semi analytical solution for three dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation abstract the three dimensional transient analysis of functionally graded annular plates with arbitrary boundary conditions is carried out in this paper the material properties of the fgm plate are assumed to vary smoothly in an exponential law along the thickness direction the plate is assumed to rest on a two parameter viscoelastic foundation a semi analytical method which integrates the state space method ssm laplace transform and its inversion as well as the one dimensional differential quadrature method dqm is proposed to obtain the transient response of the plate the state space method is used to obtain the analytical solution in the thickness direction the differential quadrature method is employed to approximate the solution in the radial direction the laplace transform and the numerical inversion are used to obtain the solution in time domain numerical results show a good agreement between the response histories obtained by the present method and finite element method the effects of the boundary conditions at the edges the material graded index the winkler and shearing layer elastic coefficients and the damping coefficient are studied numerical examples show that the peak response decreases as the material graded index the winkler and shearing layer elastic coefficients and the damping coefficient increase the results obtained in this paper can serve as benchmark data in further research

a unified approach for analyzing static and dynamic behaviors of functionally graded timoshenko and euler bernoulli beams abstract this paper presents a new unified approach for analyzing the static and dynamic behaviors of functionally graded beams fgb with the rotary inertia and shear deformation included as two special cases the euler bernoulli and rayleigh beam theories can be analytically reduced from the timoshenko beam theory all material properties are arbitrary functions along the beam thickness a single fourth order governing partial differential equation is derived and all physical quantities can be expressed in terms of the solution of the resulting equation the static result of deflection and stress distribution is presented for a cantilever fgb furthermore two branches of flexural waves propagating in fgb are obtained with different wave speeds the higher wave speed disappears when the effects of neither the rotary inertia nor shear deformation are considered free vibration of an fgb is analyzed and the frequency equation is given the natural frequencies and mode shapes of a simply supported beam are obtained for frequencies lower than equal to and higher than the cut off frequency numerical results are presented for an fgb with the power law gradient and a laminated beam the second frequency spectrum is found to exist when frequencies exceed the cut off frequency in addition double frequencies may occur for certain specified geometry of the beam previous results for a homogeneous timoshenko beam can be recovered from the present only letting the material properties be constant the suggested method is also applicable to layered timoshenko beams

yang mills connections over manifolds with grassmann structure let m be a manifold with grassmann structure i e with an isomorphism of the cotangent bundle t m e h with the tensor product of two vector bundles e and h we define the notion of a half flat connection w in a vector bundle w m as a connection whose curvature f s2e 2h end w 2t m end w under appropriate assumptions for example when the grassmann structure is associated with a quaternionic kahler structure on m half flatness implies the yang mills equations inspired by the harmonic space approach we develop a local construction of holomorphic half flat connections w over a complex manifold with holomorphic grassmann structure equipped with a suitable linear connection any such connection w can be obtained from a prepotential by solving a system of linear first order odes the construction can be applied for instance to the complexification of hyper kahler manifolds or more generally to hyper kahler manifolds with admissible torsion and to their higher spin analogs it yields solutions

special quantum field theories in eight and other dimensions we build nearly topological quantum field theories in various dimensions we give special attention to the case of eight dimensions for which we first consider theories depending only on yang mills fields two classes of gauge functions exist which correspond to the choices of two different holonomy groups in so 8 namely su 4 and spin 7 the choice of su 4 gives a quantum field theory for a calabi yau fourfold the expectation values for the observables are formally holomorphic donaldson invariants the choice of spin 7 defines another eight dimensional theory for a joyce manifold which could be of relevance in m and f theories relations to the eight dimensional supersymmetric yang mills theory are presented then by dimensional reduction we obtain other theories in particular a four dimensional one whose gauge conditions are identical to the non abelian seiberg witten equations the latter are thus related to pure yang mills self duality equations in 8 dimensions as well as to the n 1 d 10 super yang mills theory we also exhibit a theory that couples 3 form gauge fields to the second chern class in eight dimensions and interesting theories in other dimensions

rotary inertia axial and shear deformation effects on the in plane natural frequencies of symmetric cross ply laminated circular arches abstract the in plane free vibrational analysis of symmetric cross ply laminated circular arches is studied using both the timoshenko and bernoulli euler beam theories the free vibration equations are derived based on the distributed parameter model the transfer matrix method is used in the analysis the numerical algorithm available in the literature is adopted to compute the exact overall dynamic transfer matrix of the curved beam the rotary inertia axial and shear deformation effects are considered in the timoshenko analysis by the first order shear deformation theory all these effects are neglected in the bernoulli euler analysis radius of the arch thickness ratios from 5 to 25 fixed fixed fixed simple and fixed free boundary conditions and two values of the opening angles 10 and 90 are taken into consideration in the parametric study the effects of the ratio of the extensional modulus to the transverse modulus on the natural frequencies are examined non dimensional numerical results are also presented in terms of relative errors

in plane free vibration of functionally graded circular arches with temperature dependent properties under thermal environment analysis of in plane free vibration of functionally graded fg thin to moderately thick deep circular arches in thermal environments is presented based on first order shear deformation theory fsdt the material properties are assumed to be temperature dependent and graded in the thickness direction hamilton s principle is employed to derive the equations of motion and the related boundary conditions including the effects of initial thermal stresses the temperature is assumed to be uniform through the arch surface and varied through the thickness the initial thermal stresses are obtained by solving the thermoelastic equilibrium equations the differential quadrature method dqm as an efficient numerical tool is adopted to solve the thermoelastic equilibrium equations and the equations of motion the numerical solutions are validated by comparing to the solutions of the limited cases for isotropic arches as well as by examining the solutions convergence behavior parametric studies are also conducted to study the effects of the temperature rise boundary conditions and the material graded index on the frequency of the fg arches also the impact of geometrical parameters such as the thickness to mean radius ratio and the opening angle are examined

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

a hybrid layerwise and differential quadrature method for in plane free vibration of laminated thick circular arches abstract an accurate and efficient solution procedure based on the two dimensional elasticity theory for free vibration of arbitrary laminated thick circular deep arches with some combinations of classical boundary conditions is introduced in order to accurately represent the variation of strain across the thickness the layerwise theory is used to approximate the displacement components in the radial direction employing hamilton s principle the discretized form of the equations of motion and the related boundary conditions in the radial direction are obtained the resulting governing equations are then discretized using the differential quadrature method dqm after performing the convergence studies new results for laminated arches with different set of boundary conditions are developed additionally different values of the arch parameters such as opening angle thickness to length and orthotropy ratios are considered in all cases comparisons with the results obtained using the finite element software abaqus and also with those of the first and higher order shear deformation theories available in the literature are performed close agreements especially with those of abaqus are achieved

spherically symmetric solutions of gauge theories in eight dimensions linear relations among the fields of a gauge theory in eight dimensions derived from a secular equation invariant under a so 7 subgroup are particularly interesting the authors present here the spherical solutions corresponding to this case when the gauge group is so 7 or so 8 in the former case the solution can be made regular everywhere

exact two dimensional solutions for in plane natural frequencies of laminated circular arches exact analysis on the in plane free vibration of simply supported laminated circular arches is carried out based on the two dimensional theory of elasticity the method of separation of variables is employed to expand all the variables into fourier series about the longitudinal coordinate so that the system of partial differential equations is reduced to the ordinary one about the radial coordinate the state space method is used to derive a series of simultaneous first order differential equations due to the variable coefficients posed by the radial coordinate analytical solutions are rather unpractical and hence the approximate laminate model is adopted to translate the state equation into the one with constant coefficients the relation between the state vector at the inner and outer surface of the arch is finally obtained according to the continuity conditions at interfaces and the traction free conditions at the two lateral surfaces the formulation is validated by comparing the present results to those available in literature effects of geometric parameters and stacking sequences on the natural frequencies of circular arches are investigated and discussed numerical results presented in this paper provide benchmarks for future analysis of circular arches

elasticity solution for vibration of 2 d curved beams with variable curvatures using a spectral sampling surface method summary an accurate spectral sampling surface method for the vibration analysis of 2 d curved beams with variable curvatures and general boundary conditions is presented the method combines the advantages of the sampling surface method and spectral method the formulation is based on the 2 d elasticity theory which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced specifically a set of non equally spaced sampling surfaces parallel to the beam s middle surface are primarily collocated along the thickness direction and the displacements of these surfaces are chosen as fundamental beam unknowns this fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces each of the fundamental beam unknowns is then invariantly expanded as chebyshev polynomials of the first kind and the problems are stated in variational form with the aid of the penalty technique and lagrange multipliers which provide complete flexibility to describe any arbitrary boundary conditions finally the desired solutions are obtained by the variational operation copyright 2016 john wiley sons ltd

vibration analysis of functionally graded thin walled rotating blades under high temperature supersonic flow using the differential quadrature method in this study differential quadrature dq vibration analysis of a rotating thin walled blade made of functionally graded materials fgms operating under high temperature supersonic gas flow is investigated the governing equations are based on the first order shear deformation theory of beams which include the effects of the rotary inertias and the blade presetting angle quasi steady aerodynamic pressure loadings and steady wall temperature assumptions are made the explicit dq discretized form of the equations of motion and the related boundary conditions are presented the convergence of the method is examined and to verify its accuracy the results are compared with those of the galerkin method where excellent agreements are observed the effects of the mach number rotating speed geometric parameters and blade material properties on the natural frequencies are examined

some comments on the adhm construction in 4k dimensions a class of completely solvable gauge field equations is investigated these equations are shown to be closely analogous to the four dimensional self duality equations a similar geometrical interpretation is exhibited and a generalisation of the adhm construction is shown to provide solutions

oxidation of self duality to 12 dimensions and beyond using partial curvature flows and the transitive action of subgroups of rm o d mathbb z on the indices 1 ldots d of the components of the yang mills curvature in an orthonormal basis we obtain a nested system of equations in successively higher dimensions d each implying the yang mills equations on d dimensional riemannian manifolds possessing special geometric structures this matryoshka of self duality equations contains the familiar self duality equations on riemannian fourfold as well as their generalisations on complex kahler threefold and on seven and eight dimensional manifolds with g2 and spin 7 holonomy the matryoshka allows enlargement oxidation to a remarkable system in 12 dimensions invariant under sp 3 there are hints that the underlying geometry is related to the sextonions a six dimensional algebra between the quaternions and octonions

highly accurate closed form solutions for the free in plane vibration of rectangular plates with arbitrary homogeneous boundary conditions abstract in this paper highly accurate closed form solutions for the free in plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation of variable method and all solutions are presented in an elegant explicit form for plates with at least a pair of opposite edges simply supported the present solutions are the exact solutions for other homogeneous boundary conditions the accurate closed form solutions agree well with the results of the fine finite element method this work shows that the iterative separation of variables method is a powerful method to find the closed form eigensolutions of partial differential equations the present solutions can be taken as the benchmarks for the validation of numerical methods a guide in parametric design of structure and the basis of constructing new numerical methods

out of plane static analysis of circular arches by dqm the differential quadrature dq methodology introduced by the authors see comput methods appl mech engng 191 2002a 3509 int j solids struct 39 19 2002b 4927 int j numer methods engng 54 3 2003a 847 j sound vibrat 263 2 2003b 415 is employed for out of plane static analysis of circular arches under a wide spectrum of boundary conditions in addition to the classical boundary conditions elastic restraints against translation and rotation are also considered different loading conditions are examined several examples of arches with uniform continuous or stepped varying cross sections are presented to demonstrate the accuracy of the methodology the domain decomposition technique in conjunction with the present dq methodology is examined for certain cases the results are compared with those of exact solutions for several uniform or stepped sections arches and also for arches on elastic foundations accurate converged numerical solutions are obtained with only few grid points

thermo mechanical vibration of fgm sandwich beam under variable elastic foundations using differential quadrature method thermo mechanical vibration analysis of functionally graded fg beams and functionally graded sandwich fgsw beams are presented the functionally graded material fgm beams are considered to be resting on variable i winkler foundation and ii two parameter elastic foundation the material properties of these beams are assumed to be varying in the thickness direction the governing differential equations for beam vibration are being solved using the modified differential quadrature method mdqm the applied kinematic boundary conditions are implemented using the modified weighting coefficient matrix mwcm the weighting coefficients are generated from the chebyshev basis function present results for the vibration of isotropic beam with variable winkler foundation are in good agreement with those reported in the literature parametric study on the vibration response of fg beams and fgsw beams are being investigated these parameters include i temperature distributions ii power law index iii variable winkler foundation modulus iv two parameter elastic foundation modulus and v normalized core thickness of fgsw beams

free vibration and stability of laminated composite circular arches subjected to initial axial stress natural frequencies and buckling stresses of laminated composite circular arches subjected to initial axial stress are analyzed by taking into account the complete effects of transverse shear and normal stresses and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for laminated composite circular arches subjected to initial axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported circular arch in order to assure the accuracy of the present theory convergence properties of the first four natural frequencies are examined in detail numerical results are compared with those of the published existing theories the present global higher order approximate theories can predict the natural frequencies and buckling stresses of multilayered circular arches accurately with a small number of unknowns

temperature dependent vibration analysis of functionally graded rectangular plates abstract a theoretical method is developed to investigate vibration characteristics of initially stressed functionally graded rectangular plates made up of metal and ceramic in thermal environment the temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only two types of thermal condition are considered the first type is that one value of the temperature is imposed on the upper surface and the other or same value on the lower surface the second is that the heat flows from the upper surface to the lower one held at a prescribed temperature material properties are assumed to be temperature dependent and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents the third order shear deformation plate theory to account for rotary inertia and transverse shear strains is adopted to formulate the theoretical model the rayleigh ritz procedure is applied to obtain the frequency equation the analysis is based on an expansion of the displacements in the double fourier series that satisfy the boundary conditions the effect of material compositions plate geometry and temperature fields on the vibration characteristics is examined the present theoretical results are verified by comparing with those in literature

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

in plane free vibration analysis of circular arches with varying cross sections using differential quadrature method abstract a differential quadrature dq methodology recently developed by the authors is used to obtain a general and a computationally efficient and accurate dq solution for free vibration of variable cross section circular thin arches as an improvement to the classical theory and in order to evaluate the higher order natural frequencies more accurately the commonly used hypothesis of the inextensibility of the central axis is removed this enables one to study the effects of slenderness ratio on the natural frequencies especially at higher order modes rotary inertia is included in the formulation and its influence on natural frequencies is studied arches with different types of boundary conditions including those with elastic constraint against rotation at their ends are considered for the cases where a change in the cross sectional or material properties of the arch occurs a numerical domain decomposition technique in conjunction with dq methodology is developed and incorporated to verify the accuracy of the methodology the results are compared with those of exact solutions and or other approaches such as finite elements rayleigh ritz galerkin cell discretization methods and other dq methodologies in particular excellent solution agreements are achieved with those of exact solutions the generalized differential quadrature rule and the optimized rayleigh ritz method solutions

on the number of invariant polynomials of the product of matrices with prescribed similarity classes abstract we study the possibilities for the number of nontrivial invariant polynomials of the product of two nonsingular matrices with prescribed similarity classes over an algebraically closed field