Vibration and damping analysis of fluid filled orthotropic cylindrical shells with constrained viscoelastic damping

Abstract: In this article, buckling and vibration behavior of a functionally graded material (FGM) sandwich beam having constrained viscoelastic layer (VEL) is studied in thermal environment by using finite element formulation. The FGM sandwich beam is assumed to be clamped on both edges. The material properties of FGM are functionally graded in thickness direction according to volume fraction power law distribution. Temperature dependent material properties of FGM stiff layer and shear modulus of viscoelastic layer are considered to carry out buckling and vibration analysis. Numerical studies involving the understanding the effect of power law index, core to stiff layer ratio on the thermal buckling temperature as well as on vibration has been carried out. In addition influence of temperature on natural frequencies and loss factors have been examined for FGM sandwich beam.

Abstract: A linear analysis of the vibratory behaviour of initially tensioned orthotropic circular cylindrical shells conveying a compressible inviscid fluid is presented. The model is based on the three-dimensional nonlinear theory of elasticity and the Eulerian equations. A nonlinear strain-displacement relationship is employed to derive the geometric stiffness matrix due to initial stresses and hydrostatic pressures. Frequency-dependent fluid mass, damping and stiffness matrices associated with inertia, Coriolis and centrifugal forces, respectively, are derived through the fluid-structure coupling condition. The resulting equation governing the vibration of fluid-conveying shells is solved by the finite element method. The free vibration of initially tensioned orthotropic cylindrical shells conveying fluid is investigated; numerical examples are given and discussed.

Abstract: A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoulli's equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid–structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed.

Abstract: An accurate solution approach based on the first-order shear deformation theory (FSDT) is developed for the free vibration and damping analysis of thick sandwich cylindrical shells with a viscoelastic core under arbitrary boundary conditions. Laminated and sandwich theories are employed to describe the laminated composite layers and viscoelastic material layer, respectively. The present solution is based on a set of new displacement field expression in which the displacements of the middle surface are expanded as a combination of a standard Fourier series and auxiliary functions. Due to the improved displacement expansions, rapid convergence and high accuracy can be easily obtained. The current method can be universally applicable to a variety of boundary conditions including all the classical cases, elastic restraints and their combinations. Natural frequencies and loss factors under various boundary conditions and lamination schemes are calculated, which may serve as benchmark solutions in the future. The effects of some key parameters including the boundary conditions, fiber orientation angle, and number and thickness of the layers on free vibration and damping characteristics of the shells are illustrated and analyzed.

Abstract: This paper describes the method of determining the normal modes of vibrations and natural frequencies of elastic shells of revolution with an arbitrary meridian, partially filled with a fluid. The modes of vibration of the shells with fluids are determined as a linear combination of the natural modes of vibration in vacuum. The solution of the problem of hydroelastic vibrations has been obtained using the methods of the boundary element (BEM) and the finite element (FEM). Numerical investigations of vibrations of hemi-spherical shells conveying fluid have been conducted and analyzed. Illustrative examples are provided to demonstrate the accuracy and efficiency of the developed numerical procedure.

Abstract: A theory is presented for the determination of the free vibration characteristics of vertical, thin, circular cylindrical shells, partially or completely filled with stationary liquid. The shell may be uniform or non-uniform, provided it is axially symmetric. This is a finite-element theory, using cylindrical finite elements, but the displacement functions are determined by using classical shell theory. The inertial loading of the fluid is taken into account by incorporating the virtual mass of the fluid into the mass matrix of those finite elements which are below the liquid free-surface. Calculations of the natural frequencies and eigenvectors were conducted for one such shell, for which experimental data were available. Agreement between theory and experiment was found to be quite good.

Abstract: In this paper is presented an analysis of axisymmetric and unsymmetric free vibrations of conical or cylindrical shells with various boundary conditions. The shell construction may be either homogeneous or symmetrical sandwich, and the facing and core may be either isotropic or specially orthotropic. Love's first-approximation shell theory, with transverse shear strain added, was used and solutions were obtained by Galerkin's method. Comparisons were made with existing experimental results for the following boundary conditions: freely supported at both ends; clamped-clamped; and free-free.

Abstract: The vibration and damping characteristics of three-layered cylindrical shells with a viscoelastic core constrained by isotropic facings are studied by using the finite element method. The finite element developed for the study has separate rotations in its displacement field for the core and facings. The element has three nodes and seven degrees of freedom per node. Results are presented for cylindrical shells with different core to facing thickness and length to radius ratios and three boundary conditions: clamped-clamped, simply supported and clamped-free. The effects of the shear parameter on the frequency and loss factors for various geometric properties and boundary conditions are also discussed.

Abstract: The vibration and damping analysis of orthotropic cylindrical shells with a constrained viscoelastic core is carried out by using a finite element based on a discrete layer theory. The material damping of the facings is also included in the analysis. Results are represented for different geometric and material properties of the shell. The data and trends presented for various cases could be useful for designers in choosing damping treatments for composite shells.