A new solution for dynamic response of FG nonlocal beam under moving harmonic load

S.A.H. Hosseini, O. Rahmani and S. Bayat

Abstract

A Closed-form solution for dynamic response of a functionally graded (FG) nonlocal nanobeam due to action of moving harmonic load is presented in this paper. Due to analyzing in small scale, a nonlocal elasticity theory is utilized. The governing equation and boundary conditions are derived based on the Euler-Bernoulli beam theory and Hamilton's principle. The material properties vary through the thickness direction. The harmonic moving load is modeled by Delta function and the FG nanobeam is simply supported. Using the Laplace transform the dynamic response is obtained. The effect of important parameters such as excitation frequency, the velocity of the moving load, the power index law of FG material and the nonlocal parameter is analyzed. To validate, the results were compared with previous literature, which showed an excellent agreement.

Key Words

closed-form solution; dynamic response; FG Nano beam; moving harmonic load; nonlocal elasticity theory

Address

S.A.H. Hosseini:Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Qazvin, Iran O. Rahmani:Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran S. Bayat:Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran

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