Validity of the Multiple Scale Solution for a Resonance Response of a Bar with a Nonlinear Boundary Condition

비선형 경계조건을 가진 봉의 공진응답을 위한 다중시간해의 타당성

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.