amplitude of the displacement of the lifting point. It is also presented the scenarios where the equivalent linear model is accurate in comparison to the nonlinear one and how the selection of the strain point used to linearize the model affects the dynamics of the system.
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Slightam, Jonathon E., Mark L. Nagurka, and Eric J. Barth. "Sliding Mode Impedance Control of a Hydraulic Artificial Muscle." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9186.
Full textAbstract:
Hydraulic artificial muscles offer unrivaled specific power and power density and are instrumental to the improved performance and success of soft robotics and lightweight mobile applications. This paper addresses the lack of model-based impedance control approaches for soft actuators such as hydraulic artificial muscles. Impedance control of actuators and robotic systems has been proven to be an effective approach for interacting with physical objects in the presence of uncertainty. A sliding mode impedance control approach based on Filippov’s principle of equivalent dynamics is introduced and applied to a hydraulic artificial muscle. A nonlinear lumped parameter model of the system is presented and a sliding mode impedance controller is derived. Experimental results show superior performance using model-based sliding mode impedance control versus a linear impedance control law in both tracking of position and stiffness when disturbances are introduced.