周期的な軸方向加速度が作用する集中質量搭載ばりの動的不安定

概要

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Parametric vibrations of beams carrying a concentrated mass subjected to both static and periodic axial acceleration are analyzed under four sets of boundary conditions. Introducing the mode shape function, which is expressed as the product of the power series truncated to the fourth order, and the trigonometric function, we obtain the boundary conditions at both ends combined with a simply supported end or a clamped end by exchanging the coefficients of the power series. Applying the Galerkin method to basic equations, we reduce the coupled Mathieu's equations. The stability boundaries of the principal, secondary and combination parametric resonances are examined using Hsu's method. Calculations are carried out for various values of the location of the concentrated mass in each boundary condition. It is found that the inertia force caused by the concentrated mass under periodic acceleration expands the instability region extensively. In particular, the boundary is extended when the concentrated mass approaches the end with a movable axial displacement.
社団法人日本機械学会の論文
1989-06-25