Passive Design of Nonlinearity in Specific Modes of Flexural Vibrations in Thin Plates through Topology Optimization

This paper presents the first attempt to optimize the nonlinearity of flexural vibrations in thin plates using topology optimization techniques. Nonlinearity in the flexural vibrations of thin plates is characterized by an increase or decrease in natural frequencies in the frequency domain as the external force or internal energy increases, a phenomenon known as hardening/softening nonlinearity. This study adopts topology optimization techniques to identify the layout of thin plates that either enhance or mitigate this nonlinearity. The nonlinearity of the optimum layout was verified through a nonlinear frequency response curve, obtained using the harmonic balance method.