The Non-linear Vibration Analysis of the Plate Partialy Immersed in Liquid
|Keywords||added-mass sigularity function average method non-linear vibration|
In this paper, we analyse a thin plate partiarlly immersed in liquid with two short boundaries simply supported. The velocity of the plate is the same with the axis direction. There is an air knife give pressure in the middle of the plate.We calculate the nature frequencies and modes of the plate. The non-linear vibration character of the system has also been analysed.First of all, we establish the wave equation of the board and the Laplace function in the liquid. With the help of the boundary conditions of the plate and liquid, we can solve the Laplace function with separate variable method. So the problem of the force to the plate by the liquid is solved. Then we can treat the problem as a plate with different densities. By use sigularity function method, we can get the general solution. There are four boundary conditions at the interface of the liquid and two at the boundaries of the edge which are simply supported. The displacement, corner, moment and shearing force are continuous. The displacement and moment are equal to zero at the S-S boundary. So, we can get the eigenvalue function. To solve the function, we can get the frequencies and modes of the system. The results fit well with the results get by Ansys.And then, we established the non-liner wave equation. As the frequencies are very low, we take three modes into account. By using Galerkin method, differential equations in the coupling mode coordinate are gained. Here we use average method that making the non-antonomous system became autonomous system. To solve the functions, we can draw the frequency-response curves. Then we analyse the parameter vibration of the system. We study the influences of excitation displacement amplitude, damping and speed of the vibration characteristic. We also determine the stability of the cycle solutions.The study indicates that:the added mass decrease the frequencies of the plate when it is immersed into liquid; from the curves of the broad with and without air knife, we can see that the air knife increased the frequencies as the liner parameter of the air knife is just like a spring which increase the D of the plate. By diminish the excitation displacement amplitude or by increase damping or by diminish the speed, we can reduce the response amplitude and the range of interval resonance. The phenomenon is the same with the numerical solutions.