Abstract:
The analysis of the dynamic behaviour of a structure is generally approached through the use of techniques such as finite element analysis or statistical energy analysis (SEA). The computational expense of a finite element model increases rapidly with frequency, due to the number of elements required to adequately represent the spatial variations in the response. The response also becomes increasingly sensitive to perturbations in the properties of the structure, rendering the use of such an approach questionable at higher frequencies. SEA adopts a simpUfied statistical description of the structure which is more appropriate at higher frequencies. However, at lower frequencies some of the statistical assumptions used in SEA can be unrealistic. In the mid-frequency range neither technique is entirely appropriate. The combination of the two techniques to address the mid-frequency problem is the subject of this thesis. A computationally efficient way of obtaining an energy flow model from a finite element model is described. A fixed interface component mode synthesis representation is adopted and expressions obtained for the input power and subsystem potential and kinetic energies. The frequency average response to broadband excitation is found by integrating the previous expressions analytically. A numerical example of three coupled plates is presented and implemented using finite element software written in Matlab. The finite element software is verified against experiment and against an exact wave solution. The use of a stochastic energy flow model is discussed and expressions derived for the mean and variance of the response. The problem of defining a reaUstic ensemble is considered and a new approach proposed in which various statistics of the local natural frequencies of a subsystem are specified. A stochastic energy flow model is then obtained by combining a Taylor series expansion of the global eigenvalue problem with a Monte Carlo simulation. A number of numerical examples are presented in which the response statistics obtained using the proposed technique are compared with those obtained using a full Monte Carlo simulation. The agreement is generally good. However, the proposed technique results in a significant reduction in computational expense.