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Ebook Fundementals of mechanical vibration (2nd edition): Part 2

(BQ) Part 2 book "Fundementals of mechanical vibration" has contents: Forced vibrations of Multi-Degree-of-freedom systems, vibration control, vibrations of continuous systems, finite-element method, nonlinear vibrations. | chapter ystems 7.1 Introduction The forced response of a linear multi-degree-of-freedom system as for a linear one-degree-of-freedom system is the sum of a homogeneous solution and a particular solution. The homogeneous solution depends on system properties while the particular solution is the response due to the particular form of the excitation. The free-vibration response is often ignored for a system whose long-term behavior is important such as a system subject to a periodic excitation. The free-vibration solution is important for systems in which the short-term behavior is important such as a system subject to a shock excitation. Several methods are available to determine the forced response of a multi-degree-of-freedom system. The method of undetermined coefficients can be applied to any system subject to a periodic excitation. However because of algebraic complexity its usefulness is restricted to systems with only a few degrees of freedom. The Laplace transform method can be applied to determine system properties but Its usefulness is limited because its application requires the solution of a system of simultaneous equations whose coefficients are functions of the transform variable. Both the method of undetermined coefficients and the Laplace transform method can be used to determine the forced response of a system with a general damping matrix. The most useful method for determining the forced-vibrations response of a linear multi-degree-of-freedom system is modal analysis which is based on using toe principal coordinates to uncouple the differential equations governing the mo-ton of an undamped or proportionally damped system. The uncoupled differential equations are solved by the standard techniques for solution of ordinary differential equations. A more general form of modal analysis involving complex algebra is developed for systems with a general damping matrix. Often the differential equations cannot be solved in closed form. Modal analysis Catl .