Analysis of bar's free vibration with considering lateral shear strain by forced displacement method - numerical solution

Abstract

ABSTRACT

The equation of free vibration of the bar is an eigenvalue equation, with the right side equals zero, to solve this equation domestic and foreign authors have used the traditional methods to bring the coefficient matrix of the equation of free vibration of the bar to diagonal or band matrix form, strip along the main diagonal by different algorithms, such as Jacobi algorithm [4], LR [4], [5], QR[5], subspace [5].... is very complicated, to get the product of that term gives us the characteristic polynomial equation to determine the eigenvalues. Therefore, to simplify in solving the problems in this paper, the author uses a new method in [2], [3] "Forced displacement method" to find eigenvalues and eigenvectors of problems according to numerical solutions.

Keywords: forced displacement; oscillate; eigenvalues, eigenvectors.