Large-amplitude nonlinear vibrations of a Mooney–Rivlin rectangular membrane

Soares, Renata M.; Gonçalves, Paulo B.

doi:10.1016/j.jsv.2014.02.007

Cited by 31 publications

(17 citation statements)

References 33 publications

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“…In this study, without the loss of generality, the neo-Hookean constitutive model for the energy density function is initially adopted, which for an incompressible material is given by [17][18][19] …”

Section: Results Inmentioning

confidence: 99%

Analysis of the structural behavior of a membrane using digital image processing

Jurjo

Magluta

Roitman

et al. 2015

Mechanical Systems and Signal Processing

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Section: Results Inmentioning

confidence: 99%

Analysis of the structural behavior of a membrane using digital image processing

Jurjo

Magluta

Roitman

et al. 2015

Mechanical Systems and Signal Processing

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“…For the conditions of a conservative system, the elastic Cauchy stresses are derived from a strain‐energy density function W , which may be described in terms of three strain invariants I 1 , I 2 , and I 3 . Thus, the three strain invariants of the deformation field can be written in terms of the principal stretch ratios λ 1 , λ 2 , and λ 3 as

\begin{matrix} left \\ I_{1} = λ_{1}^{2} + λ_{2}^{2} + λ_{3}^{2} \\ I_{2} = {(λ_{1} λ_{2})}^{2} + {(λ_{2} λ_{3})}^{2} + {(λ_{1} λ_{3})}^{2} \\ I_{3} = {(λ_{1} λ_{2} λ_{3})}^{2} \end{matrix}

where λ 1 , λ 2 , and λ 3 are the stretch ratios in the x, y , and z directions.…”

Section: Hyperelastic Dielectric Elastomer Theorymentioning

confidence: 99%

“…They studied the dynamics of a step‐voltage‐driven homogeneously deformed DEA sandwich structure using an Euler–Lagrange equation. The linear and nonlinear vibration characteristics of hyperelastic membranes have been studied to investigate the large‐amplitude vibrations . When subject to periodic electric loading, the natural frequency of the small‐amplitude perturbation around the state of equilibrium undergoing in‐plane deformation is presented, and the damping effect is taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…In the current work, the dynamic characteristics of DEA membranes are considered using an analytical model using the Euler–Lagrange equation. The explicit expressions of the dynamic parameters of DEAs has been reported previously in the literature . However, to the authors' best knowledge, no previous studies have been conducted to investigate the linear and nonlinear vibration characteristics in the dynamic instability parameters of DEAs.…”

Section: Introductionmentioning

confidence: 99%

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Cauchy stresses and vibration frequencies for the instability parameters of dielectric elastomer actuators

Kim

Liu

Leng

2018

J of Applied Polymer Sci

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An analysis of the effect of Cauchy stresses, vibration frequency response, and instability on the transient dynamic response of step-voltage-driven dielectric elastomer actuators (DEAs) is presented in this paper. Material nonlinearities associated with the hyperelastic constitutive law are taken into account, and the membrane is assumed to be made of an isotropic, homogeneous, and incompressible material. The results for the neo-Hookean material model are further extended to analyze relatively complex multiparameter hyperelastic models (Mooney-Rivlin and Ogden) that are often employed for investigating the behavior of DEAs. The dynamic instability parameters are predicted using energy-based extraction of static instability and validated by the response of the material in the vicinity of the dynamic instability. The natural modes of the membrane are used to approximate the nonlinear deformation field using the Galerkin method. A detailed parametric analysis of the equations of motion for the prestretched membrane shows the natural frequencies and mode shapes of the membrane and the strong influence of the stretching ratios and material parameters on the linear and nonlinear oscillations of the membrane. The results of the present investigation show the electric field-frequency relations, resonance curves, and bifurcation diagrams using the nonlinear dynamics of DEAs subjected to electrical loads.Recently, several researchers have investigated the nonlinear dynamic response of DEAs subjected to a combined DC and AC voltage, on the effect of the dynamic parameters of V C 2018 Wiley Periodicals, Inc.

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“…Gonçalves et al (2009) analysed the vibrations of a pre-stretched circular hyper-elastic membrane, both analytically and numerically. The linear and non-linear vibration of a hyper-elastic rectangular membrane was additionally investigated by Soares and Gonçalves (2014) using analytical and finite element (FE) models.…”

Section: Introductionmentioning

confidence: 99%

Non-contact experimental methods to characterise the response of a hyper-elastic membrane

Kamper

Bekker

2017

Int J Mech Mater Eng

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Background: Membranes often feature in dynamic structures. The design of such structures generally includes the evaluation of their dynamic characteristics, such as natural frequecies and mode shapes. Methods: The quasi-statics ad dyamic responses of thin rubber sheeting were investigated through non-contact experimental techniques. The rubber sheeting was modelled as a membrane structure and the material was assumed to be hyper-elastic, isotopic and incompressible. Two hyper-elastic material models were considered, namely the Mooney-Rivlin model and the Neo-Hookean model. The natural frequencies and mode shapes of the hyprt-elastic membrane were anatically and numerically calculated by assuming small linear vibrations and an equi-bi-axial stress state in the membrane. To validate the mathematical analyses, experimental modal analysis was performed where the vibration response was measured with a laser Doppler vibrometer. Results and conclusions:The analytical model, shows that the natural frequencies of the membrane depend on the initial stretch. Mathematical and experimental results agree well at the lower modes. However, measurement resolution is found to be a vital factor which limits the extraction of closely spaced modes due to difficulties with the accurate identification of nodal line in a purely experimental approach.

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Large-amplitude nonlinear vibrations of a Mooney–Rivlin rectangular membrane

Cited by 31 publications

References 33 publications

Analysis of the structural behavior of a membrane using digital image processing

Analysis of the structural behavior of a membrane using digital image processing

Cauchy stresses and vibration frequencies for the instability parameters of dielectric elastomer actuators

Non-contact experimental methods to characterise the response of a hyper-elastic membrane

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