COMPARATIVE STUDY OF CONSTITUTIVE LAWS IN VIBRATIONS OF RECTANGULAR HIPERELASTIC MEMBRANES
Renato de Souza Silva1; Zenon J G Nunez del Prado1; Renata Machado Soares1; Paulo Batista Gonçalves2
1 Universidade Federal de Goiás; 2 Pontifícia Universidade Católica do Rio de Janeiro
Baixar PDF doi:10.20906/CPS/CILAMCE2015-0122
Resumo
The aim of the present work is to make a comparative study of the influence of constitutive laws on the vibration response of a pre-stretched rectangular hyperelastic membrane. The membrane is composed of an isotropic, homogeneous, hyperelastic and incompressible material, which is modeled with different constitutive laws, specifically: Yeoh, Mooney-Rivlin and neo-Hookean. First, the exact solution of the membrane under a biaxial stretch is obtained and the equations of motion of the pre-stretched membrane are derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are obtained analytically and the natural modes are used to approximate the nonlinear deformation field using the Galerkin method. The results with different constitutive laws are compared.
Palavras-chave: Rectangular hyperelastic membrane; constitutive law; Large amplitude vibrations