Structural Engineering and Mechanics

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Transverse vibrations of simply supported orthotropic rectangular plates with rectangular and circular cut-outs carrying an elastically mounted concentrated mass

  • Avalos, D.R. (Physics Department, School of Engineering, Universidad Nacional de Mar del Plata) ;
  • Larrondo, H.A. (Physics Department, School of Engineering, Universidad Nacional de Mar del Plata) ;
  • Laura, P.A.A. (Department of Engineering, Universidad Nacional Del Sur and Institute of Applied Mechanics (CONICET))
  • Published : 1999.05.25
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Abstract

Practicing a hole or an orifice through a plate or a slab constitutes a very frequent engineering situation due to operational reasons imposed on the structural system. From a designer's viewpoint it is important to know the effect of this modification of the mechanical system upon its elastodynamic characteristics. The present study deals with the determination of the lower natural frequencies of the structural element described in the title of the paper using a variational approach and expressing the displacement amplitude of the plate in terms of the double Fourier series which constitutes the classical, exact solution when the structure is simply supported at its four edges.

Keywords

References

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  2. Avalos, D.R., Larrondo, H.A., Laura, P.A.A. and Rossi, R.E. (1997), "Transverse vibrations of simply supported rectangular plates with rectangular cutouts carrying an elastically mounted concentrated mass", Journal of Sound and Vibration, 204(4), 585-592. https://doi.org/10.1006/jsvi.1997.0958
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  4. Laura, P.A.A., Susemihl, E.A., Pombo, J.L., Luisoni, L.E. and Gelos, R. (1977), "On the dynamic behavior of structural elements carrying elastically mounted masses", Applied Acoustics, 10(1), 121-145. https://doi.org/10.1016/0003-682X(77)90021-4
  5. Laura, P.A.A., Romanelli, E. and Rossi, R.E. (1997a), "Transverse vibrations of simply supported rectangular plates with rectangular cutouts", Journal of Sound and Vibration, 202(2), 275-283. https://doi.org/10.1006/jsvi.1996.0703
  6. Laura, P.A.A., Avalos, D.R., Larrondo, H.A. and Rossi, R.E. (1997b), "Numerical experiments on the Rayleigh-Ritz method when applied to doubly connected plates", Institute of Applied Mechanics (Bahia Blanca, Argentina), Publication $n^{\circ}$ 97-14.
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Cited by

  1. TRANSVERSE VIBRATIONS OF A SIMPLY SUPPORTED PLATE OF GENERALIZED ANISOTROPY WITH AN OBLIQUE CUT-OUT vol.258, pp.4, 2002, https://doi.org/10.1006/jsvi.2002.5153
  2. Displacement amplitudes and flexural moments for a rectangular plate with a rectangular cutout under a uniformly distributed static load vol.280, pp.1-2, 2005, https://doi.org/10.1016/j.jsv.2004.01.044
  3. Natural frequencies of thin, rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass vol.43, pp.14-15, 2006, https://doi.org/10.1016/j.ijsolstr.2005.03.051
  4. Effects of constraint, circular cutout and in-plane loading on vibration of rectangular plates vol.68, 2013, https://doi.org/10.1016/j.ijmecsci.2013.01.005
  5. TRANSVERSE VIBRATIONS OF A SIMPLY SUPPORTED ORTHOTROPIC PLATE WITH AN OBLIQUE CUTOUT vol.248, pp.3, 2001, https://doi.org/10.1006/jsvi.2001.3703