Abstract
Analytical results are presented on nonlinear vibrations of a post-buckled cantilevered beam constrained by string and spring at a tip end. The beam is subjected to periodic lateral acceleration. Governing equations of motion and of boundary condition, which have nonlinear coupling with an axial force, are derived by the Hamilton principle. The mode shape function is introduced to reduce the governing equations to nonlinear-coupled differential equation by the modified Galerkin procedure. Nonlinear responses are obtained by the harmonic balance method and by the numerical integration. It is shown that higher modes of vibration play important roles in chaotic vibrations of the beam constrained by string and spring.
