Ali Mokhtari - Department of Mechanical Engineering, Isfahan University of Technology, Isfahan ۸۴۱۵۶-۸۳۱۱۱, Iran
Vahid Sarvestan - Department of Mechanical Engineering, Isfahan University of Technology, Isfahan ۸۴۱۵۶-۸۳۱۱۱, Iran
Hamid Reza Mirdamadi - Department of Mechanical Engineering, Isfahan University of Technology, Isfahan ۸۴۱۵۶-۸۳۱۱۱, Iran

In this article, vibration analysis of an Euler-Bernoulli beam resting on a Pasternak-type foundation is studied. The governing equation is solved by using a spectral finite element model (SFEM). The solution involvescalculating wave and time responses of the beam. The Fast Fourier Transform function is used for temporal discretization of the governing partial differential equation into a set of ordinary differential equations.Then, the interpolating function for an element is derived from the exact solution of governing differential equation in the frequency domain. Inverse Fourier Transform is performed to rebuild the solution in the time domain.The foremost advantages of the SFEM are enormous high accuracy, smallness of the problem size and the degrees of freedom, low computational cost and high efficiency to deal with dynamic problems anddigitized data. Moreover, it is very easy to execute the inverse problems by using this method. The influences of foundation stiffness, shear layer stiffness and axial tensile (or compressive) forces on the dynamiccharacteristic and divergence instability of the beam are investigated. The accuracy of the present SFEM is validated by comparing its results with those of classical finite element method (FEM). The results show theascendency of SFEM with respect to FEM in reducing elements and computational effort, concurrently increasing the numerical accuracy.

Foundation stiffness,Shear layer stiffness,Spectral finite element model,Divergence instability,Wave domain analysis