Nontrivial periodic solutions of an \(n\)-dimensional differential system and its application
Summary: Two criteria are constructed to guarantee the existence of periodic solutions for a second-order \(n\)-dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system's damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of the nonlinear term's coefficient and the parametric excitation term, which generalizes and improves the corresponding achievements given in the known literature.
scientific article; zbMATH DE number 6306057