Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications

Younesian, Davood; Hosseinkhani, Ali; Argani, Hassan; Esmailzadeh, Ebrahim

doi:10.1007/s11071-019-04977-9

Cited by 112 publications

(46 citation statements)

References 270 publications

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“…The film deformed out of a plane only can be modeled into a beam, which greatly simplifies theoretical analysis [ 24 ]. The compliant substrate is considered to be a Winkler elastic foundation [ 47 , 48 , 49 , 50 ], whose reaction at any point is proportional to the deflection, with stiffness

and deflection of the thin film

shown in Figure 1 b, where

is the function of Cartesian coordinate

, which is along the axial direction of the thin film.…”

Section: Buckling Analysismentioning

confidence: 99%

Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Fan

Wang

et al. 2020

Sensors

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Buckling stability of thin films on compliant substrates is universal and essential in stretchable electronics. The dynamic behaviors of this special system are unavoidable when the stretchable electronics are in real applications. In this paper, an analytical model is established to investigate the vibration of post-buckled thin films on a compliant substrate by accounting for the substrate as an elastic foundation. The analytical predictions of natural frequencies and vibration modes of the system are systematically investigated. The results may serve as guidance for the dynamic design of the thin film on compliant substrates to avoid resonance in the noise environment.

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and deflection of the thin film

shown in Figure 1 b, where

is the function of Cartesian coordinate

, which is along the axial direction of the thin film.…”

Section: Buckling Analysismentioning

confidence: 99%

Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Fan

Wang

et al. 2020

Sensors

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“…where A n , B n are functions of the slow time T , which can be found by the standard procedure [32][33][34][35][36]. We suppose that A n , B n = O (1). Then, the termsX n (t, T ) produce small contributions in Y with respect to the termsX n (T ).…”

Section: The Influence Of Damping On Bucklingmentioning

confidence: 99%

“…in [1]. The review covers the simplest foundation models to the most complicated ones, and fully describes the recent theories on the topic of mechanical foundations.…”

mentioning

confidence: 99%

“…The review covers the simplest foundation models to the most complicated ones, and fully describes the recent theories on the topic of mechanical foundations. Special attention in [1] is paid to publications which consider the dynamics of an E-B beam resting on a nonlinear elastic foundation. The dynamics and buckling loads for an E-B beam resting on an inhomogeneous elastic Winkler foundation also plays an importing role in the study of problems of soil-solid interaction [2].…”

mentioning

confidence: 99%

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Dynamics and buckling loads for a vibrating damped Euler–Bernoulli beam connected to an inhomogeneous foundation

et al. 2020

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In this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of damping models. Based on the Rayleigh variation principle, beam buckling loads are computed for cases of harmonically perturbed types of inhomogeneities in the elastic foundation, for cases of point inhomogeneities in the form of concentrated springs in the elastic foundation, and for cases with rectangular inclusions in the elastic foundation. The investigation of the beam dynamics shows the possibility of internal resonances for particular values of the beam rigidity and longitudinal force. Such types of resonances, which are usually typical for nonlinear systems, are only possible for the beam due to its inhomogeneous foundation. The occurrence of so-called added mass effects near buckling instabilities under the influence of damping have been found. The analytical expressions for this “added mass” effect have been obtained for different damping models including space hysteresis types. This effect arises as a result of an interaction between the main mode, which is close to instability, and all the other stable modes of vibration.

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“…For simplicity, the base excitation is defined as BE. From the perspective of foundation flexible, the effects of a nonlinear foundation on the dynamic performance of an oscillation system cannot be ignored (Younesian et al, 2019). For completeness, the combined dynamic model, which considers the interaction between the foundation and the system rested on it, will be constructed and investigated in the next research stage.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

Liu¹,

Xiao²,

Zhao³

et al. 2020

Journal of Vibration and Control

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Stiffness and damping of a structure usually show the opposite change so that the resonant frequency and the static load bearing capacity of a mechanical system often exhibit contradiction. To solve this dilemma, a novel high-damping oscillator which is constructed by a nested diamond structure with the purpose of enhancing the damping property is proposed in this study without reducing the overall systematic stiffness. The mathematical model and geometrical relationships are established at first. And then, the steady-state solutions under base excitation are derived by using the harmonic balance method and further verified by numerical simulation. In addition, the effects of some design parameters on the equivalent damping ratio for the high-damping oscillator are studied to reveal the nonlinear characteristic. Besides, the natural frequency of the nonlinear oscillator is also presented and investigated. By using the displacement transmissibility and comparing with the traditional linear isolator with the same overall stiffness, the vibration suppression performance of the high-damping oscillator is addressed. The obtained calculating results demonstrate that the vibration control performance of the high-damping oscillator outperforms the linear counterpart around resonant frequency. Moreover, the influences of systematic parameters of the high-damping oscillator for the base excitation case on the vibration transmissibility are also discussed, respectively. Finally, an experimental campaign is conducted on an in-house-built test rig to corroborate the accuracy of the analytical solutions of the high-damping oscillation system. The results discussed in this study provide a useful guideline, which can help to design this class of high-damping oscillation system.

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Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications

Cited by 112 publications

References 270 publications

Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates

Dynamics and buckling loads for a vibrating damped Euler–Bernoulli beam connected to an inhomogeneous foundation

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

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