# Dynamic stiffness method for free vibrations analysis of partial fluid-filled orthotropic circular cylindrical shells

## The vibration frequencies for different filling ratios of cylindrical shells are obtained and compared with existing experimental and theoretical results which indicate that the fluid filling can reduce significantly the natural frequencies of studied cylindrical shells. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of orthotropic cylindrical shells. | Vietnam Journal of Mechanics, VAST, Vol. 37, No. 1 (2015), pp. 43 – 56 DOI: DYNAMIC STIFFNESS METHOD FOR FREE VIBRATIONS ANALYSIS OF PARTIAL FLUID-FILLED ORTHOTROPIC CIRCULAR CYLINDRICAL SHELLS Tran Ich Thinh∗ , Nguyen Manh Cuong, Vu Quoc Hien Hanoi University of Science and Technology, Vietnam ∗ E-mail: tranichthinh@ Received November 20, 2014 Abstract. Free vibrations of partial fluid-filled orthotropic circular cylindrical shells are investigated using the Dynamic Stiffness Method (DSM) or Continuous Element Method (CEM) based on the First Order Shear Deformation Theory (FSDT) and non-viscous incompressible fluid equations. Numerical examples are given for analyzing natural frequencies and harmonic responses of cylindrical shells partially and completely filled with fluid under various boundary conditions. The vibration frequencies for different filling ratios of cylindrical shells are obtained and compared with existing experimental and theoretical results which indicate that the fluid filling can reduce significantly the natural frequencies of studied cylindrical shells. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of orthotropic cylindrical shells. The advantages of this current solution consist in fast convergence, low computational cost and high precision validating for all frequency ranges. Keywords: Free vibration, continuous element method, dynamic stiffness method, orthotropic cylindrical shell, fluid-shell interaction. 1. INTRODUCTION The knowledge on dynamic responses of fluid-filled isotropic and orthotropic cylindrical shells is of primary importance for the design of pressure vessels, fluid tanks of propellant rockets, seismic effects on liquid storage tanks etc. For coupled fluid-cylindrical shell problems, Jain [1] obtained the natural frequency equations of simply supported orthotropic cylindrical shells, filled .

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