effects of the poisson ratio and negative thrust on the dynamic stability of a free plate subjected to a follower force abstract the macroscopic poisson ratio of a large plate like truss structure may vary due to the geometry of the truss studied are the effects of the poisson ratio and negative thrust on the dynamic stability of a flexible rectangular plate which has four free edges one of the four edges is subjected to a tangential follower thrust the model is simplified to a continuous isotropic plate and is investigated by means of modal analysis a change in poisson ratio sometimes reduces the flutter load drastically the drastic reduction comes from the existence of a weak flutter instability it is also shown that there may exist both flutter and divergence even for negative thrust and that the tensile divergence load is smaller than the compressive one

generic buckling curves for specially orthotropic rectangular plates using a double affine transformation the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion these dual representations are characterized by a single material constant called the generalized rigidity ratio whose range is predicted to be the closed interval from 0 to 1 if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect when natural boundary conditions are considered a generalized poisson s ratio is introduced thus the buckling results are valid for any specially orthotropic material hence the curves presented in the text are generic rather than specific the solution trends are twofold the buckling coefficients decrease with decreasing generalized rigidity ratio and when applicable they decrease with increasing generalized poisson s ratio since the isotropic plate is one limiting case of the above analysis it is also true that isotropic buckling coefficients decrease with increasing poission s ratio

a generalized approach for implementing general boundary conditions in the gdq free vibration analysis of plates abstract a new approach for implementing general boundary conditions in the gdq free vibration analysis of rectangular plates is presented in this paper the proposed approach directly couples the boundary conditions with the governing equations and is referred to as the cbcge approach it can be applied to any combination of simply supported clamped and free boundary conditions the generality and accuracy of the cbcge approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners in particular the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed and a new grid point distribution is suggested

a necessary condition for dynamic equivalence if two control systems on manifolds of the same dimension are dynamic equivalent we prove that either they are static equivalent i e equivalent via a classical diffeomorphism or they are both ruled for systems of different dimensions the one of higher dimension must be ruled a ruled system is one whose equations define at each point in the state manifold a ruled submanifold of the tangent space dynamic equivalence is also known as equivalence by endogenous dynamic feedback or by a lie backlund transformation when control systems are viewed as underdetermined systems of ordinary differential equations it is very close to absolute equivalence for pfaffian systems it was already known that a differentially flat system must be ruled this was a particular case of the present result in which one of the systems was assumed to be trivial or linear controllable

calculation of the natural frequencies of composite plates by the rayleigh ritz method with orthogonal polynominals orthogonal polynomials are used as admissible functions and the approach has been found to be numerically stable

transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation abstract the fundamental frequency coefficient for a rectangular plate with edges elastically restrained against both translation and rotation is calculated by using polynomial coordinate functions and the rayleigh ritz method the approach is simple and straightforward and allows the solution of a rather difficult elastodynamics problem complicating factors orthotropic properties in plane forces concentrated masses etc can also be taken into account without formal difficulties

analysis on generalized superspaces the analysis over commutative algebras generalized supercommutative algebras that is differentiation and integration for functions defined on superspace over a commutative algebra is studied

stability and accuracy of differential quadrature method in solving dynamic problems in this paper the differential quadrature method is used to solve dynamic problems governed by second order ordinary differential equations in time the legendre radau chebyshev chebyshev gauss lobatto and uniformly spaced sampling grid points are considered besides two approaches using the conventional and modified differential quadrature rules to impose the initial conditions are also investigated the stability and accuracy properties are studied by evaluating the spectral radii and truncation errors of the resultant numerical amplification matrices it is found that higher order accurate solutions can be obtained at the end of a time step if the gauss and radau sampling grid points are used however the conventional approach to impose the initial conditions in general only gives conditionally stable time step integration algorithms unconditionally stable algorithms can be obtained if the modified differential quadrature rule is used unfortunately the commonly used chebyshev gauss lobatto sampling grid points would not generate unconditionally stable algorithms

global properties of supermanifolds we construct new examples of supermanifolds and determine the vector bundle structure of the supermanifolds commonly used in physics we show that any supermanifold admits a foliation whose leaves are locally tangent to the soul directions in the coordinate charts and which is one of a nested sequence of foliations we point out that the existence of these foliations implies restrictions on the possible topologies of supermanifolds for example a compact supermanifold with a single even dimension must have vanishing euler characteristic we also show that a globally defined superfield on a nice compact supermanifold must be constant along the leaves of the foliations by this mechanism the global topology of a supermanifold can be used to impose physically interesting constraints on superfields as an example we exhibit a supermanifold which has the local geometry of flat superspace but is such that all globally defined superfields are chiral

divergence and flutter instability of elastic specially orthotropic plates subject to follower forces abstract divergence and flutter instabilities of a rectangular specially orthotropic plate simply supported on a pair of opposite sides subject to follower forces are computationally analyzed the effects of the tangential follower parameter aspect ratio boundary condition on the side opposite the loaded edge and material orthotropy on the magnitude of the critical load and the mode divergence or flutter of instability are detailed for the three boundary conditions considered built in simply supported and free free for the side opposite the loaded edge and given material orthotropy the plane is divided into regions corresponding to different governing instabilities both the number and size of these regions depend strongly upon the boundary condition considered as does the governing instability for a given boundary condition the configuration of the stability regions is independent of material orthotropy material orthotropy affects only the buckling loads corresponding to the instabilities and the size of the regions

analyzing the free vibrations of a plate using finite difference and differential transformation method this paper analyses the free vibrations of clamped and simply supported rectangular thin plates a hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations of the plate to a set of algebraic equations the investigative parameters include the order of the differential transformation the number of sub domain spaces the variable conditions and the type of initial condition the numerical simulation results indicate that the solution of the natural frequency is more accurate when calculated using a higher number of sub domains the effect of the difference transformation order value k on the solution of the natural frequency is not significant when the combined t spectra method and differential transformation method is applied the initial mode shape of the plate has a significant influence on the solution of the natural frequency the current modeling results confirm the viability of using the hybrid method proposed in this paper to solve the free vibrations and natural frequency of clamped and simply supported plates

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

the free vibrations of tapered rectangular plates using a new set of beam functions with the rayleigh ritz method abstract in19991999 academic pressacademic pressthis paper the free vibrations of a wide range of non uniform rectangular plates in one or two directions are considered the domain of the plate is bounded by copyright x 1a a and y 1b b in rectangular co ordinates the thickness of the plate is continuously varying and proportional to the power functionxsyt a variety of tapered rectangular plates can be described by giving the taper factors s and t different values s and t may be given arbitrary real numbers if both 1 0 and 1 0 or arbitrary non negative numbers if 1 0 or 1 0 the uniform rectangular plate is a special case by letting both s and t equal to zero a new set of admissible functions which are the static solutions of the tapered beam or a strip taken from the tapered rectangular plate under an arbitrary static load expanded into a taylor series is developed unlike conventional admissible functions the set of static beam functions will vary appropriately with the thickness variation of the plate the eigenfrequency equation is obtained by the use of the rayleigh ritz method a general computer program has been compiled and some numerical results are tabulated on the basis of comparison with available results in the literature it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions

natural frequencies of rectangular plates using a set of static beam functions in rayleigh ritz method abstract a fast converging series consisting of a set of static beam functions which is a combination of sine series and polynomials is developed and these functions are used as the basis functions in the rayleigh ritz method to study the vibrational characteristics of thin isotropic rectangular plates in applications a relatively small number of functions are required and consequently a modest amount of computation is necessary the approach is very simple and straightforward some numerical results are given for rectangular plates with various aspects ratios and boundary conditions good accuracy and fast convergence of the method are demonstrated by comparison with available results complicating factors orthotropic properties in plane forces etc can also be taken into account without formal difficulties

elastic stability of columns on partial elastic foundations under subtangential loading divergence and flutter instability of a cantilevered beam on a partial elastic foundation subjected to a subtangential load at the free end are investigated the dependence of divergence and flutter critical loads on the tangency coefficient is studied parametrically to illustrate the effects of the extent position and modulus of the partial foundation particular attention is paid to the stabilizing and destabilizing effects of the various parameters

nonlinear forced vibration of orthotropic rectangular plates using the method of multiple scales the method of multiple scales mms in conjunction with the galerkin method is used to analyze the nonlinear forced and damped response of a rectangular orthotropic plate subjected to a uniformly distributed harmonic transverse loading the effects of damping and in plane loads are considered the analysis considers simply supported as well as clamped plates for each case both movable and immovable edge conditions are considered by using mms all possible resonances such as primary subharmonic and superharmonic reso nances are studied for the undamped response without in plane loading comparisons of the mms results with those obtained by the finite element method show excellent agreement evelopment of composite materials comprising lam inates of orthotropic or multilayered anisotropic materi als recently has been receiving substantially growing research efforts due to the increasing demands for energy efficient high strength minimum weight aircraft designs many re searchers believe that the use of composite materials offers promising alternatives for aircraft designs thin laminated composite plates subjected to transverse periodic loadings could encounter deflections of the order of plate thickness or even higher responses of this kind cannot be predicted by using the linear theory consequently the need to study large amplitude deflection vibrations of composite structures is of paramount importance the literature survey shows that the equations of motion for the large deflection analysis of heterogeneous anisotropic plates using the von karman geometrical nonlinearity were first considered by whitney and leissa 1 based on these equa tions different methods of analysis have been developed by several researchers an excellent number of collections on nonlinear free and forced vibrations of composite plates cov ering the work through 1979 can be found in the comprehen sive book by chia 2 bert3 has conducted a survey on the dynamics of composite plates for the period 1979 81 a re view of the literature on nonlinear vibrations of plates can be found in the review paper by sathyamoorthy4 and the book by nayfeh and mook 5 large deflection analysis of symmetrically laminated rec equations of motion are presented in terms of the lateral displacement and stress function the equations are nondi mensionalized following the transformation introduced by brunelle and oyibo 9 though multimode analysis can be treated the present study is focused on single mode analysis a deflection function representing the first mode and satisfy ing the boundary conditions is assumed and subsequently the stress function is found next the galerkin method is applied to obtain the modal equation which is solved analytically by using the method of multiple scales mms 10 the mms also provides solutions for subharmonic and superharmonic reso nances the effects of damping ratio plate aspect ratio and in plane loading then are studied

superfiber bundle structure of gauge theories with faddeev popov fields in this work the mathematical structure of principal superfiber bundle ps is used to give a geometrical description of gauge theories the base space of ps is an s4 2 supermanifold xs four commuting and two anticommuting variables and the structure group an sn 0 supergroup gs where n is the dimension of the gauge group for the classical theory the body of ps is the usual principal fiber bundle p of gauge theories gauge and faddeev popov fields arise as superfields components of the connections in ps in a local coordinate system brs becchi rouet and stora and anti brs transformations are gauge transformations in ps of parameters the ghost and antighost superfields respectively in the case of soul flat connections which are connections in ps coming from connections in p the brs and anti brs transformations are finite translations along the anticommuting directions of xs and generate an s0 2 supergroup

flutter of orthotropic panels in supersonic flow using affine transformations affine transformations are used in analyzing the flutter problem of rectangular simply supported orthotropic panels subjected to supersonic flow over one surface with the help of certain defined characteristic and bounded quantities a comprehensive solution which has the isotropic panels solution as a subset is found to this problem the physics of this very important aeroelastic problem which has been so obscure for a long time because of the presence of so many parameters is thus clearly exposed by showing how the aerodynamic and the elastic forces interact to produce the panel flutter phenomenon both the aerodynamic strip ackeret theory and lifting surface theory are compared and found to agree very well in the analysis hence complete stability boundaries are determined for both flat and buckled panels using the aerodynamic strip theory the simpler of the two theories

an efficient mixed methodology for free vibration and buckling analysis of orthotropic rectangular plates abstract in this paper a simple and efficient mixed ritz differential quadrature dq method is presented for free vibration and buckling analysis of orthotropic rectangular plates the mixed scheme combines the simplicity of the ritz method and high accuracy and efficiency of the dq method the accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature it is shown that highly accurate results can be obtained using a small number of ritz terms and dq sample points the proposed method is suitable for the problem considered due to its simplicity and potential for further development

on the erdős distinct distances problem in the plane in this paper we prove that a set of n points in r 2 has at least c n log n distinct distances thus obtaining the sharp exponent in a problem of erd os we follow the setup of elekes and sharir which in the spirit of the erlangen program allows us to study the problem in the group of rigid motions of the plane this converts the problem to one of point line incidences in space we introduce two new ideas in our proof in order to control points where many lines are incident we create a cell decomposition using the polynomial ham sandwich theorem this creates a dichotomy either most of the points are in the interiors of the cells in which case we immediately get sharp results or alternatively the points lie on the walls of the cells in which case they are in the zero set of a polynomial of suprisingly low degree and we may apply the algebraic method in order to control points incident to only two lines we use the ecnode polynomial of the rev george salmon to conclude that most of the lines lie on a ruled surface then we use the geometry of ruled surfaces to complete the proof

unified aeroelastic flutter theory for very low aspect ratio panels a theory unifying the flutter analyses of orthotropic and isotropic panels having very low aspect ratios and exposed to an inviscid potential flow on the upper surfaces is developed the analysis considers an infinitely long panel of finite width simply supported on the side edges and resting on a spring foundation three dimensional linearized aerodynamic and classical plate theories are used traveling wave modes are utilized as solutions to the panel s aeroelastic equation of motion the resulting aerodynamic integral is evaluated approximately using both numerical and analytical methods the structural and aerodynamic generic variables which are instrumental in establishing this unified theory are derived using affine transformations subsonic as well as supersonic flutter and divergence boundaries are determined the effects of air to panel mass ratios and midplane forces are examined viscous structural damping is found to be destabilizing there is a general agreement between the results of this analysis and those obtained for isotropic panels by previous investigators

unified panel flutter theory with viscous damping effects the idea of a unified panel flutter theory investigated previously by the author is amplified to make the inclusion of damping effects possible the paper attempts to study the combined effects of the aerodynamic and structural types of damping on the flutter boundaries for simply supported panels in high supersonic mach number flows classical plate theory and two dimensional first order aerodynamics are used a closed form rather than modal approach is used in the solution of the partial differential equation in the analysis to avoid convergence problems the standing and traveling wave theories of panel flutter are compared the dual nature of damping stabilizing and destabilizing is exposed while the trends are similar to those already established for isotropic panels the variables compared are generically defined to account for both the isotropic as well as the orthotropic properties of the panels

integration on supermanifolds and a generalized cartan calculus a suggestion by berezin for a method of integration on supermanifolds is given a precise differential geometric meaning by assuming that a supermanifold is the total space of a fibre bundle with connection the relevant objects for integration are identified as suitable horizontal vertical projections of hyperforms the latter are generalizations of differential forms having both covariant and contravariant indices the exterior calculus of these projected hyperforms is developed analogously to the cartan calculus by introducing appropriate derivations and determining their commutators respectively anticommutators

stability of a rectangular plate under nonconservative and conservative forces abstract a study is made of the flutter and divergence instabilities of a rectangular plate with two independent loading parameters the plate is subjected to the combined action of a tangential follower force and a unidirectional axial force along one edge two opposite sides of the plate are simply supported one side being clamped and the other being a free edge where the in plane forces act depending on the relative magnitudes of the follower and axial forces the plate may lose its stability by flutter or divergence the flutter problem is solved by maximizing the flutter load over the frequency and thereby obtaining the maximum point of an eigencurve the stability boundaries are given for plates with different aspect ratios the two dimensional nature of the problem reveals some interesting results not observed in the one dimensional counterpart of the problem which is a cantilevered column under vertical and follower forces the effect of an elastic foundation on the stability boundaries are determined the influence of poisson s ratio on the flutter load and frequency is investigated it is shown that no general rule can be formulated as to the effect of poisson s ratio on the flutter load and that this effect will vary according to the aspect ratio and axial load

vibration analysis of rectangular plates with general elastic boundary supports abstract in this investigation the rayleigh ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so called residual displacement function at the edges as a result a drastic improvement of the convergence can be expected of the solution expressed as a series expansion in terms of the admissible functions perhaps more importantly this study has developed a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions several numerical examples are given to demonstrate the accuracy and convergence of the current solution

a hierarchical functions set for predicting very high order plate bending modes with any boundary conditions in this paper a new hierarchical functions set is proposed to predict flexural motion of plate like structures in the medium frequency range this functions set is built from trigonometric functions instead of polynomials as classically encountered in the literature it is shown that such a trigonometric set presents all the advantages of a classical hierarchical polynomials set and additional ones which are of interest if very high order functions are intended to be used it is stated that this new trigonometric set can be used at very high orders up to 2048 without taking care of computer round off errors while the polynomials set fail at order 46 because of the limited numerical dynamics of computers this trigonometric set can be easily implemented on a computer it does not require quadruple precision pre computed arrays only a very low number which does not depend on the function order of basic operations is needed when calling such functions moreover it is shown that this trigonometric set presents a better convergence rate than polynomials when predicting high order natural flexural modes of rectangular plates with any boundary conditions

a mechanical model for the buckling of unilaterally constrained rectangular plates a mechanical model is described for the problem of buckling of unilaterally constrained finite rectangular plates due to the nature of the imposed constraint on the plate s lateral deflection w solving for the buckling load required the solution of a nonlinear partial differential equation in w while the plates were modeled along the lines of classical plate theory the nonlinearity arose from the fact that the plates were attached to nonlinear elastic foundations exhibiting a deformation sign dependent force displacement relationship this feature was introduced to model the unilateral constraint the influence of different boundary conditions material orthotropy and transverse load distributions was investigated for each case the weak form of the governing differential equation was solved via the galerkin s method investigations of the buckling loads of rectangular plates attached to such foundations and subjected to a uniform inplane stress field showed the validity of this approach for the cases investigated and compared to some previous exact results reported in the literature

block marching in time with dq discretization an efficient method for time dependent problems abstract in this paper an efficient method is presented to solve time dependent problems the proposed method marches in the time direction block by block in each block there are several time levels and the numerical results at these time levels are obtained simultaneously the global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives the proposed method is validated by a sample problem which has an exact solution for easy comparison it was found that as compared to the conventional 4 stage runge kutta method the present method could give much higher order of accuracy for numerical results and require much less computational effort

how different are the supermanifolds of rogers and dewitt a dewitt supermanifold always has the structure of a vector bundle over an ordinary spacetime manifold whereas a rogers supermanifold is not so restricted corresponding to the vector space fibers of the dewitt supermanifold a rogers supermanifold has a foliation by submanifolds or leaves parametrized by soul coordinates only we show that the universal covering space of any leaf always admits a flat metric if the covering space is complete in this metric it must in fact be a vector space we combine this result with known theorems about foliations to give conditions under which a compact rogers supermanifold with a single even dimension is necessarily a quotient space of flat superspace we also show that a supermanifold defined by a polynomial equation in flat superspace is always of the dewitt type finally we exhibit new supermanifold structures forr2 and the 2 torus which show that the foliation of a rogers supermanifold can be quite exotic

vibrations of rectangular plates with elastically restrained edges abstract the rayleigh ritz method is used to determined natural frequencies in transverse vibration of rectangular plates with elastically restrained edges by treating an elastically restrained edge as intermediate between an appropriate pair of classical boundary conditions and using the corresponding vibration mode shapes of beams with classical boundary conditions as assumed functions a relatively small number of functions is required consequently only a modest quantity of computation is necessary the good accuracy of the method is demonstrated by solving test problems the method can be applied to a wide range of elastic restraint conditions any aspect ratio and for higher modes in addition to the fundamental the usefulness and accuracy of existing simplified approaches to the problem are assessed the effect of in plane forces on the natural frequencies and the determination of critical loads for plates with these restraint conditions are considered also

natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation natural frequencies of orthotropic rectangular plates are obtained by successive reduction of the plate partial differential equation and by solving the resulting ordinary differential equation exactly the reduction of the partial differential equation is carried out by assuming an approximate solution satisfying the boundary conditions along one direction and employing a galerkin averaging technique known as the kantorovich method the resulting ordinary differential equation along the other direction is solved exactly which provides the natural frequencies of the plate natural frequencies of the orthotropic rectangular plates with various boundary conditions are obtained by using this approach and presented along with the discussion of the convergence and accuracy of the results

on the body of supermanifolds the problem of constructing the body of a g manifold is considered it is shown that any such manifold is foliated and the body is defined to be the space of the leaves of this foliation under certain regularity conditions on the foliation the body is a smooth finite dimensional real manifold

closed form solutions for nonlinear quasi unsteady transonic aerodynamics the existence of these solutions is established the full nonlinear unsteady velocity potential equations for an airfoil are considered a suitable mapping scheme is employed in transforming these full nonlinear equations into the hodograph plane the closed form solutions can be obtained for the nonlinear unsteady aerodynamic characteristics of an airfoil in potential flow dips were observed in the pressure distributions as the freestream mach number is varied it appears that there are finite optimum reduced frequencies for the pressure distributions

accurate free vibration analysis of the completely free orthotropic rectangular plate by the method of superposition abstract the method of superposition is exploited to obtain highly accurate analytical type solutions for the free vibration of completely free orthotropic rectangular plates eigenvalues for 12 modes are provided for a particular set of problems representative of reinforced concrete and similar materials for a wide range of plate aspect ratios while it is recognized that data covering the entire range of possible problems cannot be tabulated it is hoped that the data provided will prove useful to some designers and provide a reference for other researchers to compare their results this appears to be the first study devoted to this problem to appear in the literature

free vibration solution for clamped orthotropic plates using lagrangian multiplier technique using the lagrangian multiplier technique an analysis was developed to compute the natural frequencies and mode shapes of clamped orthotropic laminated plates transverse shear deformation effects were included using a higher order plate theory predictions made with the developed analysis demonstrated excellent agreement with the available experimental test results and other analytical solutions the validated free vibration analysis has also been used to develop an analysis to predict the dynamic response of clamped orthotropic plates subjected to low velocity impact by a hard object

generic karman rostovstev plate equations in an affine space the karman rostovstev plate equations are affinely transformed into equations that depend on the generic plate constants generalized rigidity generalized extensional rigidity and generalized poisson ratio associated with the well known linearized orthotropic plate slab equations furthermore since the generalized extensional rigidity is a function of generalized rigidity and generalized poisson ratio only with generalized poisson ratio being a weak parameter the only fundamental constant is generalized rigidity this means that regardless of what analysis technique is used the results can be cast in terms of only one strong material parameter whose range is from zero to one the affine stretching is performed on the dependent variables as well as the independent variables so that the dependence of all quantities of interest on generalized rigidity and generalized poisson ratio are easily calculated e g even auxiliary quantities such as stress strain all weighted stress resultants etc some typical results static side load response collapse load limited by rib buckling are presented by modifying an approximate technique due to donnell 1976

generic free vibration of orthotropic rectangular plates with clamped and simply supported edges abstract the generic free vibration of specially orthotropic rectangular plates with combinations of clamped and simply supported edges is investigated by the superposition technique the introduction of affine transformation reduces the two rigidity parameters required for the free vibration analysis to one making complete tabulation of computed eigenvalues much easier numerical calculations are performed on clamped plates plates with one edge simply supported and plates with two adjacent edges simply supported along with a number of representative values of the generalized rigidity parameter and the affine aspect ratio

berezin integration on general fermionic supermanifolds recent results on the global structure of supermanifolds are used to define a notion of berezin integration on any purely fermionic rogers supermanifold this leads to an integration theory on a large class of supermanifolds having both bosonic and fermionic coordinates the existence of global functions and forms on such supermanifolds is discussed as is some elementary cohomology of supermanifolds

flutter and divergence instability of nonconservative beams and plates for a conservative system the only possible instability is of divergence type for a nonconservative system however instability can be of divergence flutter or both depending on the amount of nonconservativeness in this paper we study the instability of a cantilevered beam and a simply supported plate subjected to a combination of fixed and follower forces a nonconservative parameter is introduced to provide all possible combinations of these forces for the beam instability changes from divergence to flutter at a critical value of this parameter for values of the parameter above the critical value the flutter instability remains as the only instability pattern in contrast to implications in the literature for the plate the instability is governed by flutter for a certain range of the nonconservative parameter even though divergence instability still exists the range depends on the geometry aspect ratio and material property poisson s ratio of the plate

supersymmetric field theoretic models on a supermanifold we propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general space time manifold so as to include superfield models on a supermanifold we only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure our considerations are based on the catenacci reina teofillatto bryant approach to supermanifolds in particular we show that the class of supermanifolds constructed by bonora pasti tonin satisfies the criteria which guarantee that a supermanifold admits a hausdorff body manifold this construction is the closest to the physicist s intuitive view of superspace as a manifold with some anticommuting coordinates where the odd sector is topologically trivial the paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects moreover a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions which is equivalent to the requirement that all of the component fields satisfy on the body manifold a microlocal spectral condition proposed by brunetti fredenhagen kohler

dynamic stability of a non conservative viscoelastic rectangular plate abstract based on the thin plate theory and the two dimensional 2d viscoelastic differential constitutive relation the differential equation of motion of the viscoelastic rectangular plate subjected to uniformly distributed tangential follower force in laplace domain is deduced the equation is suitable for various viscoelastic models of differential type the differential equation of motion of the viscoelastic plate constituted by the kelvin voigt model under the action of uniformly distributed tangential follower force in time domain is also derived the generalized eigenequations of non conservative viscoelastic rectangular plate with four edges simply supported two opposite edges simply supported and other two edges clamped are established by the differential quadrature method and the curves of real parts and imaginary parts of the first three order dimensionless complex frequencies vs uniformly distributed tangential follower force are obtained the factors influencing the dynamic stability of the visoelastic rectangular plate are discussed

eigenvalue similarity rules for symmetric cross ply laminated plates as recently demonstrated the stability and vibration problems of orthotropic plates can be efficaciously treated in suitable affine spaces and similarity rules independent of individual problem boundary conditions can be formulated and very effectively used in analysis and design the present work extends these concepts to symmetric cross ply laminated plates by employing the affine stretching process utilizing some previous material constant definitions due to tsai and generalizing the existing similarity rules as examples similarity rules are employed to find the frequency spectrum of a cross ply symmetric plate from the corresponding isotropic solution and a similarity solution is presented for the vibration of an axially loaded simply supported cross ply symmetric plate buckling similarity rules are also presented

generalized supermanifolds iii ρ supermanifolds supermanifolds are characterized as supermanifolds modeled in a superspace s having a well behaved body tangent cotangent and tensor bundles to supermanifolds are discussed the elements of the theory of lie supergroups and principal superfiber bundles as supermanifolds are given