The periodic property of Gaylord’s oscillator with a non-perturbative method

Abstract

AbstractThe Gaylord's oscillator is a vibrating of a uniform rigid rod without slipping on a rigid circular surface with a definite radius. The dominant equation of motion was the outcome of a strongly nonlinear pendulum equation of the second order. The run article is interested in obtaining the frequency–amplitude equation and the approximate solution of Gaylord's oscillator by a simpler approach. The frequency–amplitude relationship is derived in terms of the Bessel function. Quasi-exact periodic solution derived depends on a non-perturbative approach. The validation of the analytical solution is made through the comparison with the numerical solution which shows excellent approval. Finally, the non-perturbative method is of high accuracy besides simplicity if it is compared with the other perturbative techniques in analyzing the behavior of oscillators with strong nonlinearities.