Nonlinear vibration, bifurcation and chaos of viscoelastic cracked plates

The paper aims at studying the nonlinear vibration, bifurcation and chaos of viscoelastic cracked plates. Based on the Von Karman plate: theory and the isotropic linear viscoelasticity constitutive theory, a nonlinear integral-partial differential equation of motion is established for a rectangular viscoelastic plate which has an all-over part-through crack. Using the method of separation of variables and the Galerkin method, the equation of motion is transferred into an ordinary differential equation. Numerical simulation is given using a rectangular viscoelastic cracked plate with movable simply-supported boundary conditions at all edges is used as an example. The effects of the depth and position of the crack and the viscoelastic material parameters on the nonlinear amplitude-frequency response, bifurcation and chaos are discussed in detail.