General Solution of Linear Vibration Systems

Abstract

As shown in the previous chapter each finite dimensional linear (or linearized) dynamical mechanical system can be represented in state space notation by a set of n first order differential equations

$$$$

(3.1)

where x is the n × 1 state vector, A the n × n system matrix, and f the n × 1 forcing vector. In this chapter the general solution of (3.1) and its properties are briefly reviewed in the case of a time-invariant system matrix A(t) = A = constant.