Nonlinear Dynamic Response of a Stiffened Imperfect Beam under Primary Resonance Excitation - Aal, Osama F. Abdel; Aal, Mohammad Abdel; Qaisia, Ahmad Al (Journal of Applied Nonlinear Dynamics, 2026)
This work presents an investigation on the effect of an initial geometric imperfection; wavelength, amplitude, and degree of localization on the in-plane nonlinear resonance responses of an imperfect beam. The beam was modeled as an Euler Bernoulli beam resting on an elastic foundation, hinged at one end and supported by a torsional spring at the other end. The governing model accounts for the effect of the axial force induced by mid-plane stretching. The imperfection was introduced as a rise with different shapes, different amplitudes, and wavelengths. A quantitative and qualitative analysis of the steady-state responses and their stability is obtained by computing force-frequency response curves using the Harmonic Balance method HB and the method of Multiple Scales MMS. Results have shown that the behavior of the steady-state responses may change from hardening to softening types depending on the geometrical and physical parameters of the beam under consideration. Results are presented in a dimensionless form for the steady-state forced vibration in the aid of time histories, phase planes, frequency spectrums, and Poincare maps for selected values of physical parameters. It is shown that the beam response may exhibit complicated dynamic behaviors including period multiplying and period de multiplying bifurcations, period three and period six motions, jump phenomenon, and chaos.