High-frequency Dynamic Response Prediction And Load Identificationof Uncertain Structures Based On Interval Technique

Statistical energy analysis(SEA) is an effective method to deal with the high-frequency sound and vibration problem, and the dynamic response prediction and load identification based on SEA are two different research fields that have been developed and applied widely. The damping loss factor and coupling loss factor are the pretty important parameters in SEA, and it is very difficult to accurately measure these parameters. This uncertain factor can lead to the deviation between the nominal design value and real dynamic characteristic, so the accuracy of the results of dynamic response prediction and load identification is reduced. In the SEA framework, this paper uses the interval analysis method to study the dynamic response prediction and load identification of uncertain structures. The specific contents are as follows:The effect of the measurement errors of SEA parameters on the predicted steady-state response is investigated, and the steady-state response errors caused by the measurement errors of parameters are estimated via the interval perturbation method. The power balance equations of steady-state SEA are established by the dissipated power of subsystems and transmitted power between different subsystems. Interval variables are utilized to represent the damping loss factors and coupling loss factors with the measurement errors, and then these parameter intervals are substituted into the steady-state power balance equations. The power balance equations with parameter intervals can be solved by the interval perturbation method, and the modal energy interval of each subsystem can finally be obtained. The lower bound and upper bound of the modal energy interval can well show the effect level of measurement errors of parameters on the predicted steady-state response, and the specific errors of steady-state response caused by the measurement errors of paremeters can be estimatd by the lower bound and upper bound of the modal energy interval. The effectiveness and feasibility of the presented interval approach are verified through the simulated study on a two-plate coupling system and a three-plate coupling system, and the results indicate that the measurement errors of SEA parameters have a large effect on the predicted steady-state response.The influence of the measurement errors of SEA parameters on the predicted transient response is studied, and the transient response errors caused by the measurement errors of parameters are estimated by using affine arithmetic. The two coupled subsystems are taken as the object of study, and the constant value of total energy of subsystem can be achieved by solving the transient power balance equations without considering the the measurement errors of parameters. The parameter intervals that represent the parameters with measurement errors are substituted into the constant value of total energy of subsystem, and then affine arithmetic is employed to gain the interval of total energy of subsystem. It should be noted that the interval of total energy of subsystem changed with time, and the lower bound and upper bound of the total energy interval can well show the effect level of the measurement errors of parameters on the predicted transient response, and the errors of transient response caused by the measurement errors of parameters are estimatd by the lower bound and upper bound of total energy interval.For the two different situations that are the conservative coupling and non-conservative coupling, the influence of the measurement errors of SEA parameters on the high-frequency load identification is investigated. At the same time, the power errors of loads caused by the measurement errors of parameters are estimated via the interval perturbation method. The parameter intervals and total energy intervals are substituted into the conservative power balance equations, and the interval perturbation method can be utilized to obtain the power intervals of loads. Moreover, the non-conservative power balance equations are created based on the new dissipated power of subsystems and power flow between different subsystems, and the additional damping loss factors caused by the coupling damping are also written as the interval variables. The non-conservative power balance equations with parameter intervals can be solved to acquire the power intervals of loads. A plate-shell assembled structure that is similar to the rocket fairing is used as example to compare the load identification results with considering the measurement errors of SEA parameters and that without considering the measurement errors of SEA parameters.The sensitivity analysis of SEA models based on an interval technique is presented. For the conservative coupling system, the damping loss factors and coupling loss factors are treated as the design parameters, while the modal energy of each subsystem is considered as the decision-making target. The decision-making target interval and the boundary influence interval are defined by the interval method, and the ratio between the difference of the lower bound and upper bound of boundary influence interval and the difference of the lower bound and upper bound of decision-making target interval is called the independent influence factor. All the independent influence factors constitute the sensitivity factor matrix, and the sensitivity level of decision-making target to design parameter can be shown in the sensitivity factor matrix. For the non-conservative coupling system, the additional damping loss factors caused by the coupling damping are also taken as the design parameters. In addition, the possibility that the sound power is regarded as the decision-making target is discussed.