Bending Waves in a Beam

  • B. F. Shorr
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


Studying the wave propagation in a beam, we take the following usual assumptions:
  1. i)

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

  2. ii)

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

  3. iii)

    The longitudinal ε x and shear ε xy = ε xy strains are small compared with unity;

  4. 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.



Timoshenko Beam Beam Cross Section Transverse Deflection Homogeneous Beam Element Velocity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • B. F. Shorr
    • 1
  1. 1.Central Institute of AviationMotors (CIAM)MoscowRussian Federation

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