Approximate frequency analysis of isotropic shear beams using initial value method

• Published in: Journal of engineering mathematics Vol. 148; no. 1
• Main Authors: Artan, Reha, Nur, Ceyda, Guclu, Gokhan, Demirkan, Erol, Çelik, Murat
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Boundary conditions; Computational Mathematics and Numerical Analysis; Deformation analysis; Differential equations; Distribution functions; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Shear deformation; Shear stress; Stress distribution; Theoretical and Applied Mechanics; Transfer matrices; Vibration analysis; Transfer matrix; Isotropic shear beams; Matricant; Approximate transfer matrix; Vibrration of shear beams; Initial values method
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-024-10401-y

This study investigates the vibration of isotropic shear beams (ISBs) using the unified shear deformation theory for various shear stress distribution functions. The governing differential equations and boundary conditions are obtained using the principle of virtual work. Using the initial values method, the first five frequencies for various end conditions were calculated with four digits. Frequencies for different shear stress distributions can be easily determined using the approximate transfer matrices provided in this study. To verify the accuracy of the obtained results, we compared the frequencies with the findings in the existing literature.