Abstract
Infrastructures are deteriorating and billions of dollars are spent to rehabilitate them. Civil structures usually comprise of pavements and bridge decks (plates), pipelines (cylinders), and structural members having, say, I, L, etc. cross sections. The deterioration of these structures causes flaws arising from factors such as the severity of the weather, aging, corrosion, fatigue cracks, etc... The flaws degrade the stiffness (material properties) of a structure and severe conditions eventually can result in a catastrophic failure. Thus, the detection and characterization of the flaws is important in evaluating and monitoring the integrity of existing structures and determining the viability of their continued use or a change in use. Therefore, it is necessary to employ a reliable and effective, quantitative nondestructive evaluation (QNDE) to characterize the mechanical properties and identify defects in the structures. Ultrasonic waves provide such a technique but a knowledge of guided elastic waves is required. Considerable information is available for waves in plates and cylinders but very little work has been reported in the literature on the waves in thin-walled, structural members.
In this paper, a semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members. Common structural members are considered as an assemblage of thin plates. The members are assumed to be infinitely long in the longitudinal (axial) direction. 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 equationis obtained as a standard algebraic eigenvalue problem. The accuracy of the proposed method is demonstrated by comparing the results with analytical solutions. Detailed numerical results are presented for an I shaped cross section.
