An integral equation analysis of the harmonic response of three-layer beams

https://doi.org/10.1016/0022-460X(82)90543-0Get rights and content

Abstract

The integral equations of harmonic motion have been derived and solved for three-layer sandwich beams with a constrained linear viscoelastic core. The method of solution required first the construction of the Green's vector for a beam in analytical form. Following this, the integral equations were derived and readily approximated by matrix equations which were finally solved numerically. In addition to this analysis, the corresponding eigenvalue problem has been solved so that the modal frequencies and the beam loss factor could be calculated directly. The integral equation analysis offers a fast and efficient alternative to the traditional methods based on the solution of the differential equations of motion. The method has been verified by comparison with experimental results for three-layer cantilevers and simply supported beams.

References (27)

  • Y.P. Lu et al.

    Vibrations of three layered damped sandwich plate composites

    Journal of Sound and Vibration

    (1979)
  • J.A. Agbasiere et al.

    Flexural vibration of symmetrical multi-layer beams with viscoelastic damping

    Journal of Mechanical Engineering Sciences

    (1968)
  • B.C. Nakra et al.

    Structural damping using a four layer sandwich

    Journal of Engineering for Industry

    (1972)
  • Cited by (3)

    • A finite element analysis of the harmonic response of damped five-layer plates

      1985, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
    View full text