An analytical solution based on modal decomposition is presented to investigate Lamb wave scattering at plate end. Take boundary condition into biorthogonality relation, a matrix equation is established with all matrix elements have analytical expressions. The scattering feature is then expressed in matrix form, named as reflection matrix, which has explicit expression composed of those matrixes. Calculation examples have be implemented when antisymmetric modes are reflected. Scattering coefficients are figured out in a range when frequency-thickness product vary from 0 to 8kHzm, to prove the calculation efficiency. The calculation precision is very close to the least square method based on model discretization.
Lamb wave scattering at a rectangular hole are investigated by using modal decomposition method. Take advantage of the biorthogonality relation, the scattering matrix is derived in an explicit form. The efficacy of the method is illustrated by numerical examples. The results are compared with those gotten from numerical models and the calculation accuracy is analyzed.
Based on modal decomposition, an explicit formula for edge resonance solution in circular cylinders is presented here. Using the bi-orthogonality relation and singular value decomposition, the method could get the exact edge resonance frequency of circular cylinders. The calculation results are compared with numerical simulation results for verification.
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