抄録
Analytical results are presented on nonlinear vibrations of a bowed-type beam deformed by stretched strings at both ends with a mode shape function approach. This procedure combines the procedures of modal expansion with finite element analysis. The mode shape function is introduced with the product of truncated power series and trigonometric function. The unknown coefficients of the mode shape function satisfy both of the geometric and dynamical boundary condition at the nodes of segments. First, the governing equation of the beam is obtained including the geometrical nonlinearity due to the stretch of the beam and of the string. Then, linear vibration modes of the beam are obtained under the condition of pre-buckling. Furthermore, applying the modified Galerkin procedure based on the linear mode to the nonlinear governing equation. Nonlinear periodic and non-periodic responses are calculated. The chaotic response of the beam is generated from the internal response of the sub-harmonic response of 1/4 order with the asymmetric lowest mode of vibration and of the principal resonance with the symmetric second mode accompanied by the dynamic snap-thorough.
