Keywords: hybrid element, composite cylindrical shells, vibrations, shear deformations.

Nuclear plant reliability depends directly on its component performance. The higher heat transfer performance of nuclear plant components often requires higher flow velocities through the shell and tube heat exchangers. So, these cylindrical structures are subjected to either axial or cross flow. The excessive flow-induced vibrations, which are a major cause of machinery downtime; fatigue failure and high noise, limit the performance of these structures. Therefore, the safety in the nuclear power plant's components requires an analysis of several possibilities of accident events. Considering a tube structure carrying high velocity flow and being under high pressure, these event could be: pressure oscillations in a nuclear reactor cavity, velocity oscillations of a fluid in a pipe due to external excitations and fluid-elastic instabilities, among other. These events must be fully understood so that a proper design can be developed. Consequently, a design criterion that establishes acceptable limits of vibration amplitudes and minimizes mechanical damages is necessary to increase the reliability and design life of the components. It is required to predict how long a component lasts and how much vibrations can be tolerated without excessive damage. The detrimental vibration failures, including costly plant shutdowns in terms of repairs or replace some components and large economic losses due to profit not produced during the outage, have motivated numerous investigations. There has been a significant number of experimental and analytical approaches toward understanding the flow-induced instability mechanisms occurred in the nuclear and heat exchanger components subjected to axial or cross-flow. Therefore, the evaluation of complex vibrational behavior of these structures is highly desirable in this sector of industry.

This paper presents a semi-analytical investigation of dynamic analysis of composite cylindrical shells taking into account the shear deformation and rotary inertia effects. The structure may be uniform or non-uniform in the circumferential direction. The method used is a combination of hybrid finite element analysis and the shearable shell theory. The shell is subdivided into cylindrical panels having five degree of freedoms at each nodal line. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration of the equilibrium equations instead of the usually used and more arbitrarily interpolating polynomials. This theory gives zero strains for rigid-body motions in such a way that the developed displacement functions satisfy the convergence criteria of the finite element method. Particular important in this study is to obtain the natural frequencies of the coupled system of the fluid-structure and also estimating the critical flow velocity at which the structure loses its stability. The displacement functions, mass and stiffness matrices of the structure are obtained by exact analytical integration over a hybrid element developed in this work. Linear potential flow theory is applied to describe the fluid effect that leads to the inertial, centrifugal and Coriolis forces. This theory can be used for vibration analysis of axisymmetric, beam-like and shell mode behavior of cylindrical shells. It yields the high as well as the low eigenvalues and eigenmodes with comparable high accuracy. Reasonable agreement is found with other theories and experiments.

1

M.H. Toorani, A.A. Lakis, "General Equations of Anisotropic Plates and Shells Including Transverse Shear Deformation and Rotary Inertia Effects", Journal of Sound and Vibration, 237 (4), 561-615, 2000. doi:10.1006/jsvi.2000.3073

2

M.H. Toorani, A.A. Lakis, "Shear Deformation Theory in Dynamic Analysis of Anisotropic laminated Open Cylindrical Shells Filled with or Subjected to a Flowing Fluid", Journal of Computer Methods in Applied Mechanics and Engineering, 190(37-38), 4929-4966, 2001. doi:10.1016/S0045-7825(00)00357-1

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