约束位置的修改对振动模态的影响

结构的约束位置对其固有振动特性有重要的影响，因此计算固有振动特性对约束位置的敏度是结构优化以及模型校正等的重要基础性工作．本文从广义变分原理出发，建立了约束位置的小修改导致的固有值和振动模态增量的方程，针对模态增量方程的求解，提出了一种处理原本征函数空间不完备的方法，从而可以在扩展的原本征函数空间内对振型增量进行展开．针对模态截断问题，本文又提出了一种“模态展开＋幂级数民开”的混合展开法，这种展开法的收敛性好，收敛程度易于估计，实用方便．

INFLUENCE OF SMALL CHANGES OF SUPPORT LOCATION ON VIBRATION MODE SHAPES

It is of importance to study the influence of small changes of support location on vibration mode shapes because of its necessary role in structural optimization and model correction using the generalized variational principle, the first-order purturbation equations of vibration eigenproblem are derived. In order to solve these equations two difficulties are dealt with, one is associated with the incompleteness of the unperturbed eigenfunctions, the other the truncation of the higher modes. A hybrid expansion method, "modal expansion power series", is presented to solve the perturbed equations, with the advantage of fast convergence and being easy to estimate its convergence.