Nonlinear analysis of beam on an elastic polymeric foundation: a study on transient and frequency responses

This study examines the dynamic behavior of a micro-beam resting on an elastic polymeric layer with finite depth, with a particular focus on the beam's nonlinear transient and steady-state response to a base excitation. The investigation considers both the beam's transverse motion and the elastic polymeric foundation's nonlinear squeezing motion within the coupled nonlinear governing equations. In order to examine the influence of different materials on the system's overall response, the nonlinear governing equations are discretized with respect to spatial coordinates and integrated over time, thereby obtaining transient solutions. In regard to frequency response, the coefficients of the harmonic Fourier-expanded response are obtained by balancing energy within a period. A series of numerical tests were performed, including the fast Fourier transform (FFT), the determination of time characteristics, and the phase portrait of the system. These tests encompassed a range of scenarios, including constant, stepwise, pulse, and harmonic accelerations. Furthermore, studies have been conducted to ascertain the frequency response of the system to single harmonic input signals with varying frequencies.