Wave scattering approach to power flow in frame structures and piping networks

Date of Completion

January 2000


Engineering, Civil|Engineering, Mechanical|Physics, Acoustics




A general matrix method is presented for the analysis of power flow in two- and three-dimensional frames using a wave scattering approach. Axial, torsional, and flexural wave modes are included. Since the method is intended to be used for mid and high frequency analysis, shear deformation and rotary inertia are included in the flexural wave modes. A general formulation is presented to determine wave scattering at structural junctions and boundaries. Although the finite element method can be used to calculate power flow, a large number of elements is required at mid and high frequencies to obtain accurate results. In the current method, exact wave mode expressions are used and therefore only one “element” is required for each structural member at any frequency. Power flow results using the wave scattering approach are compared to the conventional finite element method for two- and three-dimensional frames. ^ The method is extended to analyze power flow in piping networks with steady fluid flow. Currently there is no accurate and efficient method for performing this type of analysis and the wave scattering method provides an effective approach. The effect of the fluid flow is introduced through the flexural equations of motion for a pipe. With the exception of the wave mode expressions themselves which are directly influenced by the fluid flow, the matrix formulation is essentially the same as for frames without fluid. The results from the wave scattering method with fluid flow are compared to those from an exact analysis of a simply supported beam for verification. Finally, a piping network was analyzed with and without fluid flow to observe the effects of the flow on the system. ^