Nonlinear Vibration Analyses of Cylindrical Shells Composed of Hyperelastic Materials

Zhang, Jing; Xu, Jun; Yuan, Xiying; Ding, Hu; Niu, Datian; Zhang, Wenzheng

doi:10.1007/s10338-019-00114-6

Cited by 22 publications

(3 citation statements)

References 30 publications

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“…The nonlinear dynamics of cylindrical shell structures have been examined lately by many researchers. Zhang et al [135] modelled the nonlinear vibrations of thin-walled hyperelastic cylindrical shells using Donnell's nonlinear shallow shell theory. Using the Lagrange equation together with the Mooney-Rivlin strain energy density model, the equations of motion were obtained.…”

Section: Nonlinear Dynamics Of Hyperelastic Plates and Shellsmentioning

confidence: 99%

A review on the nonlinear dynamics of hyperelastic structures

et al. 2022

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This paper presents a critical review of the nonlinear dynamics of hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. Hyperelasticity requires specific constitutive laws to describe the mechanical properties of different materials, which are characterised by a nonlinear relationship between stress and strain. Due to recent recognition of the high potential of hyperelastic structures in soft robots and other applications, and the capability of hyperelasticity to model soft biological tissues, the number of studies on hyperelastic structures and materials has grown significantly. Thus, a comprehensive explanation of hyperelastic constitutive laws is presented, and different techniques of continuum mechanics, which are suitable to model these materials, are discussed in this literature review. Furthermore, the sensitivity of each hyperelastic strain energy density function to coefficient variation is shown for some well-known hyperelastic models. Alongside this, the application of hyperelasticity to model the nonlinear dynamics of polymeric structures (e.g., beams, plates, shells, membranes and balloons) is discussed in detail with the assistance of previous studies in this field. The advantages and disadvantages of hyperelastic models are discussed in detail. This present review can stimulate the development of more accurate and reliable models.

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Section: Nonlinear Dynamics Of Hyperelastic Plates and Shellsmentioning

confidence: 99%

A review on the nonlinear dynamics of hyperelastic structures

et al. 2022

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“…x , e 0 y , and e 0 z represent the spanwise direction, the chordwise direction, and the thickness direction, respectively. Based on the research done by Yao et al [23] , considering the first-order shear deformation and Kirchhoff hypothesis [24] , the dimensionless partial differential governing equations are expressed by the displacements of an arbitrary points on the neutral plane of the plate u 0 , v 0 , and w 0 along the x-, y-, and z-directions. The nonlinear dynamic oscillations of the rotating blade are investigated qualitatively.…”

Section: Equations Of Motionmentioning

confidence: 99%

Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

Yao

Zhang

et al. 2020

Appl. Math. Mech.-Engl. Ed.

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Turbo-machineries, as key components, have a wide utilization in fields of civil, aerospace, and mechanical engineering. By calculating natural frequencies and dynamical deformations, we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies. In this paper, the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed. The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations, including the centrifugal force and the aerodynamic force. In view of the first-order shear deformation theory and von-Kármán nonlinear geometric relationship, the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle. The second-order ordinary differential equations are acquired by the Galerkin approach. With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance, the averaged equation is derived by the asymptotic perturbation methodology. Bifurcation diagrams, phase portraits, waveforms, and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.

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“…Soarez et al (2020) presented the nonlinear static and dynamic motions behaviors of a hyperelastic spherical membrane under the internal pressure utilizing the Mooney–Rivlin constitutive law. Zhang et al (2019) analyzed a nonlinear vibration of an incompressible Mooney–Rivlin cylindrical shell subjected to a radial excitation. Zhao et al (2021) investigated the effects of dynamic loads and structural damping on the nonlinear behaviors of incompressible hyperelastic spherical shells modeled by the Yeoh strain energy function.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration and resonance analysis of a rectangular hyperelastic membrane resting on a Winkler–Pasternak elastic medium under hydrostatic pressure

Karimi

Ahmadi

Foroutan

2022

Journal of Vibration and Control

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In this paper, the nonlinear vibration and resonance analyses of a rectangular hyperelastic membrane embedded within a nonlinear Winkler–Pasternak elastic medium subjected to a uniformly distributed hydrostatic pressure are investigated. The material of the membrane is incompressible, homogeneous, isotropic, and hyperelastic. The constitutive law of neo-Hookean is utilized for modeling the system. The elastic foundation includes two Winkler and Pasternak linear terms and a Winkler term with cubic nonlinearity. Using the theory of thin hyperelastic membrane, Hamilton’s principle, and assuming the finite deformations, the governing equations are obtained. Then, the motion equation in the transverse direction is discretized by applying Galerkin’s method. The transverse nonlinear oscillations of the membrane are considered in two-modes. Then, utilizing the multiple scales method, the secondary resonance for the case of [Formula: see text] is analyzed. Also, to analyze the nonlinear vibration behavior, numerical methods including the fourth-order Runge–Kutta methods are utilized. In addition, in analyzing the nonlinear vibration responses of the rectangular hyperelastic membrane, the bifurcation diagram, quasi-period motion responses, and the phase portrait are examined. Finally, the influence of the geometrical characteristics and elastic foundation parameters on the resonance analysis of a rectangular hyperelastic membrane is investigated.

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Nonlinear Vibration Analyses of Cylindrical Shells Composed of Hyperelastic Materials

Cited by 22 publications

References 30 publications

A review on the nonlinear dynamics of hyperelastic structures

A review on the nonlinear dynamics of hyperelastic structures

Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

Nonlinear vibration and resonance analysis of a rectangular hyperelastic membrane resting on a Winkler–Pasternak elastic medium under hydrostatic pressure

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