PRIMARY RESONANCE OF BEAMS ON ELASTIC FOUNDATIONS SUBJECTED TO LATERAL LOADS

The nonlinear vibration of finite-length beams on the Winkler foundation subjected to the lateral loads is investigated. Based on the Winkler foundation model and the Euler-Bernoulli beam theory, the nonlinear in-plane motion equation of the finite-length beam on the Winkler foundation is obtained. The approximate solution of the finite-length beam for the case of the primary resonance is obtained by the Galerkin method and the method of multiple scales. To illustrate the characteristics of the primary resonance, the effects of major parameters on the frequency-response curves of the beam on the elastic foundation are studied, such as, the slenderness ratio, the stiffness coefficient of the foundation, the amplitude of the excitation and the damping coefficient. Comparing with the non-resonant response of the beam, the effect of the primary resonance on the actual dynamic response is analyzed. The numerical results show that the frequency-response curves of the beam have jump and delay; the damping term plays a very important role in the primary resonance of the beam, the primary resonance significantly increases the amplitude of the steady state response.