AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

The three-dimensional free vibration analysis of a multi-directional func- tionally graded piezoelectric （FGP） annular plate resting on two parameter （Pasternak） elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method （SSDQM） is used to provide an analytical solution along the thickness using the state space method （SSM） and an approximate solution along the radial direction using the one-dimensional differential quadrature method （DQM）. The influence of the Winkler and shear stiffness of the foundation~ the material property graded variations, and the circumferential wave number on the nomdimensional natural frequency of multi-directional FGP annular plates is studied.

NON-SYMMETRICAL BENDING PROBLEMS OF INFINITE ANNULAR PLATES SUPPORTED ON INNER EDGE

For non-asymmetrical bending problems of elastic annular plates, the exact solutions are not fond. To bending problems of infinite annular plate with two different boundary conditions, based on the boundary integral formula,the natural boundary integral equation for the boundary value problems of the biharmonic equation and the condition of bending moment in infinity,bending solutions under non-symmetrical loads are gained by the Fourier series and convolution formulae. The formula for the solutions has nicer convergence velocity and high computational accuracy, and the calculating process is simpler. Solutions of the given examples are compared with the finite element method. The textual solutions of moments near the loads are better than the finite element method to the fact that near the concentrative loads the inners forces trend to infinite.

Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

This paper presents a unified approach for predicting the free and forced (steady-state and transient) vibration analyses of annular sector and annular plates with various combinations of classical and non-classical boundary supports. In spite of the types of the boundary restraints and the shapes of the plates, the admissible displacement function is described as a modified trigonometric series expansion, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. Mathematically, the unification of various boundary value problems for annular sector and annular plates is physically realized by setting a set of coupling springs to ensure appropriate continuity conditions along the radial edges of concern. Numerous examples are presented for the free vibration analyses of annular sector and annular plates with different boundary restraints. With regard to the forced vibration analysis, annular sector and annular plates with different external excitations are examined. The accuracy, convergence and numerical robustness of the current approach are extensively demonstrated and verified through numerical examples which involve plates with various shapes and boundary conditions. © 2017, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.

A THREE-DIMENSIONAL ELASTICITY SOLUTION FOR TWO-DIRECTIONAL FGM ANNULAR PLATES WITH NON-UNIFORM ELASTIC FOUNDATIONS SUBJECTED TO NORMAL AND SHEAR TRACTIONS

In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.

3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.

Magneto-elastic dynamics and bifurcation of rotating annular plate

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton＇s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincare′ maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions,and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

Free vibration of piezoelectric annular plate

General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated.

NONLINEAR BENDING OF CORRUGATED DIAPHRAGM WITH LARGE BOUNDARY CORRUGATION UNDER COMPOUND LOAD

By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated annular plate with a large boundary corrugation and a nondeformable rigid body at the center under compound load are investigated. The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function. To solve the integral equations, a so_called interpolated parameter important to prevent divergence is introduced into the iterative format. Computation shows that when loads are small, any value of interpolated parameter can assure the convergence of iteration. Interpolated parameter equal or almost equal to 1 yields a faster convergence rate; when loads are large, interpolated parameter cannot be taken too large in order to assure convergence. The characteristic curves of the corrugated diaphragm for different load combinations are given. The obtained characteristic curves are available for reference to design. It can be concluded that the deflection is larger when the diaphragm is acted by both uniform load and concentrated load than when it is acted only by uniform load. The solution method can be applied to corrugated shells of arbitrary diametral sections.

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

The 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 ofmicrocomposite 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 andmoisture 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.

Non-Resonant Structure Design of Catenary Transformer in Ultrasonic Gear Honing

To solve the design problem of transformer composed of non-resonant structure in ultrasonic gear-honing, force coupling conditions for moderately thick annular plate （MTAP） and catenary horn are proposed, and the frequency equations of the transformer, which consist of an MTAP and a catenary horn, are derived based on Mindlin＇s theory. The design parameters of the transformer were obtained by solving the frequency equations with the help of MATLAB, and its mode and frequency were deduced by the modal analysis of finite element method （FEM）, which are consistent with the theoretical design demands. The transformer design can be extended from system with thin annular plate to that with MTAP as the theoretical method by the simulation analysis of various ratios of the thickness to radius.

Behavior of axially loaded tubular X-joints using bolted connection:mechanical model and validation

X-joints are one of the fundamental joint configurations used in a wide range of transmission tubular structures.Experimental investigation of four tubular X-joints with bolted connection was conducted in this study,and it was found that the annular plate was the main yielding control member of such X-joints.Moreover,the portion outside the effective width of the chord member still had a restriction effect on the annular plate,which led to reducing the yielding strength of the joint,while the gusset plate could help to improve the yield strength capacity.In the current design code of steel structures,the contribution to the strength capacity of the gusset plate has not been taken into account.Therefore,based on some mechanical assumptions,a general mechanical model was proposed.After the introduction of the gusset plate strength capacity factor,the yield capacity simplified calculation method of such X-joints was derived.Through the analyses of such X-joints with various diameters and thicknesses,it was concluded that a simple mechanical model could predict test results very well and that the contribution of the gusset plate was also taken into account.