Kang B.

An alternative analysis technique, which does not require eigensolutions as a priori, for the dynamic response solutions of one-dimensional distributed parameter systems with general boundary conditions is presented. The technique is based on that the dynamic displacement of any point in a waveguard can be determined by superimposing the amplitudes of the constituent waves, propagating and non-propagating, in the waveguard. The spatial amplitude variations of individual waves are represented by the field transfer matrix and the distortions of the wave amplitudes at point discontinuities due to constraints or boundaries are described by the wave reflection and transmission matrices. Combining these matrices in a progressive manner along the waveguard using the concepts of generalized wave reflection and transmission matrices leads to the exact transfer function of a complex distributed parameter system subjected to an externally applied force. The transient response solution can be obtained through the numerical Laplace inversion using the fixed Talbot method. The exact frequency response solution which includes infinite normal modes of the system can be obtained in terms of the complex frequency response function from the system’s transfer function. This wave-based analysis technique is applicable to any one-dimensional viscoelastic structures (strings, axial rods, torsional bar, and beams), in particular systems with multiple point discontinuities such as viscoelastic supports, attached mass, and geometric/property changes. In this paper, the proposed approach is applied to the flexural vibration analysis of a classical Euler-Bernoulli beam with multiple spans to demonstrate its systematic and recursive formulation technique.