Forced vibration of structural models with equal frequencies

Abstract

The purpose of this thesis is to present methods for analyzing and displacements and forces developed in structures that are subjected to an arbitrary dynamic loadings. Single-Degree of freedom systems are discussed and concept of dynamic load factor is introduced. The response equations of multidegree dynamic systems are formulated using matrix methods. A computer program utilizing the Jacobi method is presented which solves for the natural frequencies and mode shapes of the dynamic system. A Finite Difference technique is introduced which efficiently solves for maximum response and maximum force conditions. A computer program is utilized to augment the procedure. Finally, the response of a four degree of freedom system is considered in which two of the natural frequencies are numerically close.