Nonlinear Isolator Dynamics at Finite Deformations: An Effective Hyperelastic, Fractional Derivative, Generalized Friction Model
TL;DR: In this article, the authors present a nonlinear dynamic model of a rubber vibration isolator, where the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain.
Abstract: In presenting a nonlinear dynamic model of a rubber vibration isolator, the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation, superimposed upon the long term isolator response, is strongly dependent on static precompression, dynamic amplitude and frequency. The problems of simultaneously modelling the elastic, viscoelastic and friction forces are removed by additively splitting them, modelling the elastic force response by a nonlinear, shape factor based approach, displaying results that agree with those of a neo-Hookean hyperelastic isolator at a long term precompression. The viscoelastic force is modeled by a fractional derivative element, while the friction force governs from a generalized friction element displaying a smoothed Coulomb force. A harmonic displacement excitation is shown to result in a force response containing the excitation frequency and its every other higher-order harmonic, while using a linearized elastic force response model, whereas all higher-order harmonics are present for the fully nonlinear case. It is furthermore found that the dynamic stiffness magnitude increases with static precompression and frequency, while decreasing with dynamic excitation amplitude-eventually increasing at the highest amplitudes due to nonlinear elastic effects-with its loss angle displaying a maximum at an intermediate amplitude. Finally, the dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes.
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TL;DR: In this paper, a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means is presented, which highlights resolved and unresolved problems and recommendations for future research directions.
885 citations
TL;DR: In this article, the authors present the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics.
Abstract: The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures. DOI: 10.1115/1.4000563
491 citations
TL;DR: A new idea of intelligent foundations based on nanogenerators, which can be exploited in future smart cities for both energy harvesting and self-powered sensing applications is presented.
Abstract: This paper presents a comprehensive review on different theoretical elastic and viscoelastic foundation models in oscillatory systems. The review covers the simplest foundation models to the most complicated one and fully tracks the recent theories on the topic of mechanical foundations. It is fully discussed why each theory has been developed, what limitations each one contains, and which approaches have been applied to remove these limitations. Moreover, corresponding theories about structures supported by such foundations are briefly reviewed. Subsequently, an introduction to popular solution methods is presented. Finally, several important practical applications related to the linear and nonlinear foundations are reviewed. This paper provides a detailed theoretical background and also physical understanding from different types of foundations with applications in structural mechanics, nanosystems, bio-devices, composite structures, and aerospace-based mechanical systems. The presented information of this review article can be used by researchers to select an appropriate kind of foundation/structure for their dynamical systems. The paper ends with a new idea of intelligent foundations based on nanogenerators, which can be exploited in future smart cities for both energy harvesting and self-powered sensing applications.
96 citations
TL;DR: In this article, a nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads and is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems.
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TL;DR: In this paper, the amplitude-dependent effect, known as the Fletcher-Gent effect or Payne effect, was used to predict the dynamic stiffness of filled rubber isolators using a finite element (FE) code.
68 citations
References
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TL;DR: In this paper, a new method of modeling and solution of a large class of hysteretic systems (softening or hardening, narrow or wideband) under random excitation is proposed.
Abstract: Based on a Markov-vector formulation and a Galerkin solution procedure, a new method of modeling and solution of a large class of hysteretic systems (softening or hardening, narrow or wide-band) under random excitation is proposed. The excitation is modeled as a filtered Gaussian shot noise allowing one to take the nonstationarity and spectral content of the excitation into consideration. The solutions include time histories of joint density, moments of all order, and threshold crossing rate; for the stationary case, autocorrelation, spectral density, and first passage time probability are also obtained. Comparison of results of numerical example with Monte-Carlo solutions indicates that the proposed method is a powerful and efficient tool.
2,377 citations
"Nonlinear Isolator Dynamics at Fini..." refers background in this paper
...Alternatively, the versatile, though complex, Bouc–Wen differential example [28, 29 ] is widely used in nonlinear friction systems, e.g....
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TL;DR: In this paper, a fractional calculus is used to construct stress-strain relationships for viscoelastic materials and these relationships are used in the finite element analysis of damped structures and closed-form solutions to the equations of motion are found.
Abstract: Fractional calculus is used to construct stress-strain relationships for viscoelastic materials. These relationships are used in the finite element analysis of viscoelastically damped structures and closed-form solutions to the equations of motion are found. The attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions.
1,041 citations
681 citations
"Nonlinear Isolator Dynamics at Fini..." refers background in this paper
...Rossikhin and Shitikova [ 17 ], Shimizu and Zhang [18] present thorough reviews of fractional derivatives in dynamic analysis where the fractional standard linear solid is the most popular model applied [16, 19, 20]....
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TL;DR: In this paper, fractional time derivatives are used to deduce a generalization of viscoelastic constitutive equations of differential operator type, which result in improved curve-fitting properties, especially when experimental data from decades or spanning several frequency decades need to be fitted.
Abstract: Fractional time derivatives are used to deduce a generalization ofviscoelastic constitutive equations of differential operator type. Theseso-called fractional constitutive equations result in improvedcurve-fitting properties, especially when experimental data from longtime intervals or spanning several frequency decades need to be fitted.Compared to integer-order time derivative concepts less parameters arerequired. In addition, fractional constitutive equations lead to causalbehavior and the concept of fractional derivatives can be physicallyjustified providing a foundation of fractional constitutive equations. First, three-dimensional fractional constitutive equations based onthe Grunwaldian formulation are derived and their implementationinto an elastic FE code is demonstrated. Then, parameter identificationsfor the fractional 3-parameter model in the time domain as well as inthe frequency domain are carried out and compared to integer-orderderivative constitutive equations. As a result the improved performanceof fractional constitutive equations becomes obvious. Finally, theidentified material model is used to perform an FE time steppinganalysis of a viscoelastic structure.
175 citations
"Nonlinear Isolator Dynamics at Fini..." refers background in this paper
...Rossikhin and Shitikova [17], Shimizu and Zhang [18] present thorough reviews of fractional derivatives in dynamic analysis where the fractional standard linear solid is the most popular model applied [16, 19, 20 ]....
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TL;DR: In this article, a non-linear rubber isolator included in a dynamic system is examined where influences of dynamic amplitude and frequency are investigated through measurements and modeling, and good agreement is obtained in a wide frequency and amplitude range for a freely oscillating one degree of freedom system, with the isolator acting as a coupling between exciting foundation and mass.
Abstract: A non-linear rubber isolator included in a dynamic system is examined where influences of dynamic amplitude and frequency are investigated through measurements and modeling. The frequency dependence of the isolator is modeled by a fractional calculus element while a frictional component accounts for its amplitude dependence. The model works in the time-domain and simulations of harmonic and non-harmonic motion are compared to measurements. Good agreement is obtained in a wide frequency and amplitude range for a freely oscillating one degree of freedom system, with the isolator acting as a coupling between exciting foundation and mass, and for a single isolator showing the typical amplitude dependence known as the Payne effect. The model is found to be superior to the commonly applied Kelvin-Voigt element in modeling the dynamic isolator properties.
151 citations
"Nonlinear Isolator Dynamics at Fini..." refers methods or result in this paper
...To improve the agreement with experimental observations on dynamic, nonlinear amplitude dependent forces, a generalized friction element is applied [ 22 , 27], displaying a smoothed Coulomb force behavior....
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...Nonlinear friction is furthermore included in the analysis by Sjoberg and Kari [ 22 ] using a fractional Kelvin–Voigt model, while Brackbill et al. [23, 24] apply a nonlinear anelastic displacement field approach....
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...To effectively mimic the smooth friction force behavior of carbon black filled rubber, a generalized friction element is applied [ 22 , 27] in Figure 2; here, extended into the finite deformation domain by a straightforward model continuation, displaying a friction force that gradually develops with compression displacement....
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...First, the total force response at a finite cyclic deformation of the developed, nonlinear dynamic model of Section 2 is presented in Section 3.1 and compared to that of a previously published model [ 22 ], the latter using a fully linear elastic force element....
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...Finally, the viscoelastic force contribution (3) to the total force increases with frequency; thus resulting in a dynamic stiffness magnitude increase with frequency – in line with experimental observations [1, 15, 22 ]....
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