Guided waves in thin-walled structural members

A semi-analytical finite element (SAFE) formulation is proposed to study th e wave propagation characteristics of thin-walled members with an infinite length in the longitudinal (axial) direction. Common structural members are considered as an assemblage of thin plates. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small s o that the plane-stress assumption is valid. Employing a finite element mod eling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approxim ated by dividing the plates into several line (one-dimensional) segments an d representing the generalized displacement distribution through the segmen t by polynomial interpolation functions. By applying Hamilton's principle, the dispersion equation is obtained as a standard,algebraic eigenvalue prob lem. The reasonably good accuracy of the method is demonstrated for the low est modes by comparing, where feasible, the results with analytical solutio ns. To demonstrate the method's versatility, frequency spectra are also pre sented for I and L shaped cross sections.