二次和一般三次非线性弹性系统1/2阶亚谐共振之比较

Comparison Between 1 / 2-Order Subharmonic Resonances of Elastic Systems with Quadratic and General Cubic Nonlinearities

具有二次非线性弹性振动系统1/2阶亚谐共振在两个分叉频率之间有一不稳定域.研究表明,加入三次非线性弹性可以抑制不稳定性,而在一定频率范围出现跳跃现象,且两种系统发生1/2阶亚谐共振的条件在一阶近似下相同.

There is an unstable domain between two bifurcate frequencies in 1/2-order subharmonic resonance of elastic system with quatratic nonlinearity.Investigation presented in this paper shows that the unstability could be suppressed by adding cubic nonlinear elasticity.However, jump phenomena would occur when the exciting frequency falls into certain domain.It is also shown that the conditions of appearing of 1/2-order subharmonic resonance are the same for these two systems in the sense of the first-order approximation.