Circular Annular Plates Research Articles

Features of MHD on Secant Curved Annular Circular Plate Lubricant as a Couple-Stress Fluid with Slip Velocity

The purpose of this study is to examine the magneto-hydrodynamic (MHD) and slip velocity effect on secant curved annular circular plates lubricated with couple stress fluid and to derive the modified Reynolds’s equation for non-Newtonian fluid under various operating conditions to obtain the optimum bearing parameters. Based upon the MHD theory and Stokes theory for couple stress fluid, the governing equations relevant to the problem under consideration are derived. This paper analyses the effect of slip velocity on secant curved annular circular plates with an electrically conducting fluid in the presence of a transverse magnetic field. It is found that there is an increase in squeeze film pressure, load carrying capacity and squeeze film time in secant curved annular circular plates due to the presence of magnetic effects with couple stress fluid and slip velocity.

Free Vibration Analysis of Functionally Graded Annular Circular Plates Using Classical Thin Plate Theory Based on Physical Neutral Surface

Free Vibration Analysis of Functionally Graded Annular Circular Plates Using Classical Thin Plate Theory Based on Physical Neutral Surface

Dynamic response of an annular circular plate made of shape memory alloy using differential quadrature method

This study investigates the dynamic response of an annular circular plate with clamped edges under harmonic load. The circular plate is analyzed based on the first-order shear deformation theory (FSDT). The Boyd-Lagoudas constitutive model is used to simulate the pseudoelastic behavior, and Hamilton’s principle is used to obtain the equations of motion. Also, differential quadrature and Newmark methods are utilized to obtain the time and frequency responses of the plate. The phase transformation effects are studied on the time and frequency responses of the plate. Then, the accuracy of these results is checked with the available literature and ABAQUS software. Results indicate that the alloy phase transformation leads to reduced material strength and the nonlinear behavior of the alloy.

Natural Frequencies Calculation of Composite Annular Circular Plates with Variable Thickness Using the Spline Method

The present study adds to the knowledge of the free vibration of antisymmetric angle-ply annular circular plates with variable thickness for simply supported boundary conditions. The differential equations in terms of displacement and rotational functions are approximated using cubic spline approximation. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of the annular circular plates is examined for circumferential node number, radii ratio, different thickness variations, number of layers, stacking sequences and lamination materials.

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.

Determination of Prestress in Circular Inhomogeneous Solid and Annular Plates in the Framework of the Timoshenko Hypotheses

Determination of prestress fields in structures is of the utmost importance, since they have a significant impact on operational characteristics, and their level and distribution must be strictly controlled. In this paper, we present modeling of bending vibrations of solid and annular round inhomogeneous prestressed plates within the framework of the Timoshenko hypotheses. New inverse problems of prestress identification in plates are studied on the basis of the acoustic response subjected to some probing load. To solve direct problems on calculating oscillations and amplitude-frequency characteristics, a computational Galerkin-method-based scheme has been developed. In order to treat the inverse problems, we use a special projection approach based on the constructed weak problems statements, which makes it possible to determine the desired characteristics in the given classes of functions. The developed techniques for solving direct problems are implemented in the form of software packages realized via Maple. For both solid and annular plates, we estimate the sensitivity of the amplitude-frequency characteristics the values of which are used as the additional data in the inverse problems to a change in the prestress level; we conclude that the most favorable frequency range should be selected in the resonance vicinity. We have conducted a series of computational tests on reconstructing the plate’s prestresses of various levels and distribution patterns (decreasing, increasing, sign-changing laws). The results of computational tests revealed that the technique developed allows for the determination of the prestresses with a low error for two cases: when the cause of prestress formation and its type are known and when arbitrary prestress changing laws are considered.

Effect of Hydrostatic Pressure on Nonlinear Vibrating of Annular Circular Plate Coupled with Bounded Fluid

The present study aims to evaluate the nonlinear vibration of an annular circular plate in contact with the fluid. Analysis of plate is based on first-order Shear Deformation Theory (FSDT) by considering of rotational inertial effects and transverse shear stresses. The governing equation of the oscillatory behavior of the fluid is determined by solving the Laplace equation and satisfying its boundary conditions. The nonlinear differential equations are solved based on the differential quadrature method and obtaining nonlinear natural frequency. In addition, the numerical results are presented for a sample plate, and the effect of some parameters such as aspect ratio, boundary conditions, fluid density, and fluid height are investigated. Finally, the results are compared with those of similar studies in the literature.

Free Vibration and Transmission Response Analysis for Torsional Vibration of Circular Annular Plate

In this paper, free vibration and transmission response for the torsional vibration of circular annular plate are presented. To the author’s knowledge, few studies can be found for the torsional vibration from wave standpoint. For this purpose, in this study, natural frequencies for the torsional vibration of annular plate with clamped–clamped and free–free boundaries are calculated. The natural frequencies obtained by wave approach are compared with those derived by the classical method. Furthermore, transmissibility curves of the periodic annular model and Fibonacci annular model are analyzed. The finite element simulations are carried out to verify the theoretical results. Finally, the influence of inner radius and length ratio on the transmission response is also discussed. The obtained results are useful for the torsional vibration reduction of machinery structures.

Regenerative instabilities of spring-guided circular saws

This paper presents analytical model-based analysis of the stability of spring-guided rotating and flexible circular saws subjected to regenerative lateral cutting forces. The saw is modelled as an annular circular plate constrained by a guide modelled as a point spring. The governing equation of motion accounts for inertial, gyroscopic, and stiffness terms, and the time-dependent periodic forces generated by the saw-workpiece interaction. Stability analysis for different materials and engagements show regenerative instabilities to be influenced by the guide, and critical speed related instabilities to not change with the guide. Results are instructive to guide the design of stable sawing processes.

Free vibration of circular annular plate with different boundary conditions

This paper deals with the numerical simulation of free vibration analysis of a thin circular annular plate for various boundary conditions at the outer edge and inner edge. Classical plate theory is used to derive the governing differential equation for the transverse deflection of the thin isotropic plate. The finite element method is used to evaluate the first six natural frequencies and mode shapes of the thin uniform circular annular plate with radius ratios (r1/r2) for different boundary conditions. These natural frequencies results are compared with those available in the literature. The results are verified with classical plate theory with our Abaqus results and checked with the previous research literature on the topic.

Tensor-decomposition based matrix computation: A fast method for the isogeometric FSDT analysis of laminated composite plate

Abstract This paper presents an efficient computation method for matrices in the isogeometric analysis (IGA) of laminated composite plates, based on the First order Shear Deformation Theory (FSDT). In the method, the stiffness matrix, mass matrix and geometric stiffness matrix for static, vibration and buckling analyses are adapted into tensor-product forms and 2D integrals of the matrices are decomposed into Kronecker product of 1D integrals, which leads to the improvement of computational efficiency. Several experiments that apply the method to the static analysis and design optimization of laminated composite plates are presented in this paper to demonstrate its effectiveness. The first experiment studies the case that the domain parameterization has a diagonal Jacobian matrix (rectangular plate), and the result shows that the computation time of global matrices is drastically reduced while their accuracy is not affected compared with traditional computation methods. The second experiment is about the case of non-diagonal Jacobian matrix. The results of circular plate, annular plate and square plate with complicated cutout show that the matrices calculation is also remarkably sped up when its model is formed in NURBS. Although the tensor-decomposition incurs certain approximation in the second case, the results still show high accuracy. The third and fourth ones study the computation efficiency of design optimization, respectively about the constant-stiffness and variable-stiffness designs when the proposed method is applied to the analysis in each iteration. All the experiments prove the high efficiency of the proposed method.

Comparison for the Effect of Different Attachment of Point Masses on Vibroacoustic Behavior of Parabolic Tapered Annular Circular Plate

In this paper, a comparison for the effect of different arrangement of point masses on vibroacoustic behavior of parabolic tapered annular circular plate with different taper ratios are analyzed by keeping the total mass of the plate plus point masses constant. Three different arrangement of thickness variation are considered. The mathematical tool FEM using ANSYS is used to determine the vibration characteristic and both FEM and Rayleigh integral is used to determine the acoustic behavior of the plate. Further, Case II plate (parabolic decreasing increasing thickness variation) for all combination of point masses is found to have reduction in natural frequency parameter in comparison to other cases of parabolic tapered plate. In terms of acoustic behavior, sound power levels of different cases of plate with different point mass combination are observed. It is observed that the Case II plate with two point masses combination shows the highest sound power and the Case III plate for all cases of point mass combination is least prone to acoustic behavior. Furthermore, It is observed that at low forcing frequency average radiation efficiency of parabolic tapered plate for different arrangement of point masses is almost same, but at high forcing frequency average radiation increases for higher taper ratio. Finally, a brief discussion of peak sound power reduction and actuation for different arrangement of point masses with different taper ratios are provided.

Bending of an annular three-layer circular plate

Abstract The main objective of this work is the numerical analysis of the strength and stiffness of an annular three-layer circular plate with variable mechanical properties of the core. The plates are subjected to bending. Numerical analysis of the deflection phenomenon is carried out under different support conditions of the plate. Furthermore, the influence of the material properties of the core (linear and non-linear model) on the shear stresses and deflecions is also investigated.

Mathematical modeling for estimation of acoustic radiation from clamped free tapered annular circular plate having different parabolically varying thickness

In this study, a comparison of sound radiation characteristic of a clamped free annular circular plate with different parabolically varying thickness with different taper ratios 0.25, 0.50 and 0.75 with different excitation locations are analyzed by keeping the mass of the plate constant. Rayleigh integral is applied to determine the acoustic behavior of the plate. The same problem is also solved by FEM to draw the comparison. It is observed that excitation locations and modes have a significant effect on sound power level in comparison to stiffness variation due to different taper ratios. Further, the variation of peak sound power level is investigated with different taper ratio with different excitation locations. Finally, the design options for peak sound power are suggested for different excitation locations with different taper ratios.

Theoretical and Numerical Estimation of Vibroacoustic Behavior of Clamped Free Parabolic Tapered Annular Circular Plate with Different Arrangement of Stiffener Patches

This paper compares the vibroacoustic behavior of a tapered annular circular plate having different parabolic varying thickness with different combinations of rectangular and concentric stiffener patches keeping the mass of the plate and the patch constant for a clamped-free boundary condition. Both numerical and analytical methods are used to solve the plate. The finite element method (FEM) is used to determine the vibration characteristic and both Rayleigh integral and FEM is used to determine the acoustic behavior of the plate. It is observed that a Case II plate with parabolic decreasing–increasing thickness variation for a plate with different stiffener patches shows reduction in frequency parameter in comparison to other cases. For acoustic response, the variation of peak sound power level for different combinations of stiffener patches is investigated with different taper ratios. It is investigated that Case II plate with parabolic decreasing–increasing thickness variation for an unloaded tapered plate as well as case II plate with 2 rectangular and 4 concentric stiffeners patches shows the maximum sound power level among all variations. However, it is shown that the Case III plate with parabolically increasing–decreasing thickness variation with different combinations of rectangular and concentric stiffeners patches is least prone to acoustic radiation. Furthermore, it is shown that at low forcing frequency, average radiation efficiency with different combinations of stiffeners patches remains the same, but at higher forcing frequency a higher taper ratio causes higher radiation efficiency, and the radiation peak shifts towards the lower frequency and alters its stiffness as the taper ratio increases. Finally, the design options for peak sound power actuation and reduction for different combinations of stiffener patches with different taper ratios are suggested.

Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM

ABSTRACTThe purpose of this paper is to investigate the bending, buckling, vibration analyses of microcomposite circular-annular sandwich plate with CNT reinforced composite facesheets under hydro-thermo-magneto-mechanical loadings are presented using first order shear deformation theory (FSDT) and modified strain gradient theory (MSGT) that includes three material length scale parameters. Also, an isotropic homogeneous core is considered for microcomposite circular-annular sandwich plate. The generalized rule of mixture is employed to predict mechanical, moisture and thermal properties of microcomposite sandwich plate. By using Hamilton’s principle, governing equations are solved by differential quadrature method (DQM) for a circular annular sandwich plate. The predicted results are validated by carrying out the comparison studies for the FGM plates by modified couple stress theory (MCST). The obtained results are given to indicate the influence of the material length scale parameter, core- to-facesheet thickness ratios, magnetic effect, thermal and moisture effects on the dimensionless deflection, critical buckling load, and natural frequency of microcomposite circular sandwich plate. The results can be employed in solid-state physics, materials science, nano-electronics, and nano electro-mechanical devices such as microactuators, and microsensor.

Dynamic response of circular and annular circular plates using spectral element method

This paper presents development of the spectral element method (SEM) for analysis of circular and annular circular plates vibration under impact load. A novel formulation is proposed in frequency domain for conducting spectral element matrix. Several numerical examples are presented in order to demonstrate performance of the presented method compared to other numerical methods in literature. The presented formulation was applied in order to analyze vibration of annular circular plates with various thicknesses and various internal-to-external radius ratios. In addition, annular circular plate displacements subjected to an impact load were calculated using the presented SEM.

Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings

In this article, stresses and free-vibration behaviors of annular circular piezoelectric nanocomposite plate reinforced by functionally graded single-walled boron nitride nanotubes (FG-SWBNNTs) embedded in an elastic foundation based on modified couple stress theory (MCST) are explored. The mechanical properties of FG-SWBNNT-reinforced nanocomposite plate are assumed to be graded in the direction of thickness and estimated through the micro-mechanical approach. The governing equations are obtained using the energy method. The natural frequencies and stresses of FG-SWBNNT-reinforced nanocomposite plate are computed using the differential quadrature method (DQM). An excellent agreement is observed between the obtained results and the results in the literature. Influences of the internal radius to the external radius, the thickness to the internal radius ratio, the material length scale parameter, the functionally graded parameter, temperature changes and elastic coefficients on the natural frequencies and stresses of the hollow circular nanocomposite plate are investigated. The results of this research show that the natural frequencies of the piezoelectric nanocomposite plate increase by increasing the material length scale parameter, the elastic foundation parameters, the ratio of the inner radius to the outer radius, the ratio of the thickness to the inner radius, and decreasing the power index and temperature change. The radial stress of the nanocomposite plate varies proportionally to its mode shape. The results can be employed to design smart structures in micro-electro-mechanical systems (MEMS).

Closed-form solution for circular microstructure-dependent Mindlin plates

In this paper, we derive a general closed-form solution for the static, axisymmetric bending of solid and annular microstructure-dependent Mindlin plates based on the modified couple-stress theory. The solution is developed by employing a suitable change in displacement variables. The couple-stress solution contains modified Bessel functions which do not appear in the classical case. The stress distributions of the annular microstructure-dependent plate are obtained in terms of load resultants by using the general closed-form solution. Analytical and numerical examples considering solid and annular circular plates are presented. The examples include simply supported and clamped solid and annular plates subjected to a uniformly distributed load and annular plates attached to a point-loaded rigid shaft.

Analytical and experimental free vibration analysis of multi-layer MR-fluid circular plates under varying magnetic flux

Free vibration characteristics of sandwich annular circular plates comprising magneto-rheological (MR) fluid as the core layer are evaluated analytically and experimentally. An analytical model of the sandwich annular plate was formulated using Ritz method based on the classical plate theory. The numerical analyses were performed to study the free vibration responses of the sandwich plate in terms of resonant frequencies and loss factors considering variations in the magnetic flux and boundary conditions. The experiments were conducted on a free-free sandwich circular plate comprising two PETG (Polyethylene Terephthalate Glycol) face layers constraining the MR fluid core layer. A hollow-core electromagnet was developed for inducing variable magnetic flux over the structure. The free vibration properties of the sandwich plate were measured using MEscop VES modal analyzer. The measured data were analyzed to determine natural frequencies of the MR sandwich plate under different levels of the magnetic flux, which were subsequently used to examine validity of the analytical model. Furthermore, the effects of plate parameters on the natural frequencies and damping of the structure were investigated. The results suggested that increasing the flexibility of the face layers yields more pronounced effect of magnetic flux on the structure stiffness properties.