203 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対する解の精度について

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This paper examines the accuracy of analytical solutions for nonlinear vibration analyses of continuous systems with quadratic and cubic non-linearites. As an example, we treat a suspended homogenous elastic cable whose two supports are fixed, and investigate the primary resonance of the second (first antisymmetric) in-plane mode (Ω=ω_2), in which Ω and ω_2 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 (direct approach). In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the method of multiple scales to the obtained ordinary differential equations (discretization approach). In the discretization approach, the detuning parameter σ, which expresses the relationship between the natural frequency and the driving frequency, is change from Ω=ω_ + εσ to Ω_2 = ω^2_2 + εσ so as to improve the accuracy of the solutions. 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
2009-08-03