Abstract
Based on one-dimensional theory of elastodynamics, the vibration and wave propagation in members of a framed structure are analyzed by the recently developed method of reverberation-ray matrix. Unidirectional traveling wave solutions for axial, torsional, and two flexural waves in six modes that are reverberated in structural members through repeated reflection and multiple scattering by joints of the structure are expressed in matrix form with two sets of unknown amplitude coefficients. From joint coupling equations and from compatibility conditions of displacements in dual coordinates of each member, the two sets of unknowns are determined in terms of a reverberation-ray matrix for given source excitations at joints. Free and forced wave motion in steady-state response can all be evaluated from the matrix solutions, and transient response is determined in one more step of Fourier inverse transform. The method is particularly effective to determine the early time transient response through Neumann series expansion of the inverse transformed solution with a special numerical algorithm.
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