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

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 theFirst 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 studiedcylindrical 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.

Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid

“…Substituting α = 0 in Eqs. (6) and 7, the forces-displacements relations and the equations of motion for laminated composite cylindrical shell containing fluid can be obtained [27].…”

“…where w 0 is the normal displacement of the shell, v f is the velocity of fluid. The hydrodynamic pressure acting on the cylindrical shell is then defined by [27]…”

“…Substituting (14) in Eqs. (6) and 7, a system of ordinary differential equations in the x-coordinate for the m th mode can be expressed in the matrix form for each circumferential mode m as [25][26][27][28]…”

“…Similarly, we can obtain the dynamic stiffness matrix [K(ω)] m for cylindrical shell containing fluid [27].…”

“…The CE models for composite cylindrical shells and conical shells presented in works of Tran Ich Thinh and Nguyen Manh Cuong [25,26] imposed a considerable advancement of the study on CEM for metal and composite structures. Recently, the new research for thick laminated composite joined cylindrical-conical shells by Tran Ich Thinh, Nguyen Manh Cuong and Vu Quoc Hien [27] has emphasized the strong capacity of CEM in assembling complex structure.…”