Development and Parameter Estimation of a Low Order Model for a Hyperelastic Cantilever Plate Exhibiting 2:1 Resonant Response

Abstract This work presents the results of an experimental investigation and a low-order model development for complex resonant dynamics of a cantilever macro-plate. The plate is fabricated from a material using 3D additive manufacturing technology and the material is assumed to be ‘hyperelastic’. The geometry of the plate with cut-outs is analytically optimized assuming a linear elastic material such that the second bending mode frequency 𝜔02 is approximately twice the first twisting mode frequency 𝜔11. Based on the observed ‘near’ 2:1 resonant response under harmonic excitation near 𝜔02, a low-order 2 DOF nonlinear dynamic model is developed to simulate the plate response. A unique and novel stepwise iterative approach is developed for the modal parameter extraction. The unknown modal parameters are extracted using Harmonic Balance solutions, constructing frequency response curves, and curve-fitting techniques. The results are then validated using long-time integration for the developed model. A good agreement is observed between the analytical and experimental results for the different excitation levels considered.