NONLINEAR DYNAMIC MODELING AND PERIODIC VIBRATION OF A CANTILEVER BEAM SUBJECTED TO AXIAL MOVEMENT OF BASEMENT

摘要

Dynamic modeling of a cantilever beam under an axial movement of its basement is present-ed.The dynamic equation of motion for the cantilever beam is established by using Kane’s equation first andthen simplified through the Rayleigh-Ritz method.Compared with the older modeling method,which lineari-zes the generalized inertia forces and the generalized active forces,the present modehng takes the coupledcubic nonlinearities of geometrical and inertial types into consideration.The method of multiple scales is usedto directly solve the nonlinear differential equations and to derive the nonlinear modulation equation for theprincipal parametric resonance.The results show that the nonlinear inertia terms produce a softening effectand play a significant role in the planar response of the second mode and the higher ones.On the otherhand,the nonlinear geometric terms produce a hardening effect and dominate the planar response of the firstmode.The validity of the present modeling is clarified through the comparisons of its coefficients with thoseexperimentally verified in previous studies.