Chaotic motion of viscoelastic beams with geometric and physical nonlinearities

The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric nonlinearity is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro-differential equation. The equations further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam. The results show that chaos occurs in the motion of the beam.