Amin Ghannadiasl - Assistant Professor, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

Free vibration of the elastic body is called the natural vibration and it happens at a frequency that called natural frequency. Natural vibrations are different from forced vibration which happen at frequency of applied force. If forced frequency is equal to the natural frequency, the amplitude of vibration increases manyfold. Therefore, natural frequencies are important dynamic characteristics of the elastic body. The effect of the Pasternak elastic foundation with variable subgrade coefficient on the natural frequency of the uniform Euler–Bernoulli beam is presented in this paper. The applied method for modeling uniform Euler–Bernoulli beam on the Pasternak foundation is based on the Green Function Method. In this paper, the effect of the elastic coefficient of Pasternak elastic foundation with variable subgrade coefficient is assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function Method in the new formulation.

Natural frequency, Euler–Bernoulli beam, Pastemak foundation, Green Function Method