先端を弦張力で拘束された片持ちはりの非線形振動解析(<特集>D & D 2007)

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Analytical results are presented on nonlinear vibrations of a cantilevered beam constrained by a stretched string at the tip end. The beam is subjected to periodic lateral acceleration. Governing equations of motion and boundary condition, which have nonlinear geometrical coupling with an axial force, are derived by the Hamilton's principle. The mode shape function proposed by the senior author is introduced to reduce the governing equations to the nonlinear differential equation by the modified Galerkin method. The mode shape function is expressed with the product of the trigonometrical function and the finite power series truncated with the fourth order. The coefficients of the power series are determined by solving the homogeneous equation for the boundary condition at the buckling state of the beam. The trigonometrical function can express the form of higher mode of vibration. Nonlinear periodic responses are calculated by the harmonic balance method. Nonlinear non-periodic responses are obtained by the numerical integration. Comparing the nonlinear responses by the analyses with the approaches of single-degree-of-freedom and of multiple-degree-of-freedom, higher mode of vibration play important roles both in the periodic response and in the chaotic response. It is shown that the analysis based on the approach of the mode shape function makes fairly good prediction to the nonlinear phenomena of the cantilevered beam constrained by the stretched string.
社団法人日本機械学会の論文
2008-05-25

先端を弦張力で拘束された片持ちはりの非線形振動解析(<特集>D & D 2007)

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