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Bending Waves in a Beam

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

Abstract

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.

     

Keywords

Timoshenko Beam Beam Cross Section Transverse Deflection Homogeneous Beam Element Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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