دانلود رایگان مقاله تحلیل کمانش سیستم هدفمند پرتو تیموشنکو در فونداسیون الاستیک وینکلر - پاسترناک

Abstract

To acquire exact solutions of double-functionally graded Timoshenko beam system on Winkler-Pasternk elastic foundation, which are benchmarks of double-beam systems in the field of engineering, motion differential equations of double-beam system are derived using Hamilton’s principle. In this paper, the exact dynamic stiffness matrix of double-functionally graded Timoshenko beam system on Winkler-Pasternak under axial loading are established and the damping of the connecting layer is also taken into consideration. The exact natural frequency and buckling load are obtained using Wittrick-William algorithm. To comprehensively analyze dynamic characteristics of double beam system, the effect of gradient parameter, foundation parameters, axial loading and connecting stiffness on the frequency and buckling load is compared, and the influence of damping factor is also investigated. Finally, dynamic response of double-beam system is studied using Fourier transformation.

4. Conclusion

In this paper, To acquire exact solutions of double-functionally graded Timoshenko beam system on Winkler-Pasternk elastic foundation, which are benchmarks in the field of engineering, the exact dynamic stiffness matrix of the double-functionally graded Timoshenko beam system on Winkler-Pasternak foundation under axial loading is established. The results obtained by dynamic stiffness method are in great agreement with previous studies. Thus, the correctness and effectiveness of the method was demonstrated. After comprehensive study of this beam system, we can conclude that: 1. With the increase of gradient parameter k, the fundamental frequency of the two-beam system decreases under different boundary conditions. 2. The stiffness of connecting layer has great influence on the reverse modes of two beams, and the increase of the stiffness can significantly increase the frequencies of the two-beam system. 3. the increase of the parameters of elastic foundation will increase the frequencies of two beam system and the effects of Winkler layer and shear layer on fundamental frequency are close.