# Continuous element for vibration analysis of thick shells of revolution

## This paper presents a new numerical method: Continous Element Method (CEM) for vibration analysis of thick shells of revolution taking into account the shear deflection effects. Natural frequencies and harmonic responses of cylindrical and conical shells subjected to different boundary conditions obtained with this kind of formulation are in close agreement with finite element solutions. | Vietnam Journal of Mechanics, VAST, Vol. 33, No. 1 (2011), pp. 41 – 54 CONTINUOUS ELEMENT FOR VIBRATION ANALYSIS OF THICK SHELLS OF REVOLUTION Nguyen Manh Cuong, Tran Ich Thinh Hanoi University of Technology Abstract. This paper presents a new numerical method: Continous Element Method (CEM) for vibration analysis of thick shells of revolution taking into account the shear deflection effects. Natural frequencies and harmonic responses of cylindrical and conical shells subjected to different boundary conditions obtained with this kind of formulation are in close agreement with finite element solutions. The main advantage is the reduction of the size of the model thus allows the high precision in the results for a large frequency range. Key words: Continuous element method, Dynamic stiffness matrix, Dynamic transfer matrix, Shell of revolution, Harmonic response. 1. INTRODUCTION The Dynamic Stiffness Method is a highly effcient way to analyse harmonic responses of structures made up of many simple elements. This method, also known as the Continuous Element Method (CEM), is particularly well-suited to pylon and beam lattice structures. It is based on the so-called dynamic stiffness matrix, denoted hereafter K(ω), which gives exact relations between forces and displacements at the ends of a structural element [1]. The exactness of the relation can only be understood with regard to a given elastodynamic theory. In the case of straight beam assemblies, exact solutions of the equations of motion according to Euler - Bernoulli assumptions or the Rayleigh and Timoshenko theories have been widely used to derive the dynamic stiffness matrices [1], [8]-[11]. During the 1980s, several computer codes were developed based on this method. The calculation of the dynamic stiffness matrix for curved beams is based on an integration of the equations of motion whose associated eigenproblems has been solved beforehand [12, 13]. Using a very similar approach, an axisymmetric .

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