Research On Repsonse Prediction Of Vibrating Structures Using Energy Method

Prediction of vibration response is an important subject in aerospace and otherfields. Recent development of society demands more functions of spacecrafts andthis makes engineering structures more and more complex and dynamicalparameters are more difficult to obtain. Meanwhile, increasing complexity bringsmore computation cost for FEM and other traditional method. Computation cost andparameter uncertainty are two main problems in prediction of structural vibration.Plenty of work focuses on the two problems. Based on energy density governingequations, energy flow method uses averaged energy as a variable to reducecomputation cost dramatically and provide more precise results. Energy flowmethod is now a popular solution for response prediction. This work providesanalytical solutions for energy density governing equations. Response prediction foruncertainty structures is also studied using energy flow method. Detailed works are:Numerical solutions of energy density governing equations are introduced. Energycharacteristic of a satellite structure under excitation of a flying wheel is studied byEnergy Finite Element Method. Taking boundary effect as energy reflection,analytical solutions of energy density governing equations are derived withdisplacement. And the analytical solutions are validated by numerical solutions.Energy mean free path is introduced to describe boundary effect of two-dimensionalstructures. Frequency integral is used to obtain energy response under randomexcitation.Further, for structures with probabilistic parameters, the expectation andstandard variance of energy density are expressed by the parameter standardvariance. The response interval is obtained under certain confidence probability.Introducing perturbation technique, new control equation sets of energy density foruncertain structures are obtained. For structures with Gauss parameters, probabilityand perturbation techniques are combined to derive the energy density expressedwith standard variances of the uncertain parameters. Response variances of theenergy density and the relative variance comparing the deterministic structures areobtained.For structures whose random model is unknown, maximum entropy principle isused to prediction energy response of vibrating structures using non-parametermodel. Random perturbation method and direct probability method are provided.According to the maximum entropy, deployment is carried with random perturbationand direct probability utilizes the formulation directly. Probability densities of theparameters are derived with the two methods and the energy responses are obtainedwith energy flow method. The mean responses and the variance to the normal responses are provided. The results indicate randomness must be considered for highfrequency vibration of complex structures.Finally, for structures with non-probabilistic parameters, fuzzy structuresmethod is introduce into energy flow method. Fuzzy structure method describescomplex structures with master structure that can be modeled precisely and fuzzystructures that lack of modeling information. The master structure is described byenergy flow method and the fuzzy structures are modeled by spring and masssystems. Energy flow of structures is obtained and simulations show that fuzzystructures influence the wave velocity and energy response through wave number.For prediction of structures with interval parameters, Taylor deployment is used toobtain the energy interval. Comparison with probability method shows that intervalmethod provides smaller response interval.