A NOVEL APPROACH TO DETERMINE THE FREQUENCY EQUATIONS OF COMBINED DYNAMICAL SYSTEMS

✍ Scribed by P.D. Cha; W.C. Wong

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 152 KB
• Volume: 219
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1916

✦ Synopsis

A novel approach is presented which can be used to reduce the generalized eigenvalue problem associated with the free vibration of a linear elastic structure carrying lumped elements at s distinct locations. Using N component modes in the assumed-modes method, the free vibration of such a combined dynamical system is governed by the solution of a generalized eigenvalue problem of order N × N, whose stiffness and mass matrices consist of diagonal matrices modified by a total of s rank one matrices, where s corresponds to the number of attachment points. This generalized eigenvalue problem can be manipulated such that the natural frequencies governing free vibration can be calculated instead by solving a much smaller characteristic determinant of order s × s. Interestingly enough, this smaller and simpler characteristic determinant can also be obtained by using the Lagrange multipliers formalism in conjunction with Lagrange's equations.