Guided Waves in Thin-Walled Structural Members

Abstract

A semi-analytical finite element (SAFE) formulation is proposed to study the 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 so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equation is obtained as a standard algebraic eigenvalue problem. The reasonably good accuracy of the method is demonstrated for the lowest modes by comparing, where feasible, the results with analytical solutions. To demonstrate the method’s versatility, frequency spectra are also presented for I and L shaped cross sections.