Application of the spectral finite element method to turbulent boundary layer induced vibration of plates

The spectral finite element method and equally the dynamic stiffness method use exponential functions as basis functions. Thus it is possible to find exact solutions to the homogeneous equations of motion for simple rod, beam, plate and shell structures. Normally, this restricts the analysis to elements where the excitation is at the element ends. This study removes the restriction for distributed excitation, that in particular has an exponential spatial dependence, by the inclusion of the particular solution in the set of basis functions. These elementary solutions, in turn, build up the solution for an arbitrary homogeneous random excitation. A numerical implementation for the vibration of a plate, excited by a turbulent boundary layer flow, is presented. The results compare favourably with results from conventional modal analysis.

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