Guided waves in thin-walled structural members

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Rogers, John B. C.
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Many common structural members can be thought of as an assemblage of thin plates. For example, an I shaped cross-section can be made from three or five thin plates and an angle can be thought of as two thin: plates whose sides are rigidly attached at an angle, and so on. In this study a multi-purpose computer program was developed, based on a Rayleigh-Ritz (RR) type stiffness approximation, to investigate the wave propagation in infinitely long thin-walled members and the free vibration of thin-walled members that are simply sup orted at their ends. Also, wave propagation characteristics of these members where studied. To model the behaviour of these types of structural members, using a finite element methodology, an element that closely models the behaviour of a thin plate was created. There are two uncoupled motions of a homogeneous thin plate having material symmetry about its middle surface; one corresponds to inplane motion and the other to bending. Previous studies used a three node parabolic element to model the inplane motion of the plate. In the present work, the three node inplane element and a two node beam element were used to generate an element which models both the inplane and bending motions of a thin plate. The program was checked for accuracy against another approximate solutions as well as analytical solutions. The Rayleigh-Ritz approximation proved to be effective in calculating the wave dispersion characteristics (wavenumber and modeshapes for a given frequency) of thin-walled, infinitely long members as well as the characteristic frequencies of vibration of simply supported thin-walled structural members.