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Indexed by:Journal Papers

Date of Publication:2019-09-01

Journal:JOURNAL OF VIBRATION AND CONTROL

Included Journals:SCIE、EI

Volume:25

Issue:18

Page Number:2473-2479

ISSN No.:1077-5463

Key Words:Dynamic stiffness; general boundary condition; mode shape; natural frequency; numerical stable equations

Abstract:There are well-known expressions for natural frequencies and mode shapes of a Euler-Bernoulli beam which has classical boundary conditions, such as free, fixed, and pinned. There are also expressions for particular boundary conditions, such as attached springs and masses. Surprisingly, however, there is not a method to calculate the natural frequencies and mode shapes for a Euler-Bernoulli beam which has any combination of linear boundary conditions. This paper describes a new method to achieve this, by writing the boundary conditions in terms of dynamic stiffness of attached elements. The method is valid for any boundaries provided they are linear, including dissipative boundaries. Ways to overcome numerical issues that can occur when computing higher natural frequencies and mode shapes are also discussed. Some examples are given to illustrate the applicability of the proposed method.