City Research Online

Abstract

The free vibration behaviour of carbon-nanotubes (CNTs)-reinforced laminated Timoshenko-Ehrenfest beams resting on elastic foundation is investigated by using the dynamic stiffness method (DSM). The investigation focuses on two distinct types of through thickness distribution of axially aligned single-walled carbon nanotubes (SWCNTs)-reinforcements which are uniform distribution CNTs (UD-CNTs) and functionally graded CNTs (FG-CNTs) reinforcements. First, the governing differential equations and natural boundary conditions are derived by applying Hamilton’s principle, which are solved in an exact sense and presented in closed analytical form. The dynamic stiffness matrix is then formulated by establishing the relationship between the amplitude of the forces and the corresponding displacements at the ends of the beam. The well-known Wittrick-Williams algorithm is used to compute the natural frequencies and mode shapes of CNTs-reinforced Timoshenko-Ehrenfest beams. The effects of elastic foundation on the free vibration characteristics are investigated for different configurations. A comprehensive study is conducted to assess the accuracy and computational efficiency of the proposed method. Subsequently, the influence of various beam parameters on the free vibration characteristics of CNTs-reinforced Timoshenko-Ehrenfest beams is investigated in detail. Several interesting observations have been made from the computed results with significant conclusions drawn. The results presented in this paper can serve as bench-mark for validation of future research in the area.

Publication Type:	Article
Additional Information:	© 2025. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	CNTs-reinforced Timoshenko-Ehrenfest beams, Free vibration, Non-uniform elastic foundation, Wittrick-Williams algorithm, Dynamic stiffness method, Multilayered beam
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Departments:	School of Science & Technology
SWORD Depositor:	Symplectic Administrator

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