Free vibration of prestress Timoshenko beams resting on elastic foundation

Nguyen Dinh Kien
Author affiliations


  • Nguyen Dinh Kien Institute of Mechanics Vietnamese Academy of Science and Technology



This paper presents a finite element formulation for investigating the free vibration of uniform Timoshenko beams resting on a Winkler-type elastic foundation and prestressing by axial force. Taking the effect of prestress, foundation support and shear deformation into account, a stiffness matrix for Timoshenko-type beam element is formulated using the energy method. The element consistent mass matrix is obtained from the kinetic energy using simple linear shape functions. Employing the formulated element, the natural frequencies of the beams having various boundary conditions are determined for different values of the axial force and foundation stiffness. The vibration Characteristics of the beams partially supported on the foundation are also studied and highlighted. Specially, the effects of shear deformation on the vibration frequencies of prestress beams fully and partially supported on the elastic foundation are investigated in detail.


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How to Cite

N. D. Kien, Free vibration of prestress Timoshenko beams resting on elastic foundation, Vietnam J. Mech. 29 (2007) 1–12. DOI:



Research Article

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