中文摘要：

振动筛系统是一类非光滑度很高的多参数非线性动力系统，传统的分岔准则无法直接适用，这里采用了新的不依赖于特征值计算的显式分岔临界准则，以实现振动筛系统双Hopf分岔的反控制．首先，根据系统的运动方程得到Poincar6映射在不动点处的线性化矩阵；然后，对系统施加线性反馈控制器，得到受控后的Poincar6映射，根据分岔临界准则求得双Hopf分岔的显式临界条件；最后，通过模态叠加法对两类系统分别进行了数值模拟．结果显示，在相同的系统参数下线性反馈控制器通过调整控制参数，可以有效地实现双Hopf分岔的反控制．双Hopf分岔可以提高一些振动机械的工作效率，具有一定的实际意义．

英文摘要：

The vibrating griddle system is a kind of nonlinear multi-parameter dynamical system with high non-smoothness,and traditional bifurcation criterion can＇t be applied directly. Therefore, a new explicit bifurcation criterion independent on eigenvalue calculation was adopted to achieve the anti-control of double Hopf bifurcation for vibrating griddle system. Firstly, the Poincare mapping at the fixed point was obtained according to the motion equation of the system. Then, a linear feedback controller was applied to the system to obtain the controlled Poincare mapping,and the explicit critical condition of double Hopf bifurcation was obtained according to the bifurcation critical criterion. Finally, numerical simulation of the two types of systems was carried out by the modal superposition method. The results show that the linear feedback controller can effectively achieve the anti-control of double Hopf bifurcation by adjusting the control parameters under the same system parameters. Double Hopf bifurcation can improve the working efficiency of some vibration machinery, so it has certain practical significance.