vibration analysis of shear deformable circular arches by the differential quadrature method the differential quadrature method is applied in the computation of the eigenvalues of the equations of motion governing in plane and out of plane vibration of circular arches based on the bresse timoshenko beam theory in which both rotatory inertia and shear deformation are taken into account fundamental frequencies are calculated for arches of rectangular and circular cross sections under clamped clamped end conditions and the results are compared with numerical solutions by another method the present method gives good accuracy with only a limited number of grid points

analytical and numerical study on spatial free vibration of non symmetric thin walled curved beams for spatial free vibration of non symmetric thin walled circular curved beams an accurate displacement field is introduced by defining all displacement parameters at the centroidal axis and three total potential energy functionals are consistently derived by degenerating the potential energy for the elastic continuum to that for thin walled curved beams the closed form solutions are newly obtained for in plane and out of plane free vibration analysis of monosymmetric curved beams respectively also two thin walled curved beam elements are developed using the third and fifth order hermitian polynomials in order to illustrate the accuracy and the practical usefulness of the present method analytical and numerical solutions by this study are presented and compared with previously published results or solutions by abaqus the shell element particularly effects of the thickness curvature as well as the inextensional condition are investigated on free vibration of curved beams with monosymmetric and non symmetric cross sections

the existence and nonexistence of entire large solutions for a quasilinear schrodinger elliptic system by dual approach abstract in this paper we establish some new results on the existence and nonexistence of radial large positive solutions for a modified schrodinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach the necessary and sufficient condition for the existence of radial large positive solutions is established our results improve and extend many previous work in this field of research

influence of centerline extensibility on the in plane free vibrations of loaded circular arches free vibrations of circular arches about a prestressed static equilibrium state are investigated the equations of motion for the small amplitude free vibrations about the initial equilibrium state attained under distributed tangential and normal loading derived in a previous paper and specialized to constant curvature are used particular attention is given to the influence of centerline stretching during the vibratory motion the vanishing of the loaded free vibration frequencies signals static buckling and the load intensities at which the frequencies go to zero correspond to the static buckling loads free vibrations with no initial loading is treated as a special case of the problem considered it is shown that exact numerical values for the frequencies can be obtained in this case in general the presence of distributed initial loading precludes the possibility of obtaining closed form analytical solutions barring a few simple loading situations such as uniform constant directional pressure as the governing differential equations have variable coefficients in the present work numerical results are obtained for uniform arches subjected to gravity loading the galerkin method with polynomial trial functions that satisfy the geometric boundary conditions is employed in obtaining accurate values of free vibration frequencies convergence of the method with increasing number of terms in the assumed expansion representing the true solution is demonstrated arches with pinned and clamped end support conditions are considered considerably different frequencies are found depending upon whether one includes or ignores the influence of centerline stretching during the vibratory motion

soliton solutions for quasilinear schrodinger equations the critical exponential case abstract quasilinear elliptic equations in r 2 of second order with critical exponential growth are considered by using a change of variable the quasilinear equations are reduced to semilinear equations whose respective associated functionals are well defined in h 1 r 2 and satisfy the geometric hypotheses of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle p l lions the concentration compactness principle in the calculus of variations the locally compact case part i and ii ann inst h poincare anal non lineaire 1 1984 109 145 223 283 combined with test functions connected with optimal trudinger moser inequality

dynamic stiffness analysis for in plane vibrations of arches with variable curvature this paper provides a systematic approach to solve in plane free vibrations of arches with variable curvature the proposed approach basically introduces the concept of dynamic stiffness matrix into a series solution for in plane vibrations of arches with variable curvature an arch is decomposed into as many elements as needed for accuracy of solution in each element a series solution is formulated in terms of polynomials the coefficients of which are related to each other through recurrence formulas as a result in order to have an accurate solution one does not need a lot of terms in series solution and in taylor expansion series for the variable coefficients of the governing equations due to the consideration of variable curvature finally a dynamic stiffness matrix is formed such that it can be applied to solve more complicated systems such as multiple span arches in the whole analysis the effects of rotary inertia and shear deformation have been taken into account

in plane vibrations of an elastically cantilevered circular arc with a tip mass abstract upper and lower bounds are determined for the fundamental frequency of in plane transverse vibration of the structural system described in the title in the case of constant cross section and moment of inertia the upper bound is determined by approximating the fundamental mode shape with a polynomial co ordinate function in the angular co ordinate which includes an exponential optimization parameter the fundamental frequency equation is generated by means of the rayleigh ritz method and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter the lower bound for the frequency coefficient is obtained by means of an extension of dunkerley s method it is felt that the methodologies developed in the present study are especially useful in the case of variable cross section of the arch structure presence of internal supports etc

exact solution of in plane vibrations of circular arches with account taken of axial extension transverse shear and rotatory inertia effects exact solution of free in plane vibrations of circular arches of uniform cross section is given by considering axial extension transverse shear and rotatory inertia effects in contrast with kirchhoff s beam theory the restrictions of perpendicular cross section and inextensible arc length are removed the principal axes of the cross section are assumed to coincide with the principal normal and binormal vectors of the centerline of the beam a solution procedure is applied to obtain the fundamental matrix for various end conditions natural frequencies and mode shapes are given in figures and tables

exact dynamic and static stiffness matrices of shear deformable thin walled beam columns abstract total potential energy of non symmetric thin walled beam columns in the general form is presented by introducing the displacement field based on semitangential rotations and deriving transformation equations between displacement and force parameters defined at the arbitrary axis and the centroid shear center axis respectively next governing equations and force deformation relations are derived from the total potential energy for a shear deformable uniform beam element and a system of linear eigenproblem with non symmetric matrices is constructed based on 14 displacement parameters and then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force deformatin relationships in addition the modified numerical method to eliminate multiple zero eigenvalues and to evaluate the exact static stiffness matrix is developed for spatial stability analysis finally in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies and buckling loads are evaluated and compared with analytical solutions or results analyzed by thin walled beam elements and abaqus s shell elements

exact natural frequencies of plane structures composed of slender elastic curved members abstract exact finite elements form the basis of a new and convenient procedure for converging with certainty upon the required natural frequencies of any plane structure composed of slender elastic curved members of constant radius solution of the inherent transcendental eigenvalue problem is achieved through a variation on the powerful wittrick williams algorithm two illustrative examples are included

the extended bigraded toda hierarchy we generalize the toda lattice hierarchy by considering n m dependent variables we construct roots and logarithms of the lax operator which are uniquely defined operators with coefficients that are series of differential polynomials in the dependent variables and we use them to provide a lax pair definition of the extended bigraded toda hierarchy generalizing 4 using r matrix theory we give the bi hamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions finally we study the dispersionless limit and its connection with a class of frobenius manifolds on the orbit space of the extended affine weyl groups of the a series defined by dubrovin and zhang 1998 compos math 111 167

low frequency mode transition in the free in plane vibration of curved beams the low frequency mode transition in the free in plane vibration of beams with varying curvature and cross section is examined by using perturbation analysis a simplified zeroth order equation for beam vibration in the region of the mode transition is derived this equation shows explicitly which modes undergo a transition for a particular type of beam curvature and cross section analytic approximations for frequency and mode shape are derived by the cases of beam curvature represented by symmetric and antisymmetric polynomials and their validity is illustrated by comparison with numerical solutions many features of mode transition phenomenon are revealed analytically including the effect of beam curvature on mode shape during the transition stage the similarities and distinctions between the low mode and the high mode number transitions are discussed

multiple solutions for a quasilinear schrodinger equation abstract in this paper we consider the quasilinear schrodinger equation u v x u u 2 u g x u x r n where g and v are periodic in x 1 x n and g is odd in u subcritical and satisfies a monotonicity condition we employ the approach developed in szulkin and weth 2009 2010 15 16 and obtain infinitely many geometrically distinct solutions

in plane and out of plane free vibrations of curved beams with variable sections we present an approximate method to study the analysis for both the in plane and out of plane free vibration of horizontally curved beams with arbitrary shapes and variable cross sections the characteristic equation for free vibration can be derived by applying the green function which is obtained as a discrete type solution of differential equations governing the flexural behaviour of the curved beam under the action of a concentrated load

on the frobenius manifolds for cusp singularities abstract we show that the frobenius manifold associated to the pair of a cusp singularity and its canonical primitive form is isomorphic to the one constructed from the gromov witten theory for an orbifold projective line with at most three orbifold points we also calculate the intersection form of the frobenius manifold

limits of families of brieskorn lattices and compactified classifying spaces we investigate variations of brieskorn lattices over non compact parameter spaces and discuss the corresponding limit objects on the boundary divisor we study the associated variation of twistors and the corresponding limit mixed twistor structures we construct a compact classifying space for regular singular brieskorn lattices and prove that its pure polarized part carries a natural hermitian structure and that the induced distance makes it into a complete metric space

infinitely many solutions for quasilinear schrodinger equation with critical exponential growth in rn abstract this paper shows the existence of infinitely many solutions for the quasilinear equations of the form 0 1 n u v x u n 2 u n u 2 u k x u q 2 u h u x r n where n u is the n laplacian operator n 3 0 1 q n k l r n n n q and h is an odd continuous function having critical exponential growth the potential function v x c r n and 0 inf x r n v x sup x r n v x using mountain pass theorem and some special techniques we demonstrate that there exists 0 0 such that problem 0 1 admits infinitely many high energy solutions provided that 0 0

free vibrations of arches with variable curvature abstract the equations governing free in plane vibrations of variable curvature arches are derived and solved numerically to obtain frequencies and mode shapes for parabolic sinusoidal and elliptic geometries included are experimental validations of the lowest four predicted frequencies and mode shapes for parabolic arches

the spaces of laurent polynomials gromov witten theory of ℙ1 orbifolds and integrable hierarchies let mk m be the space of laurent polynomials in one variable x t1x tk mx where k m 1 are fixed integers and tk m 6 0 according to b dubrovin 11 mk m can be equipped with a semi simple frobenius structure in this paper we prove that the corresponding descendent and ancestor potentials of mk m defined as in 16 satisfy hirota quadratic equations hqe for short let ck m be the orbifold obtained from p by cutting small discs d1 z and d2 z 1 around z 0 and z and gluing back the orbifolds d1 zk and d2 zm in the obvious way we show that the orbifold quantum cohomology of ck m coincides with mk m as frobenius manifolds modulo some yet to be clarified details this implies that the descendent respectively the ancestor potential of mk m is a generating function for the descendent respectively ancestor orbifold gromov witten invariants of ck m there is a certain similarity between our hqe and the lax operators of the extended bi graded toda hierarchy introduced by g carlet in 7 therefore it is plausible that our hqe characterize the tau functions of this hierarchy and we expect that the extended bi graded toda hierarchy governs the gromov witten theory of ck m

ground state solutions for generalized quasilinear schrodinger equations without ar condition abstract in this paper we study the following generalized quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u h x u x r n where n 3 g r r is an even differentiable function satisfying lim t g t t 1 0 for some 1 h x t is a given function behaving like t 2 1 at infinity which does not satisfy the a r condition combining the change of variables and the monotone method developed by jeanjean in 16 we obtain the existence of positive ground state solutions for the given problem

multiple solutions for a class of quasilinear schrodinger equations in ℝn in this work we study the existence of multiple solutions to a class of quasilinear schrodinger equation pu v x up 2u p u2 u2 2u g u x rn where pu div up 2 u is the p laplacian operator and p 2 n 12 is a parameter the potential v c n is positive and bounded in n g u is odd and continuous using symmetric mountain pass lemma we obtain infinitely many solutions to schrodinger equation

a uniqueness theorem for frobenius manifolds and gromov witten theory for orbifold projective lines we prove that the frobenius structure constructed from the gromov witten theory for an orbifold projective line with at most three orbifold points is uniquely determined by the wdvv equations with certain natural initial conditions

generalized quasilinear asymptotically periodic schrodinger equations with critical growth this paper is concerned with the following quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u g u g u 2 2 g u x r n u x 0 x r n where n 3 2 2 n n 2 g u 0 u g t d t and 0 is a parameter by using a change of variable the quasilinear equation is reduced to a semilinear one whose associated functional is well defined in h 1 r n we establish the existence of positive solutions for this problem by using the mountain pass theorem in combination with the concentration compactness principle under appropriate assumptions on v x and f x u recent results from the literature are improved and extended

closed form solutions of a multi cracked circular arch under static loads abstract generalised functions have been widely adopted in structural mechanics to treat singularities of beam like structures however due to the curved geometry that couples axial and transversal displacements their use has never been explored for curved beams in this paper the capability of distributions of leading to closed form exact solutions for multi cracked circular arch is shown the exact closed form solution of a circular euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained damage under the form of concentrated cracks has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of dirac s delta functions the resulting nontrivial generalised six order differential equations have been derived and solved in closed form independently of the number of along arch concentrated cracks the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression this latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem the results have been validated through some comparisons with finite element numerical simulations examples referred to multi cracked euler arches with different boundary conditions damage and load scenarios are presented

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

closed form solutions for dynamic analysis of extensional circular timoshenko beams with general elastic boundary conditions abstract closed form solutions for dynamic analysis of extensional circular timoshenko beams with general elastic boundary conditions are derived taking the laplace transform and some procedures the system composed of three coupled governing differential equations and six coupled boundary conditions is uncoupled and reduced to a single equation in terms of the angle of rotation due to bending the explicit relations between the inward radial displacement the tangential displacement and the angle of rotation due to bending are revealed six exact normalized fundamental solutions of the uncoupled governing differential equation are obtained by the frobenius method the exact transformed general solution of the uncoupled system is expressed in terms of the six fundamental solutions using the generalized green function given by lin the systems based on the rayleigh and bernoulli euler beam theories can be obtained by taking the corresponding limiting procedures without the laplace transform the exact solutions for the steady and free vibrations of the general system are obtained the effects of the spring constants the opening angle the rotary inertia and the shear deformation on the natural frequencies are investigated

an efficient curved beam finite element the plane two node curved beam finite element with six degrees of freedom is considered knowing the set of 18 exact shape functions their approximation is derived using the expansion of the trigonometric functions in the power series unlike the ones commonly used in the fem analysis the functions suggested by the authors have the coefficients dependent on the geometrical and physical properties of the element from the strain energy formula the stiffness matrix of the element is determined it is very simple and can be split into components responsible for bending shear and axial forces influences on the displacements the proposed element is totally free of the shear and membrane locking effects it can be referred to the shear flexible parameter d and compressible parameter e systems neglecting d or e yields the finite elements in all necessary combinations i e curved euler bernoulli beam or curved timoshenko beam with or without the membrane effect applying the elaborated element in the calculations a very good convergence to the analytical results can be obtained even with a very coarse mesh without the commonly adopted corrections as reduced or selective integration or introduction of the stabilization matrices additional constraints etc for the small depth length ratio 1997 john wiley sons ltd

coupled out of plane vibrations of spiral beams for micro scale applications abstract an analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an archimedean spiral beam the deflection of the beam is due to both bending and torsion which makes the problem coupled in nature the governing partial differential equations and the boundary conditions are derived using hamilton s principle two factors make the vibrations of spirals different from oscillations of constant radius arcs the first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable it is demonstrated using perturbation techniques that the derivative of the radius terms have negligible effect on structure s dynamics the spiral is then approximated with many merging constant radius curved sections joined together to approximate the slow change of radius along the spiral the equations of motion are formulated in non dimensional form and the effect of all the key parameters on natural frequencies is presented non dimensional curves are used to summarize the results for clarity we also solve the governing equations using rayleigh s approximate method the fundamental frequency results of the exact and rayleigh s method are in close agreement this to some extent verifies the exact solutions the results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

existence and multiplicity of solutions for a class of generalized quasilinear schrodinger equations abstract this paper focuses on the following generalized quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u x r n where n 3 g s r r is a nondecreasing function with respect to s by using a change of variables and variational methods we obtain the existence and multiplicity of nontrivial solutions for the above problem when the nonlinearity is superlinear but does not satisfy the ambrosetti rabinowitz type condition

curvature based beam elements for the analysis of timoshenko and shear deformable curved beams abstract curved beam elements with six degrees of freedom and two three four and five node timoshenko straight beam elements with four five six and seven degrees of freedom respectively are proposed to eliminate stiffness locking when applied to the dynamic analysis of the beams the elements are based on curvature assumptions so that they can represent the bending energy accurately and the shear strain energy is incorporated into the formulation by way of the equilibrium equation eigenvalue problems of timoshenko and shear deformable curved beams are analyzed by using the elements the results of the eigen analysis show that the curvature based beam elements are free of locking and are efficient

normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints abstract there has been a longstanding interest in deriving conditions under which dynamic optimization problems are normal that is the necessary conditions of optimality nco can be written with a nonzero multiplier associated with the objective function this paper builds upon previous results on nondegenerate nco for trajectory constrained optimal control problems to provide even stronger normal forms of the conditions the nco developed may address problems with nonsmooth less regular data the particular case of calculus of variations problems is here explored to show a favorable comparison with existent results

a ground state solution for an asymptotically periodic quasilinear schrodinger equation abstract this article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear schrodinger equation by using a change of variables the quasilinear problem is transformed into a semilinear one then we use a nehari type constraint to get the existence result

multiple solutions to a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation abstract in this paper we consider a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation under the assumption that the potential may be vanishing at infinity the existence of both the ground state and the ground state sign changing solutions is established furthermore the behavior of these solutions is studied when the perturbation vanishes it is a surprise that we find an interesting phenomenon about the monotonicity for the quotient function as a byproduct

locking free curved beam element based on curvature the formulation of a curved beam element with 3 nodes for curvature to eliminate the shear membrane locking phenomenon is presented the element is based on curvature so that it may represent the bending energy fully and the shear membrane strain energy is incorporated into the formulation by the equilibrium equations to deal with general boundary conditions a transformation matrix between nodal curvature and nodal displacement vector is introduced several examples are presented in order to verify the element formulation and its analytical capability the solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently showing no locking phenomena and that it is also applicable to the analysis of both thin and thick curved beams

gromov witten theory of orbicurves the space of tri polynomials and symplectic field theory of seifert fibrations we compute with symplectic field theory sft techniques the gromov witten theory of mathbb p 1 alpha 1 ldots alpha a i e the complex projective line with a orbifold points a natural subclass of these orbifolds the ones with polynomial quantum cohomology gives rise to a family of polynomial frobenius manifolds and integrable systems of hamiltonian pdes which extend the dispersionless bigraded toda hierarchy carlet the extended bigraded toda hierarchy arxiv preprint arxiv math ph 0604024 we then define a frobenius structure on the spaces of polynomials in three complex variables of the form f x y z xyz p1 x p2 y p3 z which contains as special cases the ones constructed on the space of laurent polynomials dubrovin geometry of 2d topologica field theories integrable systems and quantum groups springer lecture notes in mathematics 1620 120 348 1996 milanov and tseng the space of laurent polynomials mathbb p 1 orbifolds and integrable hierarchies preprint arxiv math 0607012v3 math ag we prove a mirror theorem stating that these frobenius structures are isomorphic to the ones found before for polynomial mathbb p 1 orbifolds finally we link rational sft of seifert fibrations over mathbb p 1 a b c with orbifold gromov witten invariants of the base extending a known result bourgeois a morse bott approach to contact homology ph d dissertation stanford university 2002 valid in the smooth case

exact vibration solutions for nonuniform timoshenko beams with attachments the exact solution for the free vibration of a symmetric nonuniform timoshenko beam with tip mass at one end and elastically restrained at the other end of the beam is derived the two coupled governing characteristic differential equations are reduced into one complete fourth order ordinary differential equation with variable coefficients in the angle of rotation due to bending the frequency equation is derived in terms of the four normalized fundamental solutions of the differential equation it can be shown that if the coefficients of the reduced differential equation can be expressed in polynomial form the exact fundamental solutions can be found by the method of frobenius finally several limiting cases are studied and the results are compared with those in the existing literature a x e x g x i x j x

multiple solutions for quasilinear schrodinger equations with a parameter abstract in this paper we study the following quasilinear schrodinger equations of the form u v x u u 2 u 2 2 u g x u x r n where 1 1 2 v c r n r g c r n r r using some special techniques the existence of positive solutions negative solutions and sequence of high energy solutions are studied

in plane free vibration and stability of loaded and shear deformable circular arches the first known equations governing vibrations of preloaded shear deformable circular arches are derived according to a variational principle for dynamic problems concerning an elastic body under equilibrium initial stresses the equations are three partial differential equations with variable coefficients the governing equations are solved for arches statically preloaded with a uniformly distributed vertical loading by obtaining a static closed form solution and an analytical dynamic solution from series solutions and dynamic stiffness matrices convergence to accurate results is obtained by increasing the number of elements or by increasing both the number of terms in the series solution and the number of terms in the taylor expansion of the variable coefficients graphs of non dimensional frequencies and buckling loads are presented for preloaded clamped arches they clarify the effects of opening angle and thickness to radius ratio on vibration frequencies and buckling loads the effects of static deformations on vibration frequencies are also investigated this work also compares the results obtained from the proposed governing equations with those obtained from the classical theory neglecting shear deformation

existence of multiple solutions for modified schrdingerkirchhoffpoisson type systems via perturbation method with sign changing potential in this paper we prove the existence of positive solutions and negative solutions for the following modified schrdingerkirchhoffpoisson type systems a br3u2 u v x u u12u u2 f x u inr3 u2 inr3 where a 0 b0 v and f are continuous functions and v x is allowed to be sign changing under some certain assumptions on v and f we prove the existence of nontrivial nonnegative solutions nontrivial nonpositive solutions and sequence of high energy solutions via the perturbation method

an analytic model for the free in plane vibration of beams of variable curvature and depth in this study a flexible and powerful model is presented for the in plane vibration of a beam whose curvature and depth are arbitrary constrained only to such smoothness as can be accommodated by a quartic polynomial in the centerline arc length the model includes the effects of shear deformation rotary inertia and centerline extensibility the equations of motion are solved by an extension of the classic galerkin method wherein the effect of boundary residuals is included timoshenko models are compared to other theoretical models and to experimental results the comparisons are done for a variety of support schemes a detailed study of a cantilever beam of variable curvature and depth is done and finally the utility and flexibility of the model is demonstrated for an arch whose shape is given only by a scale drawing devoid of any other information except material properties

out of plane dynamic responses of non circular curved beams by numerical laplace transform abstract the paper presents a systematic method for analyzing the out of plane dynamic behaviours of non circular curved beams the governing equations of which take into account the effects of shear deformation rotary inertia and viscous damping the procedure consists of formulating an analytical solution for the transformed governing equations in the laplace transform domain and computing the responses in the time domain by means of numerical laplace inversion as key elements in the dynamic stiffness method the first known transformed dynamic stiffness matrix and equivalent nodal loading vector for non circular curved beams subjected to distributed external loading are established from the analytical solution developed using the famous frobenius method with a simple modification the formulation of the solution is also suitable for free vibration analysis which results in an exact solution as numerical examples for transient analysis time responses of displacement components and stress resultants are found for a two span elliptic beam subjected to a rectangular impulse the behaviours of the response due to the variation of the ratio of the long axis to the short one are investigated

exact dynamic stiffness matrix of non symmetric thin walled curved beams subjected to initial axial force abstract an improved numerical method to exactly evaluate the dynamic element stiffness matrix is proposed for the spatially coupled free vibration analysis of non symmetric thin walled curved beams subjected to uniform axial force for this purpose firstly equations of motion boundary conditions and force deformation relations are rigorously derived from the total potential energy for a curved beam element next systems of linear algebraic equations with non symmetric matrices are constructed by introducing 14 displacement parameters and transforming the fourth order simultaneous differential equations into the first order simultaneous equations and then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact 14 14 element stiffness matrix is determined using force deformation relations in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies of non symmetric thin walled curved beams subjected to uniform compressive and tensile forces are evaluated and compared with analytical and finite element solutions using hermitian curved beam elements or abaqus s shell element in addition some results by the parametric study are reported

global existence of small solutions to a relativistic nonlinear schrodinger equation on etudie le probleme de cauchy associea une equation de schrodinger non lineaire modelisant une impulsion laser ultra intense et ultra courte dans un plasma les termes non lineaires nouveaux sont dus aux effets relativistes et a la force ponderomotrice nous prouvons l existence locale et l unicite de solutions petites lorsque la dimension de l espace transverse est egale a 2 ou 3 ainsi que l existence locale pour des donnees initiales de taille arbitraire en dimension un d espace transverse

out of plane dynamic analysis of beams with arbitrarily varying curvature and cross section by dynamic stiffness matrix method abstract the first known dynamic stiffness matrix for noncircular curved beams with variable cross section is developed with which an exact solution of the out of plane free vibration of this type of beam is derived by using the laplace transform technique and the developed dynamic stiffness matrix and equivalent nodal force vector the highly accurate dynamic responses including the stress resultants of the curved beams subjected to various types of loading can be easily obtained the dynamic stiffness matrix and equivalent nodal force vector are derived based on the general series solution of the differential equations for the out of plane motion of the curved beams with arbitrary shapes and cross sections the validity of the present solution for free vibration is demonstrated through comparison with published data the accuracy of the present solution for transient response is also confirmed through comparison with the modal superposition solution for a simply supported circular beam subjected to a moving load with the proposed solution both the free vibration and forced vibration of non uniform parabolic curved beams with various ratios of rise to span are carried out nondimensional frequency parameters for the first five modes are presented in graphic form over a range of rise to span ratios 0 05 h l 0 75 with different variations of the cross section dynamic responses of the fixed fixed parabolic curved beam subjected to a rectangular pulse are also presented for different rise to span ratios

infinitely many small solutions for a sublinear schrodinger poisson system with sign changing potential in this paper we study the existence of infinitely many small solutions for a class of sublinear schrodinger poisson system with sign changing potential by using a dual approach we prove that the problem has infinitely many small solutions as a main novelty with respect to some previous results we do not require any growth condition on the nonlinear term

asymptotic analysis of the free in plane vibrations of beams with arbitrarily varying curvature and cross section abstract an asymptotic analysis is carried out for the equations of free vibrations of a beam having varying curvature and cross section the effect of splitting the asymptotic limit for eigen values into two families is revealed and its connection with boundary conditions is discussed the analysis of the properties of the asymptotic solution explains the phenomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams the asymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are difficult to analyse by other means the asymptotic behaviour of the solution is illustrated numerically for different types of curvature including antisymmetric curvature an experimental verification of the asymptotic behaviour of mode frequencies is presented

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

infinitely many solutions of quasilinear schrodinger equation with sign changing potential abstract in this paper we study the following quasilinear schrodinger equation of the form u v x u u 2 u g x u x r n where the potential v x is allowed to be sign changing and the primitive of the nonlinearity g x u is of superlinear growth at infinity in u and is also allowed to be sign changing we obtain the existence of infinitely many nontrivial solutions by using dual approach and mountain pass theorem

out of plane dynamic response of curved beams an analytical model abstract an analytical model for the vibration response of a curved beam is developed and presented the model is based on the solution closed solution of the dynamic differential equations of equilibrium for an infinitesimal element vibrating out of its initial plane of curvature and allows for inclusion of the effects of rotary inertia and or shear deformation final solutions are presented under the form of elements of the tip dynamic stiffness matrix for a free free beam the validity of the model is assessed by comparison of theoretical and experimental results for several examples of curved beams

standing waves for quasilinear schrodinger equations with indefinite potentials abstract we consider quasilinear schrodinger equations in r n of the form u v x u u u 2 g u where g u is 4 superlinear unlike all known results in the literature the schrodinger operator v is allowed to be indefinite hence the variational functional does not satisfy the mountain pass geometry by a local linking argument and morse theory we obtain a nontrivial solution for the problem in case that g is odd we get an unbounded sequence of solutions

free vibrations of spatial timoshenko arches abstract this paper addresses the evaluation of the exact natural frequencies and vibration modes of structures obtained by assemblage of plane circular arched timoshenko beams the exact dynamic stiffness matrix of the single circular arch in which both the in plane and out of plane motions are taken into account is derived in an useful dimensionless form by revisiting the mathematical approach already adopted by howson and jemah 1999 18 for the in plane and the out of plan natural frequencies of curved timoshenko beams the knowledge of the exact dynamic stiffness matrix of the single arch makes the direct evaluation of the exact global dynamic stiffness matrix of spatial arch structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes for the distributed parameter model through the application of the wittrick and williams algorithm consistently with the dimensionless form proposed in the derivation of the equations of motion and the dynamic stiffness matrix an original and extensive parametric analysis on the in plane and out of plane dynamic behaviour of the single arch for a wide range of structural and geometrical dimensionless parameters has been performed moreover some numerical applications relative to the evaluation of exact frequencies and the corresponding mode shapes in spatial arched structures are reported the exact solution has been numerically validated by comparing the results with those obtained by a refined finite element simulation

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9