Transient response of Timoshenko beams with discontinuities of cross-section

Flexural waves in beams with geometrical and material longitudinal discontinuities

Flexural wave response and failure of stepped beams

There has been little experimental work on flexural wave propagation in general and on flexural wave propagation in beams with discontinuities of cross section in particular. Experimental data are obtained for various test beams subjected to eccentric longitudinal impact. The bending strain versus time results are presented for several positions along a uniform beam and finite beams (of circular cross section) with discontinuities of cross section. Bending strain histories are recorded at several positions before and after the discontinuity. The effect of reflections on the propagated flexural wave is illustrated. The dispersion of the traveling flexural wave caused several alternating peaks within the duration of the original positive input pulse. The importance of investigating discontinuities of cross section in structures subjected to impact loading is clearly manifested.

Experimental investigation of transient flexural waves in beams with discontinuities of cross section

An investigation was carried out to determine the transient response of finite beams with discontinuities of cross section subiected to eccentric longitudinal impact. Experiments were performed on several stepped beams with increased and reduced cross section and with various end conditions.
 The analysis was based on the Timoshenko beam theory which takes into account the effects of shear deformation and rotatory inertia. The governing equations were solved as a system of two second order hyperbolic partial differential equations. The numerical solution was obtained by the method of characteristics and theoretical predictions were in excellent agreement with experimental observations at several monitoring positions along the various test beams.
 The agreement between theoretical and experimental results verified the adequacy of the Timoshenko theory and its numerical solution for describing the flexural wave propagation in beams with discontinuities of cross section.
 The effect of the discontinuity of beam cross section on the bending moment time distribution showed the importance of reflections in estimating the level of stresses and strains in structural elements when subjected to transient dynamic loading. The computer program developed in this work can be used to obtain numerical solutions for. a wide range of flexural wave propagation problems in beams with discontinuities of cross section with various end conditions and loading configurations.

M.M.M. Al-Mousawi

Papers

Transient flexural wave propagation in beams with discontinuities of cross section