ANALYSIS ON THE NONLINEAR FREE VIBRATION AND INTERNAL RESONANCE OF AXIALLY MOVING PLATES IMMERSED IN LIQUID
Zhang Yu-Fei 1，Wang Yan-Qing 2， Wen Bang-Chun1
1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;
2. Department of Mechanics, Northeastern University, Shenyang 110819, China;
3. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China
A vertically moving rectangular plate immersed in liquid is investigated. Based on the classical thin plate theory and von Kámán nonlinear geometrical relationships, the nonlinear vibrational differential equations of the fluid-structure coupling system are derived. It is assumed that the liquid is incompressible, inviscid and irrotational. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The system is solved by applying directly the method of multiple scales to the nonlinear partial-differential equations. Based on the solvable condition, the nonlinear frequency of the system is obtained. The 1:1 and 1:3 internal resonances of moving plate-fluid system are investigated. The effects of system parameters on the nonlinear dynamic characteristics of the fluid-structure coupling system are discussed in detail.
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