支承运动对悬臂梁的作用力

The Applied Forces of a Moving Support to a Cantilever Beam

该文研究了一个已知支承运动的悬臂梁。用固定支承上的悬臂梁的低阶正则模态描述该梁在支承连体系中的弹性位移。将Ｈｕｓｔｏｎ方法推广应用于梁的微元，得到微元的广义惯性力，积分后得到梁的广义惯性力。用梁单元代替梁微元，将积分化为求和。梁的广义主动力取为动支承的作用力和弹性力。由Ｋａｎｅ方程得到梁的动力学方程，进而导出了计算支承作用力的公式。

In this paper,a cantilever beam attached to a moving support is studied.The low order normalized modes of a cantilever beam attached to a fixing support are used for descriping elastic displacement of the beam in the reference frame fixed on the moving support.Huston’s method is extended and employed in kenetic analysis of differential element of the beam.The generalized inertia forces of the differential element can be derived.Integrating them yields the generalized inertia forces of the beam.The integral can be converted into summation by replacing the differential element with finite element.The generalized active forces of the beam are applied forces of the moving support and elastic forces of the beam.The dynamic equations of the beam is obtained by using Kane’s equations.The expressions for the applied forces are derived from the dynamic equations.A numerical example shows that the applied forces to a flexible beam differ markedly from those to a rigid beam.