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

Made available in DSpace on 2019-10-06T17:14:04Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-09-01 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. São Paulo State University (UNESP) School of Engineering Zayed University Dalian University of Technology Institute of Internal Combustion Engine São Paulo State University (UNESP) School of Engineering