Nonlinear vibrations and instabilities of a stretched hyperelastic annular membrane

Soares, Renata M.; Gonçalves, Paulo B.

doi:10.1016/j.ijsolstr.2011.10.019

Cited by 58 publications

(40 citation statements)

References 48 publications

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“…The sensitivity of the respective vibratory behavior to the pre-stretch configuration of the membranes is carried out in these scientific contributions. The incompressible hyperelastic material is either described by a Neo-Hookean model [5] or by Mooney-Rivlin, Yeoh, Ogden, and Arruda-Boyce models in [4]. In this latter work, the frequencyamplitude relationships for various hyperelastic models are found to be analogous.…”

Section: Introductionmentioning

confidence: 78%

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Nonlinear vibrations of thin hyperelastic plates

Breslavsky

Amabili

Legrand

2014

Journal of Sound and Vibration

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International audienceStatic deflection as well as free and forced nonlinear vibration of thin square plates made of hyperelastic materials are investigated. Two types of materials, namely rubber and soft biological tissues, are considered. The involved physical nonlinearities are described through the Neo-Hookean, Mooney-Rivlin, and Ogden hyperelastic laws; geometrical nonlinearities are modeled by the Novozhilov nonlinear shell theory. Dynamic local models are first built in the vicinity of a static configuration of interest that has been previously calculated. This gives rise to the approximation of the plate's behavior in the form of a system of ordinary differential equations with quadratic and cubic nonlinear terms in displacement. Numerical results are compared and validated in the static case via a commercial finite element software package: they are found to be accurate for deflections reaching 100 times the thickness of the plate. The frequency shift between low- and large-amplitude vibrations weakens with an increased initial deflection

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Section: Introductionmentioning

confidence: 78%

“…This approach is implemented for circular membranes in [4,5]. The sensitivity of the respective vibratory behavior to the pre-stretch configuration of the membranes is carried out in these scientific contributions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibrations of thin hyperelastic plates

Breslavsky

Amabili

Legrand

2014

Journal of Sound and Vibration

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“…The experimental results are obtained using the applied forces shown in Table 1 and Eqs. (18), (21) and (22). Fig.…”

Section: Experimental Apparatus and Resultsmentioning

confidence: 98%

“…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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“…The study of interaction mechanics of hyperelastic membranes with constraints without and with adhesion/friction can be found in recent works [36][37][38], The dynamics of hyperelastic membranes of different geometries has also been studied (see Refs. [39][40][41][42][43]). …”

Section: Introductionmentioning

confidence: 99%

Finite Inflation Analysis of Two Circumferentially Bonded Hyperelastic Circular Flat Membranes

Dhavale

Tamadapu

DasGupta

2014

Journal of Applied Mechanics

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A finite inflation analysis of two circumferentially bonded hyperelastic circular flat mem branes with uniform internal pressure is presented. The governing equations of equilib rium are obtained using the variational formulation. By making a suitable change in the field variables, the problem is formulated as a set of two coupled nonlinear two point boundary value problem (TPBVP) and is solved using the shooting method. Membranes o f identical and dissimilar material properties are considered in the analysis. For dissim ilar membranes, asymmetric inflation, and remarkably, deflation (after an initial phase of inflation) in one o f the membranes in certain cases, has been observed. The effect of infla tion pressure and material properties on the geometry of inflated configuration, state of stress, and the impending wrinkling condition of the membranes are also studied. This work has relevance to tunable inflated reflectors and lenses among other applications.

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Nonlinear vibrations and instabilities of a stretched hyperelastic annular membrane

Cited by 58 publications

References 48 publications

Nonlinear vibrations of thin hyperelastic plates

Nonlinear vibrations of thin hyperelastic plates

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

Finite Inflation Analysis of Two Circumferentially Bonded Hyperelastic Circular Flat Membranes

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