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Vibration of beams

If a deflection exists in a beam in the absence of external force, the elastic force will cause an acceleration in the vertical direction. From Eq. (F.18), using Newton s second law, the equation of motion of the beam is [Pg.370]

At the free end, z- L, the vertical force V and the torque M vanish. The boundary conditions are [Pg.371]

By going through simple algebra (we leave it as an exereise for the reader), the vibration frequency is found to be determined by the equation [Pg.372]

The lowest resonance frequency is determined by the lowest solution of Eq. (F.31), which is kLr 1.875. Substituting into Eq. (F.27), the frequency is (see Landau and Lifshitz, 1986, p. 102)  [Pg.372]

CJ Nederveen, FR SchwarzL Corrections for shear and rotatory inertia on flexural vibrations of beams. Br J Appl Phys 15 323, 1964. [Pg.865]

In order to examine the influence of shear deformation on the free vibrations of beams in the... [Pg.1604]

Forced Vibrations or Beam of Hollow Rectangular Cross Section Under Biaxial Bending In order to examine the influence of shear deformation on the free vibrations of beams in the geometrically nonlinear range, a clamped beam... [Pg.1606]

Free Vibrations of Beam of Thin-Walled l-Section Without STMDE... [Pg.1615]

Fig. 11 Time history of the twisting moment at the left end of the beam of application section Free Vibrations of Beam of Thin-Walled I-Section Without STMDE, for the case of initial twisting rotations dxa x)... Fig. 11 Time history of the twisting moment at the left end of the beam of application section Free Vibrations of Beam of Thin-Walled I-Section Without STMDE, for the case of initial twisting rotations dxa x)...
Fig. 16 Axial load F -torsional fundamental natural frequency cOf relation of Eq. 50 (Mohri et al. 2004) along with pairs of values (cty, N) obtained for application section Free Vibrations of Beam of Thin-walled I-Section with STMDE (AEM)... Fig. 16 Axial load F -torsional fundamental natural frequency cOf relation of Eq. 50 (Mohri et al. 2004) along with pairs of values (cty, N) obtained for application section Free Vibrations of Beam of Thin-walled I-Section with STMDE (AEM)...
Sapountzakis EJ, Dourakopoulos JA (2009c) Shear deformation effect in flexural-torsional vibrations of beams by BEM. Acta Mech 203 197-221 Sapountzakis EJ, Tsipiras VJ (2010a) Nonlinear nonuniform torsional vibrations of bars by the boundary element method. J Sound Vib 329 1853-1874... [Pg.1636]

Vibrations of Beams for Seismic Response Estimation, Fig. 1 Reference system of the beam model... [Pg.3880]

See other pages where Vibration of beams is mentioned: [Pg.370]    [Pg.789]    [Pg.1600]    [Pg.1615]    [Pg.1621]    [Pg.1622]    [Pg.1624]    [Pg.1636]    [Pg.3879]    [Pg.3879]    [Pg.3880]    [Pg.3881]    [Pg.3882]    [Pg.3882]    [Pg.3883]    [Pg.3884]    [Pg.3885]    [Pg.3885]    [Pg.3886]    [Pg.3887]    [Pg.3888]    [Pg.3889]    [Pg.3890]    [Pg.3891]    [Pg.3891]    [Pg.3891]    [Pg.3963]   


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