Dynamic Analysis of Modified Structural Systems

Abstract

A set of methods is developed to determine the changes in frequencies and mode shapes of a structure resulting from modifications of the structure. These modifications can involve an increase in the number of degrees of freedom of the system as well as changes in already existing entries in the mass and stiffness matrices of the model of the structure. Indeed, the modification may consist entirely of a refinement of the structural model. In the procedures used, each mode and frequency is treated separately without any need to know the other modes and frequencies. An exception is the case of multiple or close frequencies, where the whole set of equal or close eigenvalues and their eigenvectors must be treated together. Calculations are carried out by a perturbation analysis, which can be carried as far as desired in an automatic fashion. Repeated use of the same coefficient matrix in the perturbation scheme leads to considerable economy of computational effort. Light, tuned systems attached to a structure can be treated advantageously by the procedure developed, as shown in examples.