Title: Nonlinear dynamic response of the Mooney Rivlin hyperelastic beam under a distributed

Abstract

In this paper, force vibration and the dynamic lateral deflections of the hyperelastic thin beam based on a Mooney-Rivlin model and under a distributed load are studied. The surrounding elastic medium is simulated as a Pasternak foundation to study the effects of both normal and shear effects. Using Hamilton’s principle, Von Karman assumptions, Euler-Bernoulli beam theory, and Left Cauchy Green deformation tensor, the governing equations of motion and related boundary conditions are obtained. The combination of the nonlinear and coupled motion equations and boundary conditions is solved by an iterative 2D differential quadrature (DQ) spatial discretization and Newmark’s time-marching methods. In this regard, the dynamic lateral deflections are plotted to study the effects of thickness and length of the beam, surrounding elastic medium, different boundary conditions, the constitutive parameters of the hyperelastic material, and distributed compressor load magnitude. Results show the key roles of the constitutive parameters of the hyperelastic material, the combination of the edge conditions, and the shear stiffness parameters of the foundation on the dissipation manner of the vibration and performance of the structure. Furthermore, results show that the linearization errors are significant for larger loads and looser boundary conditions.