Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position

Jianguo Ding ^[1] ; Liangliang Chu ^[2] ; Libiao Xin ^[2] ; Guansuo Dui ^[2]
1. [1] Nanjing University of Science and Technology
  
  Nanjing University of Science and Technology
  
  China
2. [2] Beijing Jiaotong University
  
  Beijing Jiaotong University
  
  China
Localización: Mechanics based design of structures and machines, ISSN 1539-7734, Vol. 46, Nº. 2, 2018, págs. 225-237
Idioma: inglés
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Resumen
- In the paper work, the nonlinear vibration response of functionally graded (FG) Euler–Bernoulli beam resting on elastic foundation is studied. Based on von Kármán’s geometric nonlinearity, the partial differential governing equations describing the nonlinear vibration of FG Euler–Bernoulli beam are derived from Hamilton’s principle and are reduced to an ordinary nonlinear differential equation with quadratic and cubic nonlinear terms via Galerkin’s procedure. Due to unsymmetrical material variation along the thickness of FG beam, the neutral surface concept is proposed to remove the stretching and bending coupling effect and the rotary inertia of the cross section is incorporated to obtain an analytical solution. Numerical results are presented to show the effects of the nonlocal parameters and vibration amplitude on the frequency responses. This results may be useful in design and engineering applications.