Mechanical vibration analysis and computation

Abstract

Fundamental concepts frequency response of linear systems general response properties matrix analysis natural frequencies and mode shapes singular and defective matrices numerical methods for modal analysis response functions application of response functions - Fourier transforms discrete response calculations systems with symmetric matrices - Langrange's equations continuous systems - Rayleigh's method parametric and nonlinear effects - methods for finding the forced response of weakly-nonlinear systems - Galerkin's method, Ritz's method, Krylov and Bogoliubov's method, comparison between the methods of Galerkin and Krylov-Bogoliubov for steady-state vibrations. Appendices: logical flow diagrams - upper Hessenberg form of a real unsymmetric matrix A(N,N) using Gaussian elimination with interchanges, one iteration of the QR transform, eigenvalues of a real matrix A(N,N) by using the QR transform of the previous appendix, determinant of an upper-Hessenberg matrix by Hyman's method, eigenvectors of a real matrix A(N,N) whose eigenvalues are known, inverse of a complex matrix, one Ruge-Kutta 4th order step.