Annular Plates Research Articles

Harmonic response analysis of a circular plate subjected to moving point loads using Green’s function approach

Dynamics of circular plates under moving loads are an important class of problems in manufacturing industry, for example, cutting thin annular plates using point cutting tools and wood/bar/pipe cutting saws. These tools are subjected to excessive vibration during operation. Its dynamic behavior needs to be analyzed rigorously. In the present work, dynamics of a circular plate subjected to moving harmonic point load is analyzed using Kirchhoff’s plate hypothesis. In order to capture the geometric nonlinearity, the von Kármán strain displacement relation is used. Constitutive relations are developed using a complex modulus. Further, extended Hamilton’s principle is used to obtain the nonlinear coupled governing equations in radial, tangential, and transverse directions. Governing equations are discretized using Galerkin’s method. The novelty in the present work is to develop Green’s function incorporating viscous damping to obtain the plate response subjected to arbitrary moving load for general boundary conditions. The proposed method is capable to obtain the plate response due to single/multi point moving loads. In order to verify the accuracy of the proposed method, Green’s function solution is compared with the numerical solution obtained from the RK4 method and shows good agreement. Further, resonance instabilities are studied, which occur when a single point load rotates with critical angular velocity. Subsequently, the response of the circular plate under three-point loads, each having a magnitude of 1/3rd of the single moving point load moving circularly in a constant phase has been discussed. In the end, a parametric study of hysteresis damping on the dimensionless deflection of the plate is carried out.

Annular sector plates made of FG graphene origami-enabled auxetic metamaterial under bending and buckling loading: A VDQ-based approach

The behaviors of annular sector plates made of functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAMs) under the action of buckling and bending loads are investigated herein using a numerical approach. Multiple GOEAM layers with graphene origami (GOri) content are considered for the plate which changes in layer-wise patterns. Moreover, the material properties of the plate are calculated using novel genetic programming-assisted micromechanical models. In order to derive the governing equations, the Mindlin plate theory in conjunction with Hamilton’s principle is utilized within the framework of the variational differential quadrature (VDQ) method. The vector-matrix representation of the presented formulation can be beneficial from the viewpoint of implementing numerical approaches. The governing equations are then discretized and solved based on VDQ matrix differential and integral operators so as to obtain the critical buckling load and maximum lateral deflection of plates with different edge conditions. The effects of GOri content, folding degree and distribution pattern on the results are studied. It is revealed that increasing the GOri content leads to the negative Poisson’s ratio (NPR) effect which respectively reduces and increases the lateral deflection and the critical buckling load.

Free vibration analysis of bio-inspired helicoidal laminated composite square and annular plates having circular openings using isogeometric analysis

Present work aims to carry out free vibration analysis of bio-inspired helicoidal laminated composite square and annular-shaped plates with circular openings. Refined plate theory, created within the context of isogeometric analysis (IGA) is used during the present study. The theory is coded in MATLAB to study the behavior of the plates and the results are validated with the frequencies obtained using ABAQUS. Recursive, semi-circular, exponential, and Fibonacci helicoidal schemes are used during the present study for studying the free vibration behavior and the frequency is compared with the conventional cross-ply and quasi-isotropic laminates. Influence of position of opening, dimensions of opening, number of plies, and end condition, on the free vibration behavior of square and annular shaped bio-inspired helicoidal plates is carried out. The plates with CCCC and CCCF ends having openings at the quarter length are found to have higher frequency by 3.518 % and 0.3897 % compared to the values of the frequency of the plate with opening at the centre with the same perimeter. Opposite trend is observed for plate with PPPP, CFCF, and CFFF end conditions, where the plate with opening at centre exhibits higher value of the frequency by 2.427 %, 0.821 %, and 1.232 %, respectively. When the opening is near to the corners, the decrease in frequency by 3.913 %, 1.576 %, 1.193 %, and 1.437 % is observed for CCCC, CCFF, CCCF, and CFCF end conditions while increase by 1.490 % and 2.717 % is observed for the CFFF and PPPP end conditions. The mode shape of the plate is found to be greatly influenced by the position and dimension of the hole and end conditions of the plate.

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.

Static and dynamic analysis of a hyperelastic toroidal air-spring structure

The present work proposes a novel toroidal air-spring model consisting of two cylindrical elastomeric membranes unlike conventional convoluted air-spring with one rubber bellow. The membranes are attached with two annular plates at top and bottom in circumferential direction, forming a closed space in between. With internally pressurizing the setup, the inflated bellow in the shape of a toroidal air-spring structure is formed. The static and dynamic analysis of the air-spring model is performed under transverse loading on top plate. The static analysis is carried out by compressing the air-spring to different suspension heights, assuming adiabatic compression of the enclosed air. The conditions for impending wrinkling, its prevention measures by choosing suitable design parameters, and the effect using cord-reinforced membranes are explored. The dynamic study under harmonic forcing is performed using the method of assumed modes coupled with a perturbation technique to solve the Eigenvalue problem of the discretized membrane structure. The radial asymmetric perturbations are included in the formulation to explore the symmetry breaking during dynamic study. The Eigen frequencies of the structure are obtained for different inflation pressures of the air-spring. Interestingly, a frequency veering phenomenon is observed between a few Eigen modes associated with closely spaced natural frequencies, where the possibility of mode swapping exists. The forced vibration analysis around a few Eigen frequencies shows beating like responses. The stiffness of the proposed air-spring is found to be linear under both static and dynamic conditions, which is inline with the stiffness nature of the convectional convoluted air-springs.

Symmetric and asymmetric vibration and buckling of a thermal rotating annular-plate with Pasternak foundation

This paper studies the symmetric and asymmetric vibration and buckling modes of a rotating thermal annular plate resting on a Pasternak foundation. With considering the von Kármán geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are established via Hamilton's principle, and then solved by using the differential quadrature method. With both inner and outer boundaries constrained, the modes of the rotating system vary differently depending on the mode symmetry. The symmetric modes are mainly affected by the generated centrifugal force, while the asymmetric ones are affected by both centrifugal and Coriolis forces. The additional Coriolis, with mainly two directions, strengthens the forward travelling parts of the asymmetric modes, but makes the backward counterparts buckled more easily. Also, the thermal effect, as well as boundary elasticity and foundation coefficients, are also investigated from the viewpoint of mode symmetry. Results show that the temperature rise can shift the fundamental vibration mode from the symmetric one to the asymmetric one and backward travelling waves for rotation, which also adds to the complexity of mode variation with joint parameters. For the joint effect of the temperature rise and rotating, the annular plate tends to buckle more readily while the effects of the two factors are linearly superimposed.

Enhancing the stability and efficiency of the advanced concrete structures surrounded by an auxetic foundation

This study delves into the vibrational characteristics of concrete annular plates reinforced with graphene oxide powders (GOP), underpinned by an innovative auxetic-elastic foundation. By applying Hamilton’s principle, the governing dynamic equations are meticulously derived, incorporating the effects of internal forces and GOP geometrical properties. The Differential Quadrature Method (DQM) is utilized to solve these equations, providing a robust and efficient numerical approach for analyzing the system’s complex dynamic behavior. GOP reinforcement significantly enhances the mechanical properties of the concrete plates, yielding improved stiffness and superior damping capabilities. The auxetic-elastic foundation, known for its unique property of becoming thicker perpendicular to the applied force, plays a pivotal role in altering the vibrational response of the system. The study meticulously examines the influence of this foundation on the system’s vibrational behavior, highlighting its potential to enhance performance under varying operational conditions. A comprehensive analysis is conducted to understand the effects of different boundary conditions on the vibrational characteristics of the reinforced concrete annular plates. The results underscore the importance of integrating advanced materials like GOP and innovative foundation designs in optimizing structural components. This study provides valuable insights into the design and application of reinforced concrete structures, emphasizing the effectiveness of GOP reinforcement and auxetic-elastic foundations in enhancing vibrational performance. These findings offer a significant contribution to the field of structural engineering, paving the way for future innovations in the design of resilient and efficient structural systems.

Vibration of bolted composite cylindrical-cylindrical flanged shells considering contact characteristics

A semi-analytical model for bolted composite cylindrical-cylindrical flanged shells (BCCFS) considering the influence of the flange and the connection characteristics of the bolted flange joint is established. In the model, flanges are treated as annular plate structures and modeled using Kirchhoff plate theory. To simulate the connectivity performance of the bolted flange joint, a surface-spring model considering the pressure distribution characteristics is developed and applied to the model of the bolted structure. A method based on fractal contact theory is proposed to identify stiffness-related parameters of the surface-spring model, which avoids additional tensile experiments of the bolted joint. Sufficient modal tests are performed to validate the accuracy of the model. Furthermore, the effects of flange thickness, length ratio of two shells, and quantity of bolts on the free vibration characteristics of the structure are studied. The frequency veering phenomenon with the variation of size parameters is found and analyzed in depth.

Stability Analysis of Planetary Rotor with Variable Speed Self Rotation and Uniform Eccentric Revolution in the Rubber Tapping Machinery

Natural rubber is a critical material that is essential to industry and transportation. In order to reduce the cost of rubber tapping and improve the efficiency and profitability of rubber production, the 4GXJ-2 portable electric rubber cutter and automatic rubber tapping robot have been developed. In their vibration tool holder, the planetary rotor with variable speed self rotation and uniform eccentric revolution is the most important transmission component, and its instability will cause irregular vibration of the tapping tool, thereby reducing the accuracy of vibration cutting and increasing noise. Base on the ANCF (Absolute Nodal Coordinate Formulation) 3D-beam element and 3D REF (3D Ring on Elastic Foundation), a novel eccentric 3D REF model of a planetary rotor is proposed. By introducing multiple coordinate systems, the coupled motion of uniform eccentric revolution, variable speed self rotation and flexible deformation is decomposed and the influences of these motions on the centrifugal force and Coriolis force are more clearly derived. The model is degraded and validated by comparing with other examples of a rotating circular ring model and uniformly eccentrically revolving annular plate. According to the Floquet theory and Runge−Kutta method, the unstable region of revolution speed of a planetary rotor in rubber tapping machinery is predicted as [817 rad/s, 909 rad/s], [1017 rad/s, 1095 rad/s] and [1263 rad/s,1312 rad/s]. Compared with the rubber-tapping experiment of rubber tapping machinery, the validity of the proposed model is further verified. This model provides important design references for the speed settings of those rubber tapping machines.

Magneto Axisymmetric Vibration of FG-GPLs Reinforced Annular Sandwich Plates with an FG Porous Core Using DQM and a New Shear Deformation Theory

Based on the differential quadrature procedure (DQP), the vibrational response of functionally graded (FG) sandwich annular plates enhanced with graphene platelets (GPLs) and with an FG porous core is illustrated in this paper. The current annular plate is assumed to deform axisymmetrically and expose to a radial magnetic field. The Lorentz magnetic body force is deduced via Maxwell’s relations. The effective physical properties of the upper and lower layers of the sandwich plate are obtained by employing the Halpin–Tsai model. Our technique depends on a new four-unknown shear deformation theory to depict the displacements. In addition, the motion equations are established via Hamilton’s principle. The motion equations are solved by employing the DQP. In order to study the convergence of the DQ method, the minimum number of grid points needed for a converged solution is ascertained. In addition, the current theory’s outcomes are compared with those of previous higher-order theories. The effects of the porosity distribution type, porosity factor, GPLs distribution pattern, GPLs weight fraction, inner-to-outer radius ratio, outer radius-to-thickness ratio, magnetic field parameters, core thickness, and elastic substrate parameters on the nondimensional vibration frequencies are discussed.

Thermal buckling of the concrete structures reinforced by nanocomposites: Introducing advanced deep neural networks for thermal buckling problem

The thermal buckling behavior of concrete annular sector plates reinforced with nanocomposites is investigated in this work. The thermal buckling issue is stated using mathematical modeling, taking into account the geometric linearity and material heterogeneity caused by the nanocomposite reinforcement. The governing differential equations that are obtained from the theoretical model are solved using the discrete singular convolution (DSC) technique. To generate accurate buckling load predictions, the DSC method’s great accuracy in handling complicated boundary conditions and discontinuities is used. Furthermore, using mathematical modeling to create extensive datasets, the research aims to train deep neural networks (DNNs) to anticipate thermal buckling reactions. These datasets provide a strong basis for DNN training as they include a wide range of factors, such as geometric configurations, loading situations, and material properties. By combining DNN predictions with DSC solutions, this unique technique for solving this difficult issue seeks to improve the accuracy and efficiency of thermal buckling analysis. The findings show how well sophisticated mathematical methods and machine learning models work together, opening the door to creative solutions for the design and analysis of concrete structures reinforced with nanocomposite under complicated stress.

Introducing hybrid deep neural networks to predict the transient vibrations of the sandwich systems reinforced by multi-phase nanocomposites

In advanced materials engineering, understanding transient vibrations in sandwich annular plates reinforced by multi-phase nanocomposites is essential. To adequately represent the geometry of these systems, a generic cylindrical coordination system is often used in modeling. The heterogeneous laminated plate is homogenized into an analogous uniform medium to facilitate analysis. In order to represent precise stress and strain distributions, taking into account rotating inertia and transverse shear deformation, a higher-order theory based on a hyperbolic function is used. The governing equations of motion are derived using Hamilton’s principle in polar coordinates, guaranteeing compliance with energy laws. The 2D generalized differential quadrature (GDQ) method effectively discretizes the governing equations for numerical solutions while retaining a high degree of accuracy in recording transient reactions. Furthermore, by solving the differential equations in the frequency domain, the Laplace transform approach sheds light on the dynamic behavior of the system. Using the deep neural networks (DNNs)-fuzzy approach improves the prediction of these composite structures’ vibrational activity. This hybrid approach uses fuzzy logic to control uncertainty and DNN for pattern identification. The DNN-fuzzy approach reliably predicts the intricate vibrational properties of multi-phase sandwich systems reinforced with nanocomposite using datasets from mathematical modeling. This combined use of mathematical techniques, theoretical models, and predictive algorithms improves our knowledge of complex composite structures’ transient vibrations and makes them more useful in a range of engineering domains.

Coupled thermo-mechanical analysis of creep in a rotating FGMEE annular plate under complex thermal loading considering solar radiation, convection, and internal heat source

In this analysis, the creep responses of a non-constant thickness annular plate was presented. The material of disc is assumed functionally graded magneto-electro-elastic (FGMEE) in which the material properties change through the radius. Also, the heat transfer coefficients for convection and conduction are functions of radius and temperature. At first, the equation of heat transfer accounting for thermal gradient, convection boundary conditions, internal heat generation, and solar radiation effects was derived. The differential transformation method (DTM) was used to solve the resulting nonlinear differential equation. The equilibrium equation for the annular plate including creep strain effects was then obtained. Ignoring creep strains, an analytical solution was obtained for the zero-time of this equation. Then, creep strains were introduced using Norton's law and the Prandtl-Reuss relations to find the stress and strain rates under fixed temperature boundary conditions. Next, the equation of strain rates including creep strains was solved analytically. Finally, an iterative approach was used to evaluate the time-dependent redistribution of creep stresses at any time point. Numerical examples highlighted the influences of key parameters like internal heat generation, convective heat transfer, grading index, solar radiation, thickness profile, and angular speed on the stresses, deformations and electric and magnetic potentials.

Influence of combinational distortion generator geometrical parameters on the steady and dynamic components of the total pressure distortion

To construct a method for designing a total pressure distortion generator with adjustable, steady, and dynamic components, we experimentally investigated the influences of combinational distortion generator geometrical parameters on the steady and dynamic components of the total pressure distortion based on an indraft wind tunnel. Different types of annular plates and cylindrical rods were installed upstream of a traditional baffle total pressure distortion generator; the total pressure distortion was then measured using rotatable total pressure rakes. The installation of cylindrical rods upstream of the baffle plate could maximally reduce the ratio of steady and dynamic components of total pressure distortion by 30%. Increasing the number and height of the rods, as well as the axial distance between the rod and baffle plate, were effective methods of reducing the steady components of total pressure distortion. Similarly, changing the geometrical parameters of the annular plate was also an effective method for adjusting the ratio of steady and dynamic components of total pressure distortion. The ratio of the steady and dynamic components of total pressure distortion first experienced a decrease and then increased variance law with the increase in the height and circumferential scale of the annular plate. During this procedure, the steady and dynamic components ratio of total pressure distortion could be maximally reduced by 24% and maximally increased by 20%.

Cryostability of HTS Magnet Stacked by Annular Plates With Bath/Gas-Cooled Modes

Cryostability of HTS Magnet Stacked by Annular Plates With Bath/Gas-Cooled Modes

Nonlinear free vibration analysis of an elastically supported annular plate in nonuniform induced magnetic field

The aim of this article is to investigate nonlinear free vibration and electromagnetic mechanical behavior of a conductive annular plate with elastic boundary in induced non-uniform magnetic field. On basis of magneto-elastic vibration control equation of conductive plates, displacement solution for plates under complex elastic constraints is first solved, and the axisymmetric nonlinear differential equation for plate is derived by combining Galerkin method. Introducing the multi-scale method to solve the differential equation of elastic boundary plate in induced magnetic field to achieve the analytical expression for natural frequency including current and elastic stiffness terms, and the variation of system singularity is analyzed through stability discriminant. Through numerical method, the nonlinear frequency variation curves, electromagnetic characteristic curves, stability area and phase trajectory graphics of singularities with various control parameters are presented. The result accuracy verification was also conducted in comparison to relevant literature and numerical solutions. The interesting and key findings revealed that, under internal diameter clamped and outer diameter elastically supported boundary, the variation of natural frequency with current, time, the nonlinear soft and hard characteristics are completely opposite to rest two boundaries. The elastic stiffness may significantly increase natural frequency, but does not change the soft or hard characteristics of system. With influence of elastic boundaries, the distribution of electromagnetic force and torque in radial direction of plate becomes quite complex under non-uniform magnetic field. In addition, wire current may change the type of system singularity as current increases.

Numerical-analytical approach to solving problems of non-stationary thermal conductivity of a non-thin annular plate

This paper considers the first stage of calculating the initial boundary value problem of non-stationary thermal conductivity of cylindrical bodies using a modified method of lines, namely dimension reduction of the original differential equations, initial and boundary conditions. The original equations of thermal conductivity are defined in a cylindrical coordinate system in a spatial setting. An object is a cylindrical body with commensurate dimensions. This area of research is relevant, because when calculating the load bearing elements of structures to thermal effects, the first step is to determine the distribution of temperature fields. Boundary conditions are considered as conditions of convective heat transfer, which by means of boundary transition are transformed into boundary conditions of the first and second types. Dimension reduction with respect to spatial coordinate is performed by the Bubnov-Galorkin-Petrov projection method using local basis functions. These functions are called "cover" functions, which are related to the lines drawn on the domain of the task. Normalized trigonometric series are used to reduce the dimensionality of the equations with respect to circular coordinate. All transformations are performed in index form. In addition to differential equations, the projection method reduces the dimensionality of the initial and boundary conditions. In this paper, the most optimal form of writing reduced equations is determined, which provides the ease of reducing the dimensionality of the original differential equations. Initial and boundary conditions take into account the impact of the environment. All this makes it possible to set a reduced initial boundary value problem for further calculation by numerical finite difference methods.

Vibration analysis of cylindrical shell discontinuously coupled with annular plate with arbitrary boundary conditions

Discontinuously coupled cylindrical shell-plates or plate-like structures are common components of underwater vehicles, and their vibration characteristics change significantly due to modal coupling. The vibration of discontinuously coupled annular plate-cylindrical shell structures is analyzed based on the wave propagation method(WPM) and virtual spring(VS). Taking uniform annular plates and cylindrical shells as spectral elements, the displacement solutions are described by the trigonometric function and Bessel function respectively, and the vibration responses of the annular plate-cylindrical shell with arbitrary boundaries are obtained. Based on VS and weighted least square norm least square method(WLSNLSM), the discontinuous coupling between the annular plate and cylindrical shell is described as the non-uniform distribution of stiffness of virtual spring by continuity condition, and the dynamic stiffness matrices of continuously and discontinuously coupled structure can be obtained simultaneously. The reason for vibration characteristic change under discontinuous coupling is explained from the perspective of modal superposition. Finally, a finite element model is established to verify the accuracy of the proposed method. The influence of general discontinuous coupling on the dynamic behavior of shell structure is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous coupling.

Modeling and free vibration analysis of bolted composite flanged cylindrical-cylindrical shells under partial bolt loosening conditions

The bolted composite coupled cylindrical shell is a common substructure in modern engineering, which may encounter the issue of local loosening conditions during service. Meanwhile, the influence of flanges on the structural vibration characteristics is often overlooked in dynamic numerical analysis. In this paper, a semi-analytical dynamic model for the bolted composite flanged cylindrical-cylindrical shell structure under arbitrary connection conditions is established, and the free vibration characteristics of locally loose structures are emphatically studied. In the model, the annular plate modeling method is developed to achieve the simulation of the flange part. To fully reflect the connection characteristics of the bolted joint, a spring surface model and the corresponding parameter determination method based on fractal contact theory are developed. The equations of motion of the structure are obtained utilizing the Lagrange equations. The accuracy of the model and its predictive ability for the vibration characteristics of the bolted composite flanged cylindrical-cylindrical shell under local loosening conditions are fully demonstrated through numerous comparisons with experimental results from other literature and modal test results obtained under various working conditions. Furthermore, the influence of the number and degree of loosening bolts on the free vibration characteristics of the structure and the coupling phenomenon between different modes are discussed. The research in this paper is expected to provide references for the design of bolted composite flanged cylindrical shell structures and the monitoring of bolt connection defects.

Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness

Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness