Dynamic stiffness method for free vibration of beams and frameworks with cutouts

Banerjee, J. Ranjan and Kennedy, David ORCID: https://orcid.org/0000-0002-8837-7296 2026. Dynamic stiffness method for free vibration of beams and frameworks with cutouts. Mechanics of Advanced Materials and Structures 33 (1) , 2699288. 10.1080/15376494.2026.2699288

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Abstract

The free vibration behavior of beams and frames with rectangular cutouts is investigated by the dynamic stiffness method. Essentially, the beam is split into three parts with the first and third parts representing the intact beam whereas the second part lying in between the first and third parts represents the cutout part. The dynamic stiffness matrices of the three individual parts of the beam are assembled algebraically through the application of symbolic computation. The four nodes of the three-part beam are numbered in a way that nodes 1 and 2 are the intermediate nodes representing the ends of the cutout part whereas nodes 3 and 4 represent the left and right end nodes of the beam. Next, the usual Gauss elimination is performed algebraically on the rows of the last but two nodes of the assembled matrix. What would be left at the bottom of the resulting partially triangulated matrix corresponds to nodes 3 and 4 which is essentially the dynamic stiffness matrix of the beam with cutout. Both in-plane and out of plane free vibration behavior of the beam are considered. The Wittrick-Williams algorithm is applied to analyze the free vibration characteristics. Representative results are presented with important conclusions drawn.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Engineering
Publisher:	Taylor and Francis Group
ISSN:	1537-6494
Date of Acceptance:	26 June 2026
Last Modified:	15 Oct 2026 13:45
URI:	https://orca.cardiff.ac.uk/id/eprint/188644

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