Annular Plates Research Articles

Refined Deformation Model for Metal-Composite Plates of Regular Layered Structure in Bending Under Conditions of Steady-State Creep

The problem of the mechanical behavior of metal-composite plates of regular layered structure in bending under conditions of steady-state creep of all phase materials is formulated. Equations describing, with various degrees of accuracy, the stress and viscous creep states of such plates with account of their weakened resistance to transverse shears are obtained. The relations of the classical Kirkhoff theory, the nonclassical Reissner theory results, and the second variant of Timoshenko theory result as special cases of these equations. For asymmetrically loaded annular plates with one edge clamped and statically loaded other one, a simplified variant of the refined theory, whose complexity in practical realization is comparable to that of the Reissner theory, is developed. The bending deformations of such annular plates at different levels of thermal actions are calculated. It is shown that, with increasing temperature, the accuracy of calculations within the framework of the traditional theories decreases sharply and neither of them provides an accuracy for the calculated compliance of the structure even within 20%.

The Experiment of the Clog Reduction in a Plane Silo

The flow of particles may be clogged when they pass through a narrow orifice. Many factors can change the probability of clogging, such as the outlet size, the presence of obstacles and external perturbation, but the detailed mechanisms are still unclear. In this paper, we present an experimental study of reduction of the clogging probability in a horizontal plane silo, which consists of a layer of elastic particles transported on an annular flat plate rotating with a constant angular velocity passing through a hopper structure. We found the exponential distributions of the avalanche size for different sizes of orifice and the power law tails of the passing time between two particles. We did not confirm whether there was a critical size of orifice above which the clogging became impossible. We explored the effect of the obstacle on the probability of clogging: and if we chose a proper obstacle placed at a proper position, the probability of clogging could be reduced by a factor of about seven.

Buckling of an annular plate under tensile point loading

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.

Static analysis of non-uniform heterogeneous circular plate with porous material resting on a gradient hybrid foundation involving friction force

This paper is concerned with the static analysis of variable thickness of two directional functionally graded porous materials (FGPM) circular plate resting on a gradient hybrid foundation (Horvath-Colasanti type) with friction force and subjected to compound mechanical loads (e.g., transverse, in-plane shear traction and concentrated force at the center of the plate).The governing state equations are derived in terms of displacements based on the 3D theory of elasticity, assuming the elastic coefficients of the plate material except the Poisson‟s ratio varying continuously throughout the thickness and radial directions according to an exponential function. These equations are solved semi-analytically by employing the state space method (SSM) and one-dimensional differential quadrature (DQ) rule to obtain the displacements and stress components of the FGPM plate. The effect of concentrated force at the center of the plate is approximated with the shear force, uniformly distributed over the inner boundary of a FGPM annular plate. In addition to verification study and convergence analysis, numerical results are displayed to show the effect of material heterogeneity indices, foundation stiffness coefficients, foundation gradient indices, loads ratio, thickness to radius ratio, compressibility, porosity and friction coefficient of the foundation on the static behavior of the plate. Finally, the responses of FG and FG porous material circular plates to compound mechanical loads are compared.

Determining Method of Distorted Scaling Laws of the Thin Walled Annular Plates’ Structures

Determining Method of Distorted Scaling Laws of the Thin Walled Annular Plates’ Structures

Application of Non-classical Shells Theories for Free Vibration Analysis of Annular Plates

In the present paper, the problem of evaluation natural frequencies of a transversely isotropic circular plate is considered and the impact of the material properties of the plate on its natural frequencies is studied. The classical Kirchhoff-Love (KL) theory only takes into account material properties of the midplane. That is why the fundamental frequencies for isotropic and transversely isotropic plates are equal for the classical theory. The Ambartsumyan (A) theory of anisotropic shells takes into account the impact of the shear deformation in the thickness direction on the stress-strain state of the plate. In the general case, the theory of anisotropic plates and shells developed by Rodionova, Titaev, and Chernykh (RTC) permits one to take into account not only the transverse shears, but also the deformation of normals to the midplane. In the present paper, the problem of determining the fundamental frequencies is solved both with A and RTC theories, which improve the KL theory. To study the impact of the radial inhomogeneity on the plate fundamental frequencies, the calculations are carried out using the commercial finite element software COMSOL Multiphysics (v. 5.0). It is shown that the inhomogeneity of the plate affects greatly the fundamental (lowest) frequency of the plate, while the plate non-isotropy has a greater influence on the second and higher vibration modes

A Unified method for vibration analysis of moderately thick annular, circular plates and their sector counterparts subjected to arbitrary boundary conditions

The vibrations of circular, annular and sector plates are different boundary value problems due to different edge conditions and thus have been treated separately using different solution algorithms and procedures. In this paper, a unified method is proposed for vibration analysis of moderately thick annular, circular plates and their sector counterparts with arbitrary boundary conditions. The unification of these plates is physically achieved by applying the coupling spring’s technique at the radial edges to ensure appropriate continuity conditions. Irrespective of the shape of the plate and the type of boundary conditions, each of the displacement function is expressed as a new form of trigonometric expansion with high convergence rate. Unlike most of the previous studies the current method can be universally applied to a wide range of vibration problems involving different shapes, boundary conditions, varying materials and geometric properties without modifying the solution algorithms and procedure. Furthermore, the current method can easily be applied to sector plates with an arbitrary inclusion angle of 2π. The accuracy, reliability and versatility of the proposed method are fully demonstrated with several numerical examples for different shapes of plates and under different boundary conditions.

Exact elasticity-based finite element for circular plates

In this paper, a general elasticity solution for the axisymmetric bending of a linearly elastic annular plate is used to derive an exact finite element for such a plate. We start by formulating an interior plate problem by employing Saint Venant’s principle so that edge effects do not appear in the plate. Then the elasticity solution to the formulated interior problem is presented in terms of mid-surface variables so that it takes a form similar to conventional engineering plate theories. By using the mid-surface variables, the exact finite element is developed both by force- and energy-based approaches. The central, non-standard feature of the interior solution, and the finite element based on it, is that the interior stresses of the plate act as surface tractions on the plate edges and contribute to the total potential energy of the plate. Finally, analytical and numerical examples are presented using the elasticity solution and the derived finite element.

A comparative study on the smart damping capabilities of cylindrically orthotropic piezoelectric fiber–reinforced composite actuators in vibration control of simply supported/fully clamped isotropic annular plate

For active control of vibration of plane structures of revolution, a cylindrically orthotropic piezoelectric fiber–reinforced composite actuator is addressed in a recent study. Some other available piezoelectric composites, which are originally constructed in Cartesian coordinate frame, can also be reconstructed in polar coordinate frame for similar application. Making use of all these piezoelectric composites in polar coordinate frame of an annular plate, a comparative study on their control capabilities is performed at present. All the piezoelectric composites are used in the form of patches which are optimally configured over the host plate surface and utilized as smart dampers. The geometrical and material properties of the piezoelectric composites are taken in uniform manner and the corresponding electric fields in function of applied voltage are evaluated for derivation of a closed-loop finite element model of the smart annular plate. First, the patches of every piezoelectric composite are optimally configured through the proposition of a new methodology. Next, the control/damping capabilities of the piezoelectric composites are evaluated for fundamental symmetric/asymmetric mode of vibration of the plate. The numerical results first illustrate the implementation and suitability of the present methodology for optimal size and locations of actuator patches. Subsequently, the results demonstrate damping capabilities of all the piezoelectric composites to label potential ones.

A Modified Fourier Solution for Free Damped Vibration Analysis of Sandwich Viscoelastic-Core Conical Shells and Annular Plates with Arbitrary Restraints

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

Lumped element modeling of air-coupled capacitive micromachined ultrasonic transducers with annular cell geometry

Air-coupled capacitive micromachined ultrasonic transducers (CMUTs) based on annular cell geometry have recently been reported. Finite element analysis and experimental studies have demonstrated their significant improvement in transmit efficiency compared with the conventional circular-cell CMUTs. Extending the previous work, this paper proposed a lumped element model of annular-cell CMUTs. Explicit expressions of the resonance frequency, modal vector, and static displacement of a clamped annular plate under uniform pressure were first derived based on the plate theory and curve fitting method. The lumped model of an annular CMUT cell was then developed by adopting the average displacement as the spatial variable. Using the proposed model, the ratio of average-to-maximum displacement was derived to be 8/15. Experimental and simulation studies on a fabricated annular CMUT cell verified the effectiveness of the lumped model. The proposed model provides an effective and efficient way to analyze and design air-coupled annular-cell CMUTs.

Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method

Abstract In this study, free vibration analysis of conical and cylindrical shells and annular plates made of composite laminated and functionally graded materials (FGMs) is investigated. Carbon nanotubes reinforced (CNTR) composite case is also taken consideration for FGM. The equations of motion for conical shell are obtained via Hamilton's principle using the transverse shear deformation theory. To obtain the eigenvalue problem of the system, the method of discrete singular convolution is employed. Material properties are graded in the thickness direction according to a volume fraction power law and four-parameter power law indexes for FGM cases. Five types of distributions of CNTR material are also considered. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. Free vibrations of cylindrical shells and annular plates with FGM are treated as special cases. Results are also presented for carbon nanotubes reinforced (CNTR) composite cylindrical shells and annular plates. It is found that the convergence and accuracy of the present DSC method is very good for vibration problem of shells with functionally graded materials (FMG) and CNTR functionally graded materials.

Guided wave propagation in rotating functionally graded annular plates

Elastic guided wave propagation in a rotating functionally graded material (FGM) annular plate is presented in this paper. The material properties are assumed to vary continuously along the radial direction. The elastodynamic equation of annular plates which take into account initial hoop, centrifugal and Coriolis effects is derived, and the wave finite element method is extended to model wave motion related to rotation with 3D-Chebyshev spectral elements. Firstly, wave properties in a straight bar are computed and compared to that of the Rayleigh–Ritz method. Then, wave propagation in the FGM annular plate with various material gradient indexes is considered and the results indicate that the index has large influence on wave characteristics. With contour profiles of transverse sections, propagating wave modes in the plate can be identified distinctly. Besides, the effects of rotation on wave propagation are discussed, which show that the extensional-like and shearing-like wave modes are very sensitive to the rotation at low frequencies but the flexural are not. In addition, the curve veering phenomenon existing in FGM annular plates is also found, which analyzes the influences of material gradient index and rotating speed and points out the variations in the relative critical frequencies.

Frequencies of FGM shells and annular plates by the methods of discrete singular convolution and differential quadrature methods

Free vibration analysis of curved structural components such as truncated conical shells, circular cylindrical shells and annular plates has been investigated numerically in this paper. The method of discrete singular convolution (DSC) and the method differential quadrature (DQ) are used for numerical simulations, respectively. Related partial differential equations governed the motion of the structures obtained from higher-order shear deformation theory have been solved by using these two methods in the space domain. Different material properties have been considered such as isotropic, laminated and functionally graded material (FGM). Four-parameter power law and simple power law distributions have been used for ceramic volume fraction in FGM cases. The numerical results related to free vibration of conical shells have obtained by the present two techniques compare well with the results available in the literature. Results for circular cylindrical shells and annular plates have also been presented for different geometric and material parameters. The effects of grid number and types of the grid distribution have also been investigated for annular plate and shells.

Axisymmetric Problem of Thermoplasticity for a Piecewise Homogeneous Ring

We develop an analytic approach to the determination and analysis of axisymmetric thermoplastic states in piecewise homogeneous rings subjected to nonstationary heating. The numerical analyses of the thermoplastic states of two- and three-layer annular plates are performed. An example of the problem of determination of compressive residual stresses in a plate subjected to local heating by a normal circular heat source illustrates the efficiency of the proposed approach in the case where the yield strength is a function of temperature.

Customizable tool geometries by additive manufacturing for mechanical rheometry of soft matter

The advent of low-cost, customizable, additive manufacturing methods of 3D printing offers promise for applications in mechanical rheometry. By taking advantage of the high in-plane resolution of a consumer-grade fused-deposition 3D printer and using solvent welding, we design and manufacture both standard and customized plastic tool geometries suitable for use in mechanical rheometers. In particular, 3D-printed tools can be designed to match available sample volumes of soft materials, and, while these plastic tools can be reused in many cases, they can also be disposable, especially when certain materials can be very difficult to clean. Here, we demonstrate the versatility of this approach by designing and producing a raised annular parallel plate geometry, which offers a more uniform strain field and a higher torque than a standard parallel plate geometry. We also show that customized tool roughness can be directly printed, and we demonstrate that 3D-printed roughened tools can provide a noticeable improvement over smooth metal tools in mechanical rheometry. Overall, selective design and use of consumer-grade 3D printers opens up many exciting directions in mechanical rheometry.

Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading

Abstract The main objective of this paper is to present the buckling and vibration analysis of thermally pre-stressed functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates resting on the elastic foundation via the variational differential quadrature (VDQ) method. The material properties of nanocomposite plate are considered to continuously vary across the thickness and are estimated according to the modified rule of mixture. The governing equations are derived on the basis of first order shear deformation theory. Applying two-dimensional generalized differential quadrature (GDQ) method, the energy functional of the structure is discretized. Then, based on Hamilton's principle and the VDQ method, the reduced forms of mass and stiffness matrices are obtained. After verifying the accuracy of the present method, comprehensive numerical results are presented to examine the effects of important parameters on the stability and vibrational behavior of the nanotube-reinforced composite annular sector plates. The results indicate that functionally graded distributions of CNTs in the thickness direction and the increase of elastic foundation coefficients can improve the stability of the structure.

Stability of Three-Layered Annular Plate with Composite Facings

Paper presents the behaviour of three-layered annular plates subjected to loads acting in plate plane. Plates are composed of laminated fibre-reinforced composite facings and foam core. The static and dynamic parameters of plate critical state were evaluated. The sensitivity of composite structure of plate to the acting of quickly increasing in time loads is shown. The problem has been solved numerically using the finite element method. Results have been compared with ones obtained for plate models with isotropic layers. These plate models have also been calculated solving formulated task analytically and numerically by means of the finite difference method. Solutions to the problem concern the axisymmetrical and asymmetrical plate buckling modes. Numerous presented tables and figures create the image of the stability behaviour of examined composite plates.

Discrete singular convolution method for the free vibration analysis of rotating shells with different material properties

Using the discrete singular convolution (DSC) method, this paper presents the free vibration analysis of rotating truncated conical shells, circular shells and panels. Isotropic, orthotropic, functionally graded materials (FGM) and laminated material cases are considered. The influences of centrifugal and Coriolis accelerations and the effects of initial hoop tension have been taken into account. The present analysis is based on Love’s first approximation shell theory. Frequency values are obtained for different types of boundary conditions, rotating velocity, circumferential wave number, geometric and material parameters. To verify the accuracy of this method, comparisons of the present results are made with results available in the literature. Some results related to rotating annular plates are also presented via conical shell equations. It is shown that the present method is reliable and applicable for vibration analysis of rotating shells and plates.

Trapping and manipulation of a small object in the space between two pipes placed to the counter direction

A small object can be trapped in the space between two pipes which are placed to the counter direction and radiated traveling acoustic waves from the pipe ends. In the study, two pipes vibrating in axisymmetric flexural damped traveling wave to generate acoustic flow in the pipe inside are used. The flow propagates in the pipe inside and is radiated for traveling acoustic waves from the pipe end. The pipe made of polycarbonate is used for ultrasonic transmission pipe and two piezo-ceramic annular plates are adhered at the each pipe end for exciting the vibration modes. The first radial vibration mode of the annular plate is used and its resonance frequency is about 59 kHz. When the two vibrators are driven in opposite phase, a small object can be trapped at intermediate point in the space between two pipe ends. The gap of the space is about 10 mm. The trapping object can be shifted its position corresponding to the phase difference of the two driving voltages. That is, the object can be moved on non-contact manipulation in the space between the two pipe ends. These results are confirmed experimentally and by simulation according to FEA.