Nonlinear Vibration, Bifurcation and Chaos of Viscoelastic Cracked Plates

摘要

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.