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.

本文提出了一种联合实验和理论方法来研究超弹性板的动力学和质量敏感性，包括具有模态相互作用的情况。对于理论方法，分别使用 Mooney-Rivlin 超弹性应变能密度模型和 von-Kármán 几何非线性假设板结构经受大应变和变形。使用连续介质力学定义和 Kirchhoff-Love 板理论对板进行建模。耦合的平面内和平面外运动方程是使用 Hamilton 方程获得的，然后使用 Galerkin 程序与动态平衡技术的组合求解。对于实验分析，首先通过按照 ASTM D-412 标准对样品进行一组应力-应变测试来获得材料的性能，然后使用相同的橡胶材料制造板结构，并进行外部驱动的振动测试. 研究了具有和不具有集中质量的结构的非线性频率响应，并讨论了该结构的质量传感能力。通过获得外加周期性载荷作用下结构的幅频响应，采用理论和实验方法，表明该模型在模拟不同条件下超弹性板结构的非线性动力学时具有良好的精度。此外，提出了一组使用集中质量和长宽比对不同内部共振下超弹性板的非线性强迫振动行为的分析。这项研究的结果可用于设计涉及超弹性板的系统，例如软机器人和软功能设备。