Title

Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions

ORCID Identifiers

0000-0001-7983-5665

Document Type

Article

Source of Publication

JVC/Journal of Vibration and Control

Publication Date

9-1-2019

Abstract

© The Author(s) 2019. 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.

ISSN

1077-5463

Publisher

SAGE Publications Inc.

Volume

25

Issue

18

First Page

2473

Last Page

2479

Disciplines

Life Sciences

Keywords

Dynamic stiffness, general boundary condition, mode shape, natural frequency, numerical stable equations

Scopus ID

85068347170

Indexed in Scopus

yes

Open Access

no

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