2/1 SUPERHARMONIC SOLUTION OF A CIRCULAR PLATE WITH QUADRATIC NONLINEAR VISCOELASTICITY

The nonlinear dynamic equation of a circular plate under a harmonic force is derived under the consideration of the viscoelastic effects. A superimposing iteration harmonic balance method (SIHB) is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system, which is described as a second order ordinary differential equation, can be expressed to be a basic differential equation with basic harmonics and incremental differential equation with bifurcate harmonics. The 2/1 superharmonic solution for a circular plate is investigated by the superimposing iteration harmonic balance method. The results of the superimposing iteration harmonic balance method are in good agreement with those of numerical integration. In addition, the asymptotical stability of the 2/1 superharmonic oscillations is examined.