Analysis Of Nonlinear Vibration Of Rectangular Liquid-elastic Shell Coupled System

In practical engineering, there are many liquid-solid coupled problems, which are of great applied value. By now, many Chinese and foreign scholars have done lots of studies about this kind of problems. Linear theory developed in good time. In addition, the actions of the non-linear factors in the liquid-solid coupled system are beyond ignoring. There are many papers reporting on non-linear vibration of the liquid-solid coupled system, but less about the rectangular liquid-elastic shells coupled system.The paper is on the phenomenon of low-frequency and large-amplitude gravity waves generated by high-frequency excitation in coupled liquid and elastic shell system. According to the appearance of the gravity waves and the data of the waves and the parameter of the system mode, the reasons and the features of the gravity waves as well as the influence of the exciting force to the gravity waves are researched by means of theoretical numerical methods.1. According to hydromechanical basal equations and the boundary conditonns of the system, a set of differential equations describing the liquid in coupled system are obtained. Then solve the non-dimentional differential equations by means of separating variables, getting the non-dimentional velocity potential of the liquid.2. Based on the experimental phenomenon that the low-frequency and large-amplitude gravity waves may be generated by the high-frequency external excitation in the liquid-elastic shell coupled system, expand the velocity potential,free surface of the liquid and the displacement of the shell in linear mode function. Expand the kinetic energy and the potential energy of the system with a dynamic surface in non-linear form. At last, a set of discrete non-linear vibrational equations are constructed according to variational principle.3. Using the simulink model in matlab application, the numerical value emulation model of the four degrees of freedom, strong coupled and strong non-linear equations can be set up. By means of the Runge-Kutta method, the mumerical solution to the non-linear vibrational equation is carried out. The time history curves and amplitude-requency curves of coupled system are obtained, which is consistent with the experimental results.4. According to the umerical analysis, the relations between the changed amplitude of the gravity waves and altered frequency and amplitude of the exterior exciting force are found which could explain the precondition of the emergence of the waves well. The same gravity wave, generated at the different frequency needs the different critical exterior exciting force. The citical exciting force curves have a good explaination to the conditions of generation of the gravity waves. Under the given amplitude exciting force, the amplitude-frequency curves of the two gravity waves and the shell of the system are obtained by changing the frequency of the exciting force, which describe the character of the non-linear resonance of the rectangular liquid-elastic shell coupled system visually.According to Lagrange equation, a set of non-linear equations for four degrees of freedom coupled modes are construct. By mumerical analisis, the gravity waves generated by the high-frequency external excitation in the liquid-elastic shell coupled system were ulteriorly researched, the reasons of the appearance of the gravity waves were well explained. So it shows that the set of non-linear vibration equations of the rectangular liquid-elastic shell coupled system can describe the non-linear vibration character of the system very well.