Vibration and stability of a variable thickness annular plate subjected to a torque

The free vibration and stability of a variable thickness annular plate subjected to a torque are analyzed by the Ritz method. For this purpose, the transverse deflection of an annular plate is written in a series of the deflection functions of a uniform thickness annular plate without the action of a torque. The kinetic and strain energies of the plate are evaluated analytically and the frequency equation of the plate is derived by the conditions for a stationary value of the Lagrange functional. The present method is applied to annular plates with two types of radial thickness variation, power law and exponential, and the natural frequencies (the frequency parameters) and the divergence torques are calculated numerically, from which the effects of the varying thickness, inner/outer radii ratio and edge conditions are studied.     

Vibration and stability of a free circular plate subjected to non-conservative loading

This paper is concerned with the stability and vibration of a completely free circular plate subjected to a non-conservative edge loading. The eigencurves and mode shapes of the plate are obtained for various values of the non-conservativeness parameter. Numerical results are presented for the asymmetrical mode shapes of the plate. Interesting conclusions are drawn from these results some of which are verified analytically.     

Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force

This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.     

Stability of transverse vibration of a circular plate subjected to a periodically varying torque

The paper is concerned with transverse vibration of a circular plate subjected to periodically varying torsion. The instability regions are found and plotted for the plate under a tangent uniform load and a tangent concentrated force.     

The measurement of structural mobilities of a circular cylindrical shell

Structural mobility is useful for the estimation of structural power flows in coupled systems. Although the methods of measuring structural mobilities are easily found for one-dimensional beam structures, few are available for cylindrical shells. In this paper, a new method is proposed for the measurement of the structural mobilities of a circular cylindrical shell. A point force excitation is used instead of circumferential modal forces which are difficult to implement in practice. This method utilizes the least squares technique to obtain the transfer function components of different circumferential modes from the measured data. Experiments were carried out on a circular cylindrical shell with different end conditions excited by a point force to verify the feasibility of this proposed method.     

压电圆管换能器振动特性的薄壳理论分析

本文运用弹性力学中的薄壳理论，分析了径向极化压电陶瓷圆管换能器的振动特性，并在此基础上推导出换能器等效电路的特性阻抗，为换能器的设计提供了依据。分析及计算结果表明，本文的理论与以往常用的薄膜理论相比，不仅在物理模型的描述上更为完整准确，在计算精度上也更接近实际。     

Vibration and stability of a non-uniform Timoshenko beam subjected to a follower force

An analysis is presented for the vibration and stability of a non-uniform Timoshenko beam subjected to a tangential follower force distributed over the center line by use of the transfer matrix approach. For this purpose, the governing equations of a beam are written in a coupled set of first-order differential equations by using the transfer matrix of the beam. Once the matrix has been determined by numerical integration of the equations, the eigenvalues of vibration and the critical flutter loads are obtained. The method is applied to beams with linearly, parabolically and exponentially varying depths, subjected to a concentrated, uniformly distributed or linearly distributed follower force, and the natural frequencies and flutter loads are calculated numerically, from which the effects of the varying cross-section, slenderness ration, follower force and the stiffness of the supports on them are studied.     

Dynamic behaviour of a simply supported circular cylindrical panel subjected to an initial bending moment

The vibration of cylindrical panels with simply supported boundary conditions in the presence of an initial bending moment is investigated. The analysis is based on the theory of Herrmann and Armenàkas. The results for the stability and free vibration of the panels are obtained as special cases.     

Vibration analysis and design optimization of viscoelastic sandwich cylindrical shell

Damping properties of viscoelastic sandwich structure can be improved by changing some parameters such as thickness of the layers, distribution of partial treatments, slippage between layers at the interfaces, cutting and its distribution at the top and core layers. Since the optimization problem may result in a thick core layer, for achieving more accuracy a new higher-order Taylor's expansion of transverse and in-plane displacement fields is developed for the core layer of sandwich cylindrical shell in which the displacement fields at the core layer are compatibly described in terms of the displacement fields at the elastic faces. The presented model includes fewer parameters than the previously developed models and therefore decreases the number of degree of freedom in the finite element modeling. The transverse normal stress in the core layer is also considered. The formulations are developed to consider the slippage between layers at the interfaces. Finally, by combining the finite element method and the optimization algorithms based on the genetic algorithm and sequential quadratic programming technique, a design optimization methodology has been formulated to maximize the damping characteristics using the optimal number and location of cuts and partial treatments with optimal thicknesses of top and core layers.     

Axially symmetric stability of a completely free circular plate subjected to a non-conservative edge load

This paper presents a study on the behaviour of the vibration and stability of a two dimensional structure: i.e., a completely free circular plate subjected to non-conservative radial loading. The eigencurves and mode shapes of the circular plate are presented for various values of the non-conservativeness parameter. Some interesting conclusions concerning the behaviour of a completely free plate are drawn from the analytical investigation of the solution of the problem and from the numerical calculations as well.     

Vibration and stability of a circular plate of unidirectionally varying thickness

An analysis is presented for the vibration and stability of an elastically restrained circular plate of unidirectionally varying thickness subjected to an in-plane force. For this purpose, the transverse deflection of a circular plate of variable thickness is written in a series of the deflection functions of a uniform circular plate without the action of a force. The dynamical energies of the plate are evaluated analytically, and the frequency equation of the plate is derived by the Ritz method. The analysis is applied to circular plates of unidirectionally tapered or stepped thickness; the natural frequencies and the divergence loads are calculated numerically, and the effects of the varying thickness and edge conditions on the vibration and stability are studied.     

Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments

This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid–structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.     

Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators

A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.     

Vibration and stability analysis of polar orthotropic uniform discs subjected to peripheral hydrostatic loading

An analysis based upon the annular finite element method is carried out of the transverse vibration and stability of uniform polar orthotropic discs subjected to peripheral hydrostatic loading. Both the axi- and anti-symmetrical modes are considered for both clamped and simply supported at the outer peripheral radius. By separation of the flexural and geometric (membrane) components, the effect on both with respect to the degree of orthotropy is plotted and subsequently both components can be easily combined to produce the natural frequencies of the loaded disc. A simple relationship is derived to determine whether the lowest critical buckling mode is that containing zero nodal diameters and circles or some higher mode.