Academic literature on the topic 'Nonlinear Hysteresis Damping'
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Journal articles on the topic "Nonlinear Hysteresis Damping"
1
Ghodke, Sharad, and R. S. Jangid. "An Empirical Formulation for the Damping Ratio of Shape Memory Alloy for Base-Isolated Structures." International Journal of Structural Stability and Dynamics 19, no. 07 (June 26, 2019): 1950074. http://dx.doi.org/10.1142/s0219455419500743.
Full textAbstract:
Shape Memory Alloys (SMAs) are now widely used as a damping element into the isolation systems. The pre-stressed SMAs exhibit hysteretic damping through a nonlinear flag-shaped hysteresis loop. Many nonlinear models of the SMA are available to depict such behavior. The nonlinear models require a lot of effort and computational time for the analysis of base-isolated structures. Therefore, the codes recommend that a nonlinear model can be replaced by an equivalent linear model in the analysis. Linearization is a method to convert the nonlinearity of a system into a system with analogues linear parameters. This paper proposes an empirical equation for a damping ratio to get a linear damping coefficient of the SMAs which can be used in the seismic analysis of base-isolated structures. The evaluation of any damping ratio using the traditional system identification method does not give precise solutions due to variation in hysteretic parameters and the unpredictable nature of an earthquake. The empirical equation is proposed using a set of optimal statistical data obtained from the seismic analysis of a base isolated structure. Moreover, analysis of the base isolated structure using the newly modified equivalent elastic-viscous SMA model gives comparable and conservative results with a nonlinear SMA model as compared to the existing elastic-viscous SMA model. Since the hysteresis parameters are used to derive the empirical equation for the damping ratio, this equation is also applicable for any type of structure.
2
Miwadinou, C. H., A. V. Monwanou, L. A. Hinvi, V. Kamdoum Tamba, A. A. Koukpémèdji, and J. B. Chabi Orou. "Nonlinear Oscillations of Nonlinear Damping Gyros: Resonances, Hysteresis and Multistability." International Journal of Bifurcation and Chaos 30, no. 14 (November 2020): 2050203. http://dx.doi.org/10.1142/s021812742050203x.
Full textAbstract:
This paper addresses the issues on the dynamics of nonlinear damping gyros subjected to a quintic nonlinear parametric excitation. The fixed points and their stability are analyzed for the autonomous gyros equation. The number of fixed points of the system varies from one to six. The approximate equation of gyros is considered by expanding the nonlinear restoring force and parametric excitation for the study of the dynamics of gyros. Amplitude and frequency of possible resonances are found by using the multiple scales method. Also obtained are the principal parametric resonance and orders 4 and 6 subharmonic resonances. The stability conditions for each of these resonances are also obtained. Chaotic oscillations, multistability, hysteresis, and coexisting attractors are found using the bifurcation diagrams, the Lyapunov exponents, the phase portraits, the Poincaré section and the time histories. The effects of the damping parameter, the angular spin velocity and the parametric nonlinear excitation are analyzed. Results obtained by using the approximate gyros equation are compared to the dynamics obtained with the exact equation of gyros. The analytical investigations are complemented by numerical simulations.
3
Viola, Francesco, P. T. Brun, and François Gallaire. "Capillary hysteresis in sloshing dynamics: a weakly nonlinear analysis." Journal of Fluid Mechanics 837 (January 5, 2018): 788–818. http://dx.doi.org/10.1017/jfm.2017.860.
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The sloshing of water waves in a vertical cylindrical tank is an archetypal damped oscillator in fluid mechanics. The wave frequency is traditionally derived in the potential flow limit (Lamb, Hydrodynamics, Cambridge University Press, 1932), and the damping rate results from the combined effects of the viscous dissipation at the wall, in the bulk and at the free surface (Case & Parkinson, J. Fluid Mech., vol. 2, 1957, pp. 172–184). Still, the classic theoretical prediction accounting for these effects significantly underestimates the damping rate when compared to careful laboratory experiments (Cocciaro et al., J. Fluid Mech., vol. 246, 1993, pp. 43–66). Specifically, theory provides a unique value for the damping rate, while experiments reveal that the damping increases as the sloshing amplitude decreases. Here, we investigate theoretically the effects of capillarity at the contact line on the decay time of capillary–gravity waves. To this end, we marry a model for the inviscid waves to a nonlinear empiric law for the contact line that incorporates contact angle hysteresis. The resulting system of equations is solved by means of a weakly nonlinear analysis using the method of multiple scales. Capillary effects have a dramatic influence on the calculated damping rate, especially when the sloshing amplitude gets small: this nonlinear interfacial term increases in the limit of zero wave amplitude. In contrast to viscous damping, where the wave motion decays exponentially, the contact angle hysteresis can act as Coulomb solid friction, thus yielding the arrest of the contact line in a finite time.
4
Yan, Lulu, Jinxin Gong, and Qin Zhang. "Investigation of Global Equivalent Damping and Statistical Relationship of Displacement between Nonlinear Static and Dynamic Analysis of Reinforced Concrete Frame Structures." Earthquake Spectra 34, no. 3 (August 2018): 1311–38. http://dx.doi.org/10.1193/021517eqs031m.
Full textAbstract:
The assessment of the seismic performance of reinforced concrete (RC) frame structures using the equivalent linearization approach requires comprehensive insight into the nonlinear response of the system, and most previous researches focused on the analysis of a single-degree-of-freedom (SDOF) system. To describe the hysteretic behavior of a multi-degree-of-freedom (MDOF) system accurately, monotonic and cyclic pushover analyses for 88 RC frames structures with various configurations and design parameters are carried out and a unified hysteresis loop expression modeling the cyclic pushover results of RC frame system is developed. Then, a global equivalent damping based on Jacobsen's approach is derived, and comparisons between the displacements obtained by nonlinear static analysis (NSA) utilizing the derived global equivalent damping and those obtained by nonlinear time history analysis (NTHA) are made. Finally, a modified global equivalent damping is presented by calibrating the derived Jacobsen's equivalent damping through NTHA results. Based on the modified equivalent damping, the statistical analysis of the ratios of the results obtained by NTHA to those obtained by NSA is implemented to predicate the probabilistic seismic displacement demands of RC frame structures.
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Fangnon, R., C. Ainamon, A. V. Monwanou, C. H. Miwadinou, and J. B. Chabi Orou. "Nonlinear Dynamics of the Quadratic-Damping Helmholtz Oscillator." Complexity 2020 (November 8, 2020): 1–17. http://dx.doi.org/10.1155/2020/8822534.
Full textAbstract:
In this paper, the Helmholtz equation with quadratic damping themes is used for modeling the dynamics of a simple prey-predator system also called a simple Lotka–Volterra system. From the Helmholtz equation with quadratic damping themes obtained after modeling, the equilibrium points have been found, and their stability has been analyzed. Subsequently, the harmonic oscillations have been studied by the harmonic balance method, and the phenomena of resonance and hysteresis are observed. The primary and secondary resonances have been researched by the multiple-scale method, and the conditions of stability of the amplitudes of oscillations are determined. Chaos is detected analytically by the Melnikov method and numerically using the basin of attraction, the bifurcation diagram, the Lyapunov exponent, the phase portrait, and the Poincaré section. The effects of all the parameters of the system are analyzed in detail, and special emphasis is placed on the new parameters. Through this analysis, the complex phenomena such as hysteresis, bistability, amplitude jump, resonances, and chaos have been obtained. The control of the parameters and the necessary conditions to control the aforementioned phenomena have been found.
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Jiang, Feng, Zheyu Ding, Yiwan Wu, Hongbai Bai, Yichuan Shao, and Bao Zi. "Energy Dissipation Characteristics and Parameter Identification of Symmetrically Coated Damping Structure of Pipelines under Different Temperature Environment." Symmetry 12, no. 8 (August 3, 2020): 1283. http://dx.doi.org/10.3390/sym12081283.
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In this paper, a symmetrically coated damping structure for entangled metallic wire materials (EMWM) of pipelines was designed to reduce the vibration of high temperature (300 °C) pipeline. A series of energy dissipation tests were carried out on the symmetrically coated damping structure at 20–300 °C. Based on the energy dissipation test results, the hysteresis loop was drawn. The effects of temperature, vibration amplitude, frequency, and density of EMWM on the energy dissipation characteristics of coated damping structures were investigated. A nonlinear energy dissipation model of the symmetrically coated damping structure with temperature parameters was established through the accurate decomposition of the hysteresis loop. The parameters of the nonlinear model were identified by the least square method. The energy dissipation test results show that the symmetrically coated damping structure for EMWM of pipelines had excellent and stable damping properties, and the established model could well describe the changing law of the restoring force and displacement of the symmetrically coated damping structure with amplitude, frequency, density, and ambient temperature. It is possible to reduce the vibration of pipelines in a wider temperature range by replacing different metal wires.
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Niu, Mu-Qing, and Li-Qun Chen. "Nonlinear Vibration Isolation via a NiTiNOL Wire Rope." Applied Sciences 11, no. 21 (October 26, 2021): 10032. http://dx.doi.org/10.3390/app112110032.
Full textAbstract:
Vibration isolators with both stiffness and damping nonlinearities show promise for exhibiting compound advantages for broadband vibration isolation. A nonlinear isolator with a NiTiNOL wire rope is proposed with cubic stiffness, hysteretic damping, and pinching effects induced by geometric constraints, inner frictions, and phase transitions, respectively. A combined method of a beam constraint model and a Bouc-Wen model is presented to characterize the restoring force of the NiTiNOL wire rope. The frequency responses of the nonlinear isolator were analyzed through a harmonic balance method with an alternating frequency/time domain technique. The generalized equivalent stiffness and the generalized equivalent damping ratio were defined for a comprehensive understanding of the nonlinear characteristics. The isolator exhibited a stiffness-softening-hardening characteristic. The pinching effect, the Bouc-Wen hysteresis, and the cubic stiffness mainly influenced the equivalent stiffness at the initial value, the small displacements, and the large displacements, respectively. The rate-independent damping ratio increased and then decreased with increasing displacement, and the parameters influenced the damping ratio change in different ways. Compared to an isolator with a steel wire rope, the isolator with a NiTiNOL wire rope exhibited less initial stiffness and a stronger damping effect, and thus, better vibration isolation performance. The relationships of the peak displacement transmissibility and the resonant frequency with the excitation amplitude were both non-monotonic due to the non-monotonic changes of the stiffness and the damping ratio. The minimum peak transmissibility, the lowest resonant frequency, and their corresponding excitation amplitudes depended on the isolator parameters. The isolator demonstrated stiffness–softening and stiffness–hardening types of jump phenomena with different parameters.
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Berger, E. J., and C. M. Krousgrill. "On Friction Damping Modeling Using Bilinear Hysteresis Elements." Journal of Vibration and Acoustics 124, no. 3 (June 12, 2002): 367–75. http://dx.doi.org/10.1115/1.1473831.
Full textAbstract:
Massless bilinear hysteresis elements are often used to model frictional energy dissipation in dynamic systems. These quasi-static elements possess only two describing parameters, the damper stiffness and the force at which it slips. Bilinear hysteresis elements capture the qualitative nature of friction-damped forced response, but sometimes have difficulty with quantitative comparisons. This paper examines the performance of massless bilinear hysteresis elements as well as the role of damper mass in energy dissipation, and specifically evaluates its influence on the kinematic state of the damper (pure slip, stick-slip, pure stick). Differences between the massless and non-zero mass case are explored, as are the implications on both damper and system response. The results indicate that even small damper mass can have a qualitative effect on the system response, and provide advantages over the massless case. Further, we develop transition maps, describing damper response kinematics in the damper parameter space, which segment the space into two linear analysis regions (pure slip, pure stick) and one nonlinear analysis region (stick-slip). The results suggest non-zero mass dampers which are tuned as optimal vibration absorbers provide substantial resonance response attenuation and substantially reduce the size of the nonlinear analysis region in the damper parameter space.
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Koh, K. H., J. H. Griffin, S. Filippi, and A. Akay. "Characterization of Turbine Blade Friction Dampers." Journal of Engineering for Gas Turbines and Power 127, no. 4 (March 1, 2004): 856–62. http://dx.doi.org/10.1115/1.1926312.
Full textAbstract:
This paper discusses an approach for characterizing the dynamic behavior of a friction damper. To accomplish this, the deflection of the damper is measured as a function of an applied force for a range of amplitudes, normal loads, and excitation frequencies. The resulting hysteresis curves are used to generate curves of nonlinear stiffness and damping as a function of the amplitude of motion. A method of presenting this information in a dimensionless format is demonstrated. This format allows direct comparisons of the nonlinear stiffness and damping of actual dampers with that often used in analytical models to compute the dynamic response of frictionally damped turbine blades. It is shown that for the case of a damper with a spherical head significant differences exist between the actual behavior of the damper and that often assumed in simple analytical models. In addition, Mindlin’s analysis of a sphere on a half space is used to estimate the damper’s stiffness as well as its theoretical hysteresis curves. The hysteresis curves are then used to determine dimensionless stiffness and damping curves. The results compare favorably with those found experimentally.
10
Monti, M. D., J. X. Zhao, C. R. Gannon, and W. H. Robinson. "Mental results and dynamic parameters for the Penguin Vibration Damper (PVD) for wind and earthquake loading." Bulletin of the New Zealand Society for Earthquake Engineering 31, no. 3 (September 30, 1998): 177–93. http://dx.doi.org/10.5459/bnzsee.31.3.177-193.
Full textAbstract:
Penguin Engineering Ltd has developed a compact, efficient, hysteretic damping device, the Penguin Vibration Damper (PVD). Experimental test results show that the PVD can provide a significant amount of damping at displacements as small as 50 micro-metres.
The hysteresis behaviour of the PVD can be described well either by a model having a linear spring in parallel with a viscous dashpot, or by a bi-linear model, with the parameters of both models being displacement-amplitude dependent. For large displacements, the bi-linear model gives an accurate representation of the PVD's hysteresis loops, and the parameters for the bi-linear model can be taken as constants. Non-linear models, such as the hyperbolic, Ramberg-Osgood and multi-surface plasticity models, can also be used and have an advantage of displacement-amplitude-independent parameters. However, it can be shown that nonlinear models do not correctly predict the amount of damping that a PVD provides at large displacement even though the equivalent spring coefficient can be well approximated. When the PVDs are expected to undergo large displacements, it is possibly best to use a simple bi-linear model in dynamic nonlinear structural analyses, because the bi-linear model with suitably selected parameters can produce the correct amount of damping derived from the experimental data.
The changes of the PVD's dynamic behaviour are small after a fatigue test of 144 000 cycles with a displacement amplitude of 2 mm.
An analysis of a 6-storey reinforced concrete moment resisting frame is used to demonstrate the effect of the damper. Equivalent first modal damping ratios are estimated for various levels of earthquake excitations. The example shows that the dampers can provide a large amount of damping to the structure and enhance the structural capacity, for resisting earthquakes, by 50-100%.
Dissertations / Theses on the topic "Nonlinear Hysteresis Damping"
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Mathis, Allen MATHIS. "Theory and Application of Damping in Jointed Structures." University of Akron / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1555940863603165.
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Wei, Sicong. "A 3D Sliding Bearing Finite Element Based on The Bouc-Wen Hysteretic Model : Mathematical modelling and numerical implementation." Thesis, KTH, Bro- och stålbyggnad, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-289480.
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Bridge bearing is an essential component with the function of connecting the superstructure and substructure of the bridge, transmitting load and providing movability to the superstructure. Under dynamic conditions, the internal friction of bridge bearing dissipates the vibration energy and therefore reduces the dynamic response of the bridge. Meanwhile, bearing friction is considered to have possible contribution to some nonlinear dynamic behaviour of the bridge structure, which requires further investigation.However, bearing friction, in most cases, are ignored or considered roughly and implicitly as part of structural damping in current bridge designing codes and methods. Most previous research was also focusing on bearing friction’s effect under high-amplitude vibration conditions, such as earthquake or heavy wind load. Bearing friction’s effect under common low-amplitude vibration in SLS such as train-induced vibration and vehicle-induced vibration is less attended. Although the effect of such low-amplitude vibration is less significant to structural safety, it plays an essential role to the bridge’s traffic safety and comfort. Meanwhile, the cumulative effect of such vibration can significantly influence the life and durability of bridge bearings due to its high occurring frequency. Hence, a clearer understanding of bearing dynamic behaviour is required to improve the understanding of bridge and bearing dynamics.In this thesis, an advanced numerical tool is developed for dynamic analysis of bearing friction. A 3D pot bearing finite element that can be implemented in commercial FE software ABAQUS, is programmed based on the mathematical friction models developed in previous research and the Bouc-Wen hysteretic model. Numerical results that accord with the results of relevant friction tests are produced by the calibrated and validated bearing finite element, giving proof that the element is capable to reflect the dynamic friction response of bridge pot bearing in reality.The 3D shell numerical model of Banafjäl bridge located on the Bothnia Line in Norrland, Sweden, is built as a study case of bridge dynamic analysis in this thesis, with implementation of the newly developed bearing element. The feasibility of implementing the bearing element in bridge dynamic analysis is proven by the numerical results. The nonlinear influence of bearing friction on the dynamic response of bridge structure, especially the influence on structural damping properties, is discussed preliminarily. The analysis results show that with the consideration of bearing friction, the damping presents a clear amplitude-dependency, which accords the phenomenon reported in previous research.
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Phillips, Adam Richard. "Large-Scale Cyclic Testing and Development of Ring Shaped - Steel Plate Shear Walls for Improved Seismic Performance of Buildings." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/73513.
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A novel shear wall system for building structures has been developed that improves upon the performance of conventional steel plate shear walls by mitigating buckling. The new structural system, called the Ring Shaped - Steel Plate Shear Wall, was investigated and developed through experimental and computational methods. First, the plastic mechanism of the system was numerically derived and then analytically validated with finite element analyses. Next, five large-scale, quasi-static, cyclic experimental tests were conducted in the Thomas M. Murray Structures Laboratory at Virginia Tech. The large-scale experiments validated the system performance and provided data on the boundary frame forces, infill panel shear deformation modes, buckling mode shapes, and buckling magnitudes.
Multiple computational modeling techniques were employed to reproduce different facets of the system behavior. First, detailed finite element models were constructed to accurately reproduce the cyclic performance, yielding pattern, and buckling mode shapes. The refined finite element models were utilized to further study the boundary element forces and ultra-low cycle fatigue behavior of the system. Second, reduced-order computational models were constructed that can accurately reproduce the hysteretic performance of the web plates. The reduced-order models were then utilized to study the nonlinear response history behavior of four prototype building structures using Ring Shaped - Steel Plate Shear Walls and conventional steel plate shear walls. The nonlinear response history analyses investigated the application of the system to a short period and a long period building configuration. In total 176 nonlinear response history analyses were conducted and statistically analyzed.
Lastly, a practical design methodology for the Ring Shaped - Steel Plate Shear Wall web plates was presented. The experimental tests and computational simulations reported in this dissertation demonstrate that Ring Shaped - Steel Plate Shear Walls are capable of improving seismic performance of buildings by drastically reducing buckling and improving cyclic energy dissipation.Ph. D.
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Mukherjee, Indrajit. "Localization Induced Base Isolation In Fractionally And Hysteretically Damped Nonlinear Systems." Thesis, 2007. https://etd.iisc.ac.in/handle/2005/580.
Full textAbstract:
This Thesis comprises of two parts containing similar studies of Nonlinear Localization induced Base Isolation of structural systems. The present method of base isolation,like other nonlinear vibration isolation methods, enjoys certain merits like capability of absorbing broad band vibrations, attenuating heavy shocks etc. The research in this thesis is an extension of this base isolation strategy first proposed by Vakakis and co-author. The strategy involves augmenting an appendage referred to as the secondary system with the main structural unit or the primary system, which we want to isolate from disturbances at the base. The primary system is coupled to the secondary system through a stiffness element. Both the primary and secondary systems have nonlinear dynamic behavior. It is seen that for certain choice of values of the coupling element, steady state vibration of very small magnitude is induced in the primary system. This result was established by considering a general discrete nonlinear system with viscous damping. Now it is a well known fact that viscous damping, though being widely used in literature as well as in practice doesn't turn out to be accurate enough to capture structural damping behaviors. Moreover, the actual damping mechanism if governed by some nonlinear function of the system variables, may influence the physics governing the nonlinear localization phenomenon in a manner rendering the present method not suitable for structural systems at the very outset. So in the present study we focus our attention in establishing the robustness and hence utility of the method by considering technically more defensible models of structural damping. These models efficiently capture certain complex phenomena which structures are known to exhibit. The occurrence of localization induced vibration isolation in structural systems in the presence of these damping models is taken as a proof of the efficacy of the method and its applicability to a wide range of situations. The present study establishes existence of localization through relevant analytical and numerical exercises.
In the first part of the thesis we take up the study of nonlinear localization induced base isolation of a three degrees of freedom system having cubic nonlinearities under sinusoidal base excitation. The damping forces in the system are hysteretic in nature. In the present setting this is captured by Bouc-Wen model of hysteresis. Bouc-Wen model is one of the most widely used phenomenological model of hysteresis to have a ready-to-use mathematical description of hysteretic patterns appearing in structural engineering systems. The nature of responses of the different degrees of freedom as excitation frequency varies is a better way of analyzing the performance of the vibration isolation system. We adopt this line of approach for the present study. Normally Harmonic Balance Method (HBM) serves this purpose very well but in the present case as the hysteretic variable is not explicitly related to the system variables, HBM cannot be straightway implemented. Moreover, the hysteretic variable is related to other state variables through a relation which contains non-smooth terms. As a result, Incremental Harmonic Balance (IHB) method is used to obtain amplitude frequency relationship of the system response. The stability analysis of the solution branches is done by using Floquet Theory. Direct numerical simulation is then made use of to support our results that are obtained from this approximate numeric-analytic estimate of the amplitudefrequency relationships of the system, which helps us to analyze the efficacy of this method of base isolation for a broad class of systems.
In the next part we consider a similar system where the damping forces in the system are described by functions of fractional derivative of the instantaneous displacements. Fractional Derivative based damping model has been found to be very effective in describing structural damping. We adopt half-order fractional derivative for our study, which can capture damping behavior of polymeric material very well. Typically linear and quadratic damping is considered separately as these are the two most relevant representations of structural damping. Under the assumption of smallness of certain system parameters and nonlinear terms an approximate estimate of the response at each degree of freedom of the system is obtained using Method of Multiple Scales. We then consider a situation where the nonlinear terms and certain other system parameters are no longer small. For the case where asymptotic methods are no longer valid, the assessment of performance of the vibration isolation system is made from amplitude-frequency relations. As a result, we take recourse to the Harmonic Balance Method in conjunction with arc length based continuation technique for obtaining the frequency amplitude plot for linear damping and Incremental Harmonic Balance method for quadratic damping, each of which is validated against results obtained from direct numerical simulation of the system.
It needs to be appreciated that base isolation obtained this way has no counterpart in the linear theory.
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Mukherjee, Indrajit. "Localization Induced Base Isolation In Fractionally And Hysteretically Damped Nonlinear Systems." Thesis, 2007. http://hdl.handle.net/2005/580.
Full textAbstract:
This Thesis comprises of two parts containing similar studies of Nonlinear Localization induced Base Isolation of structural systems. The present method of base isolation,like other nonlinear vibration isolation methods, enjoys certain merits like capability of absorbing broad band vibrations, attenuating heavy shocks etc. The research in this thesis is an extension of this base isolation strategy first proposed by Vakakis and co-author. The strategy involves augmenting an appendage referred to as the secondary system with the main structural unit or the primary system, which we want to isolate from disturbances at the base. The primary system is coupled to the secondary system through a stiffness element. Both the primary and secondary systems have nonlinear dynamic behavior. It is seen that for certain choice of values of the coupling element, steady state vibration of very small magnitude is induced in the primary system. This result was established by considering a general discrete nonlinear system with viscous damping. Now it is a well known fact that viscous damping, though being widely used in literature as well as in practice doesn't turn out to be accurate enough to capture structural damping behaviors. Moreover, the actual damping mechanism if governed by some nonlinear function of the system variables, may influence the physics governing the nonlinear localization phenomenon in a manner rendering the present method not suitable for structural systems at the very outset. So in the present study we focus our attention in establishing the robustness and hence utility of the method by considering technically more defensible models of structural damping. These models efficiently capture certain complex phenomena which structures are known to exhibit. The occurrence of localization induced vibration isolation in structural systems in the presence of these damping models is taken as a proof of the efficacy of the method and its applicability to a wide range of situations. The present study establishes existence of localization through relevant analytical and numerical exercises.
In the first part of the thesis we take up the study of nonlinear localization induced base isolation of a three degrees of freedom system having cubic nonlinearities under sinusoidal base excitation. The damping forces in the system are hysteretic in nature. In the present setting this is captured by Bouc-Wen model of hysteresis. Bouc-Wen model is one of the most widely used phenomenological model of hysteresis to have a ready-to-use mathematical description of hysteretic patterns appearing in structural engineering systems. The nature of responses of the different degrees of freedom as excitation frequency varies is a better way of analyzing the performance of the vibration isolation system. We adopt this line of approach for the present study. Normally Harmonic Balance Method (HBM) serves this purpose very well but in the present case as the hysteretic variable is not explicitly related to the system variables, HBM cannot be straightway implemented. Moreover, the hysteretic variable is related to other state variables through a relation which contains non-smooth terms. As a result, Incremental Harmonic Balance (IHB) method is used to obtain amplitude frequency relationship of the system response. The stability analysis of the solution branches is done by using Floquet Theory. Direct numerical simulation is then made use of to support our results that are obtained from this approximate numeric-analytic estimate of the amplitudefrequency relationships of the system, which helps us to analyze the efficacy of this method of base isolation for a broad class of systems.
In the next part we consider a similar system where the damping forces in the system are described by functions of fractional derivative of the instantaneous displacements. Fractional Derivative based damping model has been found to be very effective in describing structural damping. We adopt half-order fractional derivative for our study, which can capture damping behavior of polymeric material very well. Typically linear and quadratic damping is considered separately as these are the two most relevant representations of structural damping. Under the assumption of smallness of certain system parameters and nonlinear terms an approximate estimate of the response at each degree of freedom of the system is obtained using Method of Multiple Scales. We then consider a situation where the nonlinear terms and certain other system parameters are no longer small. For the case where asymptotic methods are no longer valid, the assessment of performance of the vibration isolation system is made from amplitude-frequency relations. As a result, we take recourse to the Harmonic Balance Method in conjunction with arc length based continuation technique for obtaining the frequency amplitude plot for linear damping and Incremental Harmonic Balance method for quadratic damping, each of which is validated against results obtained from direct numerical simulation of the system.
It needs to be appreciated that base isolation obtained this way has no counterpart in the linear theory.
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Tsavachidis, Spiridon. "Deterministic and stochastic analysis of nonlinear systems with Biot hysteretic damping." Thesis, 2001. http://hdl.handle.net/1911/17472.
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Time domain analysis of nonlinear systems with hysteretic damping is conducted. Specifically, the viscoelastic model proposed by Biot is examined. This hysteretic element represents an integral transform in the time domain. Thus, it yields integro-differential equations when it is incorporated into the system dynamics models. Two numerical methods are proposed to solve these equations. The first method approximates the kernel of this integral transform by a sum of exponentials making the computational cost minimal. The second method uses digital filters designed to match the transfer function, real and imaginary parts, of the Biot hysteretic element. These techniques are employed in calculating the response of a single-degree-of-freedom (SDOF) system with hysteretic damping and nonlinear stiffness subjected to deterministic, seismic, and random excitation. The method of statistical linearization is used to estimate the variance of the response of the SDOF system subjected to white noise. The accuracy of the results is verified by pertinent Monte Carlo studies. The presented approaches can be extended to treat multi-degree-of-freedom (MDOF) systems with hysteretic behavior.
Book chapters on the topic "Nonlinear Hysteresis Damping"
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Semenov, Mikhail E., Andrey M. Solovyov, Peter A. Meleshenko, and José M. Balthazar. "Nonlinear Damping: From Viscous to Hysteretic Dampers." In Springer Proceedings in Physics, 259–75. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63937-6_15.
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Hu, Xiaoying, and Chunyan Zhou. "Analysis of Dynamic Behavior Affecting the Isolation Effect of the QZS System with Nonlinear Hysteretic Damping." In Lecture Notes in Electrical Engineering, 319–36. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5912-6_24.
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Ruderman, Michael. "Modeling of Elastic Robot Joints with Nonlinear Damping and Hysteresis." In Robotic Systems - Applications, Control and Programming. InTech, 2012. http://dx.doi.org/10.5772/25494.
Full textConference papers on the topic "Nonlinear Hysteresis Damping"
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Medgyesi, Erik. "Stability of a Simple Rotor With Nonlinear Internal Damping." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0339.
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Abstract The paper contains a stability analysis of the assumed inplane motion of a simple rotor with nonlinear damping, the form of which can approximate different hysteresis loop shapes. The analysis is carried so far as possible without resorting to numerical methods.
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Taló, Michela, Walter Lacarbonara, Giovanni Formica, and Giulia Lanzara. "Hysteresis Identification of Carbon Nanotube Composite Beams." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-86228.
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Nanocomposites made of a hosting polymer matrix integrated with carbon nanotubes as nanofillers exhibit an inherent hysteretic behavior arising from the CNT/matrix frictional sliding. Such stick-slip mechanism is responsible for the high damping capacity of CNT nanocomposites. A full 3D nonlinear constitutive model, framed in the context of the Eshelby-Mori-Tanaka theory, reduced to a 1D phenomenological model is shown to describe accurately the CNT/polymer stick-slip hysteresis. The nonlinear hysteretic response of CNT nanocomposite beams is experimentally characterized via displacement-driven tests in bending mode. The force-displacement cycles are identified via the phenomenological model featuring five independent constitutive parameters. A preliminary parametric study highlights the importance of some key parameters in determining the shape of the hysteresis loops. The parameter identification is performed via one of the variants of a genetic-type differential evolution algorithm. The nanocomposites hysteresis loops are identified with reasonably low mean square errors. Such outcome confirms that the 1D phenomenological model may serve as an effective tool to describe and predict the nanocomposite nonlinear hysteretic behavior towards unprecedented material optimization and design.
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Taniguchi, Tomoyo. "Capability for Growth in Nonlinear Response of SDOF With Bilinear Hysteresis." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-77562.
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To approximate nonlinear response of structures subjected to an earthquake excitation, the displacement method in U.S. or the energy method in Japan has been practically used. However, unless these methods include the nature of dynamics of nonlinear structure well, the nonlinear response is not adequately calculated. Applying the equivalent linearization technique to a Single Degree Of Freedom (SDOF) system with bilinear hysteresis subjected to white noise base acceleration, this paper mathematically quantifies deterioration in a spring constant and increase in a damping coefficient with the progress of nonlinearity in the restoring force system as a function of the ensemble ductility ratio. As the nonlinearity progresses, the spring constant rapidly deteriorates and the damping substantially increases. Increments of damping of the lightly damped linear SDOF system are more than that of the moderately damped one. A comparison of the response of the equivalently linearized system to that of the corresponding linear system reveals the capability for growth in the nonlinear response. The nonlinear response predicable by either method is identified by values of the ensemble ductility ratio and damping ratio of the linear SDOF system. In addition, in a range of the ensemble ductility ratio where the bulk of the engineered structures are included, neither method can properly evaluate the nonlinear response. Although the results presented herein give the mean nature of the nonlinear response and phase and amplitude characteristics of accelerograms make the nonlinear response vary around the mean, uniform application of either displacement method or energy method to approximating the nonlinear response may be reconsidered.
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Shibuya, Yotsugi, Hiroshi Nasuno, Hirohisa Sakurai, and Katsuaki Sunakoda. "Evaluation of Nonlinear Damping Properties of Magnetorheological Gels Under Shear Loading." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97821.
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Rheological properties of magnetorheological gels can be changed reversibly by applied magnetic fields. Magnetorheological gels with different material system are characterized the dynamic response of the material by shearing test in magnetic field. Nonlinear behavior is observed in the dynamic response of the material. To understand mechanism of the behavior, dynamic properties of magnetorheological gels are evaluated by experiment and nonlinear viscoelastic model. Magnetorheological gels used in this study consist of three types of paramagnetic particles and a cyclic-poly-siloxane gel matrix. Three material systems of magnetic particles are chosen: Fe-Si-Ni, Si-Fe and Fe-Si-B-Cr types. Shear testing is conducted in magnetic field 0mT, 105mT and 211mT. The stress-strain response under shear deformation is characterized by non-ellipsoidal hysteresis loop due to nonlinearity of the response. To identify the nonlinear properties, analysis in frequency domain is applied to identify the dynamic response of the material. Nonlinear viscoelastic model with high order components is made and phenomenon of the non-ellipsoidal hysteresis loop in the stress-strain relation and damping properties are illustrated.
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Ramakrishnan, Subramanian, and Md Raf E. Ul Shougat. "On Quality Factor Improvement in a NEMS Resonator With Nonlinear Damping." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98505.
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Abstract Nonlinear damping effects have been reported in experiments on nanoelectromechanical (NEMS) resonators and suggested as a pathway to improve the quality (Q) factors of the resonators. In particular, in a nonlinearly damped Duffing NEMS resonator operating in the hardening regime, it has been shown that white noise excitation can shrink the hysteresis region resulting in higher Q factors. In this paper the authors: (1) find that an analytical expression they previously derived using the method of harmonic balance for the frequency-amplitude relationship of a weakly-excited, nonlinearly damped Duffing NEMS resonator is valid for strong excitation, (2) show analytically and verify numerically that for constant values of the nonlinear damping coefficient, higher amplitude of forcing leads to increase in the resonant frequency, (3) find that white-noise induced stochastic parametric excitation can lead to enhanced Q factors and (4) show that decreasing the nonlinear damping coefficient leads to higher Q-factor. The results, in addition to being theoretically significant, are expected to be important in sensing applications using NEMS resonators.
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Balasubramanian, Prabakaran, Giulio Franchini, Giovanni Ferrari, Brian Painter, Kostas Karazis, and Marco Amabili. "Nonlinear Vibrations of Beams With Bilinear Hysteresis at Supports: Interpretation of Experimental Results." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-70268.
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Abstract Several structures of important industrial relevance feature large-amplitude vibration, which can have an initially hardening or a softening behavior. Models with quadratic and cubic nonlinear stiffness terms are often used to predict the nonlinear dynamics of such structures. If boundary conditions constitute an important cause of nonlinearity, however, it may not be possible to describe the nonlinear behavior of these systems by means of these nonlinear terms. The bundles of fuel rods immersed in the coolant flow of pressurized water reactors constitute an important example of extreme softening behavior, which is not described accurately by the simple adoption of nonlinear stiffness terms proportional to the square and to the cube of displacement in the equation of motion. In fact, the spacer grids, which support the nuclear fuel rods inside the reactors, constitute nonlinear boundary conditions, and are responsible of the peculiar softening behavior. Dedicated experiments on the rotational constraint applied by the spacer grids were performed, revealing a softening stiffness, which conforms extremely well with a bilinear model with hysteresis, such as the one formulated by Caughey. Therefore, a single degree-of-freedom equation with bilinear stiffness terms was employed to model the large-amplitude vibrations of single and bundled fuel rods immersed in quiescent water, which were detailed by previous stepped-sine experiments. A viscous dissipative term was initially retained for modelling damping, since several sources of dissipation are present for fuel rods immersed in water, besides hysteresis at the spacer grid supports. A satisfying fit of the experimental frequency- and time-domain curves was achieved through the use of an optimization algorithm for the tuning of stiffness and damping terms. Viscous damping, however, is not constant during large-amplitude vibrations, but is amplitude-dependent. Therefore, the value of the relevant parameter had to be changed at each forcing level. The model was then refined by introducing four additional switch points for stiffness, besides the initial one. Moreover, a nonlinear damping term of the quadratic type, suitable for softening structures immersed in fluids, was included. The resulting equation of motion with a five-switch piecewise linear stiffness describes with improved accuracy the experimental results. Also, one set of damping parameters is capable of describing the experimental results in the entire forcing (vibration amplitude) range. All this clarifies that a simple multilinear stiffness model, with the inclusion of quadratic damping, can be successfully employed to describe the behavior of rods immersed in fluid, in presence of nonlinear boundary conditions introduced by spacer grids.
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Ma, F., C. H. Ng, H. Zhang, A. Bockstedte, G. C. Foliente, and P. Paevere. "On Parametric Analysis of Differential Hysteresis." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/cie-48213.
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The extended Bouc-Wen differential model is one of the most widely accepted phenomenological models of hysteresis in mechanics. It is routinely used in the characterization of nonlinear damping and in system identification. In this paper, the differential model of hysteresis is carefully re-examined and two significant issues are uncovered. First, it is found that the unspecified parameters of the model are functionally redundant. One of the parameters can be eliminated through suitable transformations in the parameter space. Second, local and global sensitivity analyses are conducted to assess the relative sensitivity of each model parameter. Through extensive Monte Carlo simulations, it is found that some parameters of the hysteretic model are rather insensitive. If the values of these insensitive parameters are fixed, a greatly simplified model is obtained.
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Hong, Jie, Bin Zhu, and Yanhong Ma. "Theoretical and Experimental Investigation on Nonlinear Characterization of Metal Rubber." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-45772.
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Metal Rubber (MR) can be widely used in many aspects such as damping of blade and support, pipe and equipment in air space technology, vehicle and ship. A theoretical method was performed to describe hysteretic properties and nonlinear stiffness and damping characteristics of Metal Rubber component. Spiral wire was considered as the micro-element structure of MR material by analyzing the manufacture process of MR component. Based on the material mechanics and coulomb friction theory, a mechanical model of spiral wire was established which is combined with the cylindrical compression coil spring theory. It was easy to explain the mechanism of hysteresis loop and the nonlinear stiffness and damping characteristic of MR component by means of analyzing contact conditions of micro-element. The quasi-static experiments were conducted to MR component with different material parameters. The influencing laws of material parameters on the performance of MR component were studied. The research was valuable for the analysis of the material mechanics and the design of MR component. It provides theoretical support for the further engineering application of MR material in the field of vibration reduction.
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Hoogeveen, Maas, Hugo Hofstede, and Amir M. Kaynia. "Enhanced Kinematic Hardening Model for Load-Dependent Stiffness and Damping of Jack-Up Foundations." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77285.
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Dynamic analysis of jack-up platforms is generally carried out using approximated linear foundation springs and equivalent viscous damping. Advanced geotechnical analysis of foundations of jack-up platforms results in load-dependent stiffness and damping. Such analyses are often based on the finite element method as used for detailed site specific analyses with proper nonlinear soil models to generate nonlinear response curves, the so-called backbone curve, for the relevant loading conditions. The same FE model can be used to compute the strain energy in the soil elements and assign the corresponding energy losses in the elements based on lab tests or literature data, and integrate over the domain to compute the foundation hysteretic damping as function of loading. The state of the art method of using the backbone curve together with a kinematic hardening model to account for the hysteretic foundation response does not provide a good match between the simulated and computed damping. The hysteresis model proposed in this paper is a kinematic hardening model enhanced with a non-linear spring. It is an engineering solution to implement both a given load-dependent stiffness and load-dependent damping of a complex element subject to an irregular loading signal for purposes of time domain simulation. This model combines a kinematic hardening model which provides the required hysteresis with a non-linear elastic spring which provides the required stiffness. This model is suitable for time domain simulation of irregular loads and yields a propeller-like shape in the load-displacement plane. This paper introduces the problem of load-dependent stiffness and damping through a case study considering time domain simulation of the dynamic behavior of a jack-up platform. The paper presents a validation of the proposed model and a comparison between the common practice model and the enhanced kinematic hardening model.
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Ma, F., and A. Imam. "Sensitivity Analysis of the Extended Bouc-Wen Model of Hysteresis." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84035.
Full textAbstract:
The extended Bouc-Wen differential model is one of the most widely accepted phenomenological models of hysteresis in random vibration. It is routinely used in the characterization of nonlinear damping and in system identification. In this paper, the differential model of hysteresis is carefully re-examined and two significant issues are uncovered. First, it is found that the unspecified parameters of the model are functionally redundant. One of the parameters can be eliminated through suitable transformations in the parameter space. Second, local and global sensitivity analyses are conducted to assess the relative sensitivity of each model parameter. Through extensive Monte Carlo simulations, it is found that some parameters of the hysteretic model are rather insensitive. If the values of these insensitive parameters are fixed, a greatly simplified model is obtained.