FREE VIBRATION OF COMBINED DYNAMICAL SYSTEMS

A method for analysing the free vibration of combined linear undamped dynamical systems attached at discrete points is shown. The method uses separation of variables to exhibit the harmonic motion of the system and to derive a generalised differential equation for the normal modes. Green's functions for the vibrating component systems are used to solve the generalised differential equation and derive the characteristic equation for the natural frequencies of the system. The characteristic equation can then be solved for the exact natural frequencies and exact normal modes. The method is demonstrated for two types of dynamical systems involving beams and oscillators. For two particular systems, approximate natural frequencies determined through a Galerkin's method and the finite element method are compared to the exact natural frequencies. The generalised orthogonality relation for each system is derived.

• Supplemental Notes:
  • J. Engng. Mechanics 112 (1986), p. 1 (Jan.) [13 pp., 24 ref., 2 tab., 2 fig.]
• Authors:
  • Nicholson, J W
  • Bergman, L A
• Publication Date: 1986

Language

• English

Subject/Index Terms

• Subject Areas: Marine Transportation;

Filing Info

• Accession Number: 00689261
• Record Type: Publication
• Source Agency: British Maritime Technology
• Files: TRIS
• Created Date: Aug 14 1995 12:00AM