Theory and experiment for dynamics of hyperelastic plates with modal interactions

Abstract

This paper presents a joint experimental and theoretical approach to the dynamics and mass sensitivity of hyperelastic plates including cases with modal interactions. For the theoretical approach, the plate structure is assumed to undergo large strains and deformations using the Mooney-Rivlin hyperelastic strain energy density model and the von-Kármán geometric nonlinearity, respectively. The plate is modelled using the continuum mechanics definitions and the Kirchhoff–Love plate theory. The coupled in-plane and out-of-plane equations of motion are obtained using Hamilton's equation and solved afterwards using a combination of Galerkin's procedure together with a dynamic equilibrium technique. For the experimental analysis, the properties of the material are first obtained by performing a set of stress-strain tests on the samples following the ASTM D-412 standard, and then from the same rubber material, a plate structure is fabricated, and an externally actuated vibration test is performed. The nonlinear frequency response of the structure both with and without a concentrated mass is investigated and the capability of the structure for mass sensing is discussed. By obtaining the amplitude-frequency response of the structure due to the applied external periodic load, using both theoretical and experimental approaches, it is shown that the given model has good accuracy in simulating the nonlinear dynamics of the hyperelastic plate structure under different conditions. Furthermore, a set of analyses on the nonlinear forced vibration behaviour of hyperelastic plates at different internal resonances, using concentrated mass and the length-to-width ratio is presented. The results of this study are useful in designing systems involving hyperelastic plates, such as soft robots and soft functional devices.