Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam

摘要: In this paper, a Fourier expansion-based differential quadrature (FDQ) method is developed to analyze numerically the transverse nonlinear vibrations of an axially accelerating viscoelastic beam. The partial governing equation discretized in space region and time domain using FDQ Runge–Kutta–Fehlberg methods, respectively. accuracy proposed represented by two numerical examples. dynamical behaviors, such as bifurcations chaotic motions beam, are investigated bifurcation diagrams, Lyapunov exponents, Poincare maps, three-dimensional phase portraits. diagrams for in-plane responses mean axial velocity, amplitude velocity fluctuation, frequency fluctuation are, respectively, presented when other parameters fixed. exponents calculated further identify existence periodic conclusion drawn from simulation results that simple efficient analysis dynamics