This paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form. | Volume 36 Number 3 3 2014 Vietnam Journal of Mechanics, VAST, Vol. 36, No. 3 (2014), pp. 201 – 214 AN ANALYTICAL APPROACH TO ANALYZE NONLINEAR DYNAMIC RESPONSE OF ECCENTRICALLY STIFFENED FUNCTIONALLY GRADED CIRCULAR CYLINDRICAL SHELLS SUBJECTED TO TIME DEPENDENT AXIAL COMPRESSION AND EXTERNAL PRESSURE. PART 1: GOVERNING EQUATIONS ESTABLISHMENT Dao Van Dung1 , Vu Hoai Nam2,∗ University of Science, VNU, Vietnam 2 University of Transport Technology, Hanoi, Vietnam 1 Hanoi ∗ E-mail: Received December 25, 2013 Abstract. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Galerkin method, this paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form. Keywords: Functionally graded material, discontinuous reinforcement, buckling, elasticity, analytical modelling. 1. INTRODUCTION Many authors studied the static buckling and postbuckling of FGM cylindrical shells subjected to the mechanic and thermal loading. Shen [1, 2] investigated the nonlinear postbuckling of thin FGM cylindrical shells and FGM hybrid cylindrical shells in thermal environments under lateral pressure and axial loading, respectively. Bahtui and Eslami [3] investigated the coupled thermo-elasticity of FGM cylindrical shells. Batra and Iaccarino [4] presented the exact solutions for radial deformations of a functionally graded isotropic and incompressible second-order elastic cylinder. Huang and Han [5–7] studied the buckling and .
