Nonlinear dynamics analysis of a cracked beam subjected to combined harmonic excitations by precise integration method

A simply supported beam with a breathing crack subjected to two external harmonic excitations is shown in Figure 1. The beam is uniformly divided into n elements. The left support as Node-1, and the nodes are numbered from left to right consecutively (each element has two nodes). The beam subjected to two external harmonic excitations, denoted by f1cosω1t and f2cosω2t, respectively.