an algorithm to control chaotic behavior in one dimensional maps abstract an algorithm is proposed whereby any chaotic transformation i e one merely possessing a dense orbit can be modified slightly to in order to attain a desired target probability density function f the algorithm can be used in practical examples such as controlling the long term population distribution of a species whose dynamics is described by a point transformation

flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables a set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the rayleigh ritz method the set of orthogonal polynomials is constructed by employing the gram schmidt orthogonalization procedure the first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted results are compared with those obtained previously by other methods

in plane free vibration of circular annular disks abstract this paper presents a generalized formulation for the in plane modal characteristics of circular annular disks under combinations of all possible classical boundary conditions the in plane free vibration of an elastic and isotropic disk is studied on the basis of the two dimensional linear plane stress theory of elasticity the boundary characteristic orthogonal polynomials are employed in the rayleigh ritz method to obtain the natural frequencies and associated mode shapes two approaches have been used to represent a clamped boundary condition the first approach assumes a polynomial expression that satisfies the clamped conditions while the second approach uses a disk with free boundary supported on artificial springs with stiffness tending to infinity the natural frequencies are tabulated and compared with data available in the literature mode shapes are presented to illustrate the free vibration behavior of the disk

a remark on the global solvability of the cauchy problem for quasilinear parabolic equations abstract the present paper is concerned with the global solvability of the cauchy problem for the quasilinear parabolic equations with two independent variables ut a t x u ux uxx f t x u ux we investigate the case of the arbitrary order of growth of the function f t x u p with respect to p when p conditions which guarantee the global classical solvability of the problem are given

synchronization of chaotic trajectories using control we demonstrate that two identical chaotic systems can be made to synchronize by applying small judiciously chosen temporal parameter perturbations to one of them this idea is illustrated with a numerical example other issues related to synchronization are also discussed

axisymmetric vibration of circular plates and its analog in elliptical plates using characteristic orthogonal polynomials the axisymmetric vibration of circular plates and its analog in elliptic plates with clamped simply supported and free boundary conditions are investigated using boundary characteristic orthogonal polynomials in the rayleigh ritz method modified polar coordinates are employed to analyze the vibration of elliptical plates with circular plates as a special case axisymmetric vibration of circular plates and its analog in elliptical plates with concentric nodal elipses require only one dimensional shape functions in the rayleigh ritz method the first six natural frequencies and the parameters associated with nodal ellipses are tabulated

kinetic stabilization of a nonlinear sonic phase boundary we consider a system arising in the study of phase transitions in elastodynamics a system of two conservation laws in a single space dimension the system has two hyperbolic regions with an elliptic zone in between a phase boundary is a strong discontinuity in a solution with left and right states belonging to different hyperbolic regions we call such a solution a phase wave

analytical and experimental investigation on vibrating circular plates with stepped thickness over a concentric circular region transverse vibrations of the structural elements described in the title are studied for the case where the edges are elastically restrained against translation and rotation since finding an exact solution is a difficult task it was considered convenient to approximate the response of the plate in the case of free axisymmetric vibrations by means of a summation of simple polynomial coordinate functions that satisfy the governing boundary conditions the ritz method is used in order to generate the frequency equation the natural frequency coefficients are optimized by minimizing each eigenvalue with respect to an undetermined exponential parameter included in each coordinate function

the problem of dirichlet for evolution one dimensional p laplacian with nonlinear source in the present paper we consider the dirichlet problem for one dimensional p laplacian with nonlinear source we obtain new a priori estimates of a solution and of the gradient of a solution and formulate conditions guaranteeing the global solvability of this problem our consideration includes singular case as well

examples of parabolic problems with blowing up derivatives abstract a number of parbolic problems with blowing up space derivatives are described based upon theorem 1 the main result of the paper further examples will also be constructed examining the significance and sharpness of the more than quadratic growth condition for the occurrence of the derivative blow up it is shown that this condition is sufficient for a wide class of equations described in section 6

a perturbation approach for evaluating natural frequencies of moderately thick elliptic plates natural frequencies for moderately thick elliptic plates are calculated by perturbing initial values corresponding to the kirchhoff classical theory of plate bending the proposed approach utilizes a universal algebraic equation for perturbed eigenvalues previously derived by the authors for elliptic plates of a small eccentricity a dual procedure is developed to evaluate the sought for natural frequencies starting from those for a circular thin plate a comparison with finite element computations is presented an importance of the perturbation techniques in question for interpreting of finite element data is emphasized

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

controlling chaotic dynamical systems abstract we describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter the time periodic motion results from the stabilization of one of the infinite number of previously unstable periodic orbits embedded in the attractor the present paper extends that of ott grebogi and yorke phys rev lett 64 1990 1196 allowing for a more general choice of the feedback matrix and implementation to higher dimensional systems the method is illustrated by an application to the control of a periodically impulsively kicked dissipative mechanical system with two degrees of freedom resulting in a four dimensional map the double rotor map a key issue addressed is that of the dependence of the average time to achieve control on the size of the perturbations and on the choice of the feedback matrix

classical jacobi polynomials closed form solutions for transverse vibrations this paper deals with transverse vibrations of nonuniform homogeneous beams and plates classes of beams and axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations respectively can be reduced to an eigenvalue singular problem singularities occur at both ends of orthogonal polynomials are reported exact natural frequencies and jacobi polynomials as exact mode shapes which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials are reported for these classes the above classes of beams and plates hereafter called jacobi classes are given by geometry and boundary conditions the geometry consists of parabolic thickness variation with respect to the axial coordinate for beams and with respect to the radius for plates beams belonging to this class have either one or two sharp ends singularities along with certain boundary conditions plates have zero thickness at zero and outer radii the boundary value problems associated with plates and beams of two sharp ends are free boundary problems two other boundary value problems hinged free and sliding free are reported for beams with one sharp end also exact natural frequencies and mode shapes for uniformly rotating beams with hinged free boundary are reported

higher dimensional targeting this paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations such a procedure is called targeting previous work on targeting for chaotic attractors has been in the context of one and two dimensional maps here it is shown that targeting can also be done in higher dimensional cases the method is demonstrated with a mechanical system described by a four dimensional mapping whose attractor has two positive lyapunov exponents and a lyapunov dimension of 2 8 the target is reached by making very small successive changes in a single control parameter in one typical case 35 iterates on average are required to reach a target region of diameter 10 sup minus 4 as compared to roughly 10 sup 11 iterates without the use of the targeting procedure

three dimensional elasticity solutions to vibration of cantilevered skewed trapezoids an accurate three dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented the method is formulated on the basis of a linear small strain three dimensional elasticity theory with the ritz minimization procedure the solution method uses sets of uniquely defined one and twodimensional polynomial functions to approximate the trial displacements in the thickness and surface directions respectively these functions are orthogonally generated and have been proven to be highly efficient and numerically stable the proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform the accuracy of these results whenever possible is validated through comparison with the analytical and experimental data parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios skew angles and chord ratios have been carried out for the first time the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three dimensional mode shape plots

a new approach to controlling chaotic systems abstract given a piecewise monotonic transformation which is strongly transitive and preserves an invariant probability density function f a construction is described which modifies very slightly but which changes f significantly in order to possess desired properties this construction permits control of the global long term behavior of chaotic dynamical systems

the problem of dirichlet for anisotropic quasilinear degenerate elliptic equations we consider the dirichlet problem for a class of anisotropic degenerate elliptic equations new a priori estimates for solutions and for the gradient of solutions are established based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated the results are new even in the semilinear case when the principal part is the laplace operator

transverse vibrations of a clamped elliptical plate carrying a concentrated mass at an arbitrary position free vibrations of clamped thin elliptical plates carrying a concentrated mass at an arbitrary position are studied in order to analyze the mass effect on the natural frequencies and mode shapes of the plate a variational approach the well known ritz method is used where the displacement amplitude is approximated by polynomial expressions in the cartesian coordinates the present proposal exhibits excellent agreement with particular cases of the problem available in the literature and also with an independent solution obtained by means of the finite element method some new results are presented for the natural frequencies and modes of clamped elliptical plates with a concentrated mass

a boundary perturbation method for circularly periodic plates with a core fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically a boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem the method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions clamped simply supported and free circular cores are considered approximate analytical formulations of the fundamental frequency for such plates with core are obtained

controlling hamiltonian chaos the method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by ott grebogi and yorke ogy is not directly applicable to chaotic hamiltonian systems the reason is that an unstable periodic orbit in such systems often exhibits complex conjugate eigenvalues at one or more of its orbit points in this paper we extend the ogy stabilization method to control hamiltonian chaos by incorporating the notion of stable and unstable directions at each periodic point we also present an algorithm to calculate the stable and unstable directions other issues specific to the control of hamiltonian chaos are also discussed

input to state stability with respect to boundary disturbances for a class of semi linear parabolic equations abstract this paper studies the input to state stability iss properties for a class of semi linear parabolic partial differential equations pdes with respect to boundary disturbances in order to avoid the appearance of time derivatives of the disturbances in iss estimates some technical inequalities are first developed which allow directly dealing with the boundary conditions and establishing the iss based on the method of lyapunov functionals the well posedness analysis of the considered problem is carried out and the conditions for iss are derived two examples are used to illustrate the application of the developed method