Approximate Limit Cycles for Vortex-Induced Vibration of a Sprung Cylinder

Abstract

The homotopy analysis method (HAM) is an analytical approximate method to solve nonlinear problems, which is employed to give series solutions of a sprung cylinder's vortex-induced vibration. The wake flow is modeled by a classical van der Pol oscillation coupled with a cylinder by an acceleration term. The frequency and initial conditions of all possible limit cycles are obtained as Maclaurin series of an embedding parameter. A series of algebraic equations for eliminating secular terms are derived and solved to obtain the priori unknown coefficients, such as the initial conditions and frequency. The validity and efficiency of the HAM are conducted by numerical integration solutions and the harmonic balance method (HBM). The influence of fluid velocity on the frequencies and amplitudes of the limit cycles are obtained very accurately compared with numerical ones.