Experimental and Analytical Study of Initial Condition Effects On Nonlinear Vibrations of Thin-Walled Beams

In this work, an experimental and analytical study has been presented to investigate the effect of initial conditions on the nonlinear free vibration behavior of thin-walled beams. The nonlinear equations of motion have been extracted based on the first-order shear deformation theory (FSDT) and von Kármán relations to account for moderately large deflection. These equations have been solved analytically using the multiple-scale method to extract the linear and nonlinear natural frequencies and frequency response curves, analytically. Also, the free vibration data have been extracted from an experimental free vibration test by exciting the beam with an initial deflection. To study the effect of moderately large initial deflections on the free vibration response and natural frequency, different initial conditions have been applied, and the frequency analysis has been conducted using the power spectrum density (PSD) and Fast Fourier Transforms (FFT) for each case. Finally, the hardening and softening behavior was investigated in some samples. This study presents a novel application of a portable accelerometer with a simplified setup for nonlinear free vibration analysis, offering a practical and accessible alternative to conventional methods.