Dynamic Stability Of Thin-Walled Structure

The dynamic stability of thin-walled structure subjected to periodically alternating axial force is discussed in this paper. A system of second-order differential equations with periodic coefficients of the Mathieu type describes dynamic stability of thin-walled structure without damping.And a Mathieu-Hill type equation is used to thin-walled structure with damping.To solve the problem the finite element method is applied which can greatly reduce the process of simplification.Using MATLAB package, a computer program was developed to calculate the regions of dynamic instability without damping & with damping. Examples are given in this paper. The MATLAB computer program resolves the commonness of dynamic stability of thin- walled structure. And by using a diagram of dynamic instability of thin-wafled structure, one can determine whether or not dynamic stability is really happened, when frequence, static part and dynamic part of exciting force is known. One can also infer the critical exciting force of dynamic stability from the diagram when both static and dynamic characteristics of thin-walled structure are given.Compared with dynamic stability of thin-walled structure with damping and without damping, a conclusion is made that since regions of dynamic instability is continuous increasing damping is not a good way to hold back the infinitely rise of vibration swing. What抯 more, dynamic stability is likely to occur even if frequence of exciting force is less than or more than the natural frequence.Analysing sympathetic vibration and vibration caused by the dynamic instability ,the paper points out that they are two different forms of vibration. And should not be mixed up.The paper puts forward that it more difficult to avoid dynamic instability of thin- walled structure than to avoid sympathetic vibration.Common vibration absorption method has little use to dynamic instability, so much as to prick up the vibration. A more effective method is wanted to avoid the dynamic instability of thin-walled structure.