Displacement (psychology)

Physics

Engineering

Mathematical analysis

Finite element method

Psychology

Composite material

Boundary value problem

Materials science

Vibration

Acoustics

Helmholtz free energy

Fluid–structure interaction

Shell (structure)

Mathematics

Psychotherapist

Mechanics

Quantum mechanics

Structural engineering

Applied Mathematical Modelling

In this paper, a novel energy approach is proposed for fully coupled fluid-structure problems of functionally graded porous (FGP) fluid-filled cylindrical shells under arbitrary boundary conditions. Kinds of continuous FG materials are considered including various patterns in which the voids distributed. A modified variational principle is developed in fluid domain as well as in structural domain, naturally reinforcing the restrains on the boundaries and interfaces between adjacent subdomains. Energy functions in structural and fluid domain are deduced based on the first-order shear deformable shell theory (FSDT) and Helmholtz equation, respectively. The fluid-structure interactions are successfully introduced with the work done by the sound pressure and displacement continuous conditions at fluid-structural interface. A semi-analytical solution is obtained by expanding the displacement and sound pressure components analytically in the circumferential direction and numerically in the axial direction. Good convergence, high accuracy, superior efficiency and flexibility in using admissible functions are demonstrated by comparing reasonably many proposed results with those in literatures or obtained by FEM/BEM. Numerous examples are developed to examine the effects of material properties and boundary conditions on free vibration of FGP cylindrical shells with and without water. With added mass factor introduced, the influences of the key parameters on the fluid-structure coupling are also presented. The slight dependences of the added mass factor on material and boundary conditions greatly broaden the applied scope of the numerical results.

Vibration analysis of functionally graded porous cylindrical shells filled with dense fluid using an energy method