Combined parametrical transverse and in-plane harmonic response of an inclined stretched string

In this paper, a two-point boundary value problem for an integrodifferential equation is studied. This equation describes the dynamics of an inclined stretched string suspended between a fixed support and a vibrating support. Due to the inclination, the string will vibrate under combined parametrical and transversal excitation. The attention will be focused on time-periodic solutions consisting of one mode (semi-trivial solution) generated by transverse (external) excitation and two modes (non-trivial solution) generated by combined parametrical and transverse excitation.