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Abstract

This article presents a formulation for the vibration analysis of plane frames. The strain gradient notation is utilized to determine the mass and stiffness matrices. The obtained matrices can easily be parameterized due to their simple structure. Both Euler-Bernoulli- and Timoshenko-beam elements are investigated in this study. The parameterized stiffness and mass matrices are optimized for accurate performance in the vibration analysis of frame structures. Some numerical examples are solved to show the advantages of the presented scheme. Results of these sample vibration problems indicate that the proposed technique increases the accuracy of analysis, when these new stiffness and diagonal mass matrices are used.

Keywords

Euler-Bernoulli-beam finite element mass matrix stiffness matrix Timoshenko-beam vibration analysis

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Vibration analysis of plane frames by customized stiffness and diagonal mass matrices

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