Combined Parametrical and Transversal Excitation of a Stretched String in an Elastic Medium

In this paper we consider a two-point boundary alue problem for an integrodifferential equation. This equation can be considered as a nonlinearly perturbed telegraph equation including both parametrical and transversal excitation. The attention will be focused on time-periodic solutions consisting of two modes. The first mode is generated by parametrical excitation and the second one is generated by vertical (transversal) excitation. This interaction of two modes can occur for special combinations of values of two parameters in the equation For the study of time-periodic solutions the averaging method will be used and the stability of the time-periodic solutions will be analyzed in linear approximation.