Bending Waves in a Beam

Abstract

Studying the wave propagation in a beam, we take the following usual assumptions:

• i) The beam possesses the symmetry plane xy, with x the axis of the beam, and transverse deflections y(x,t) within this plane;

• ii) The material of the beam is elastic and homogeneous with density p, Young’s E and shear G module;

• iii) The longitudinal ε _x and shear ε _xy = ε _xy strains are small compared with unity;

• iv) The square of the deformed axis slope $\psi = \partial y/\partial x$ is small compared with unity, then $\sin \psi \approx \psi ,\cos \psi \approx 1$. At first, the cross-sectional area A and the moment of inertia of the beam cross section J are assumed constant.