Continuous systems with odd nonlinearities: A general solution procedure
Summary: We consider a general equation of motion with odd nonlinearities. The nonlinearities of third and fifth order are represented in the form of arbitrary operators. The equation of motion, in its general form, can model a class of partial differential equations describing vibrations of continuous systems. Approximate analytical solutions are sought using the method of multiple scales and a perturbation technique. Forced vibrations with viscous damping are considered, and frequency-response relation is derived in its most general form. Finally, we give an application to a specific problem.
scientific article; zbMATH DE number 1229962