733 2次および3次の非線形性を有する連続体の非線形振動解析について(非線形振動解析)(OS.06 : 振動基礎)

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This paper examines the validity of nonlinear vibration analyses of continuous systems with quadratic and cubic nonlinearities. As an example, we treat a hinged-hinged Euler-Bernoulli beam resting on a nonlinear elastic foundation with distributed quadratic and cubic nonlinearities, and investigate the primary (Ω ≈ ω_n) and subharmonic (Ω = 2ω_n) resonances of the first and second modes, in which Ω and ω_n are the driving and natural frequencies, respectively. The steady-state responses are found by using two different approaches. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure where the displacement of the beam is approximated by the linear first and second mode shapes, and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by the finite difference method.
一般社団法人日本機械学会の論文
2001-08-03