forced responses of solid axially polarized piezoelectric ceramic finite cylinders with internal losses a method is presented to determine the forced responses of piezoelectric cylinders using weighted sums of only certain exact solutions to the equations of motion and the gauss electrostatic conditions one infinite set of solutions is chosen such that each field variable is expressed in terms of bessel functions that form a complete set in the radial direction another infinite set of solutions is chosen such that each field variable is expressed in terms of trigonometric functions that form a complete set in the axial direction another solution is used to account for the electric field that can exist even when there is no vibration the weights are determined by using the orthogonal properties of the functions and are used to satisfy specified arbitrary axisymmetric boundary conditions on all the surfaces special cases including simultaneous mechanical and electrical excitation of cylinders are presented all numerical results are in excellent agreement with those obtained using the finite element software atila for example the five lowest frequencies at which the conductance and susceptance of a stress free cylinder of length 10 mm and radius 5 mm reach a local maximum or minimum differ by less than 0 01 from those computed using atila

vibration analysis of coupled conical cylindrical spherical shells using a fourier spectral element method this paper presents a fourier spectral element method fsem to analyze the free vibration of conical cylindrical spherical shells with arbitrary boundary conditions cylindrical conical and cylindrical spherical shells as special cases are also considered in this method each fundamental shell component i e cylindrical conical and spherical shells is divided into appropriate elements the variational principle in conjunction with first order shear deformation shell theory is employed to model the shell elements since the displacement and rotation components of each element are expressed as a linear superposition of nodeless fourier sine functions and nodal lagrangian polynomials the global equations of the coupled shell structure can be obtained by adopting the assembly procedure the fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution numerical results show that the fsem can be effectively applied to vibration analysis of the coupled shell structures numerous results for coupled shell structures with general boundary conditions are presented furthermore the effects of geometric parameters and boundary conditions on the frequencies are investigated

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

kolmogorov complexity and cellular automata classification we present a new approach to cellular automata ca classification based on algorithmic complexity we construct a parameter which is based only on the transition table of ca and measures the randomness of evolutions is better in a certain sense than any other parameter recursively definable on ca tables we investigate the relations between the classical topological approach and ours our parameter is compared with langton s parameter turns out to be theoretically better and also agrees with some practical evidences reported in literature finally we propose a protocol to approximate and make experiments on ca dynamical behavior

dynamic analysis of generally supported beams using fourier series the applicability of fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored for the simplicity of presenting the analysis procedure beams having zero end displacement are used in the discussion numerical results for free vibration and dynamic response based on the present analysis procedure are compared with existing results for natural frequencies and dynamic behavior obtained by the conventional modal analysis these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis

take off analysis of the olympic ski jumping competition hs 106m abstract the take off phase approximately 6 m of the jumps of all athletes participating in the individual hs 106 m hill ski jumping competition at the torino olympics was filmed with two high speed cameras the high altitude of the pragelato ski jumping venue 1600 m and slight tail wind in the final jumping round were expected to affect the results of this competition the most significant correlation with the length of the jump was found in the in run velocity r 0 628 p n 50 this was a surprise in olympic level ski jumping and suggests that good jumpers simply had smaller friction between their skis and the in run tracks and or the aerodynamic quality of their in run position was better angular velocity of the hip joint of the best jumpers was also correlated with jumping distance r 0 651 p n 10 the best jumpers in this competition exhibited very different take off techniques but still they jumped approximately the same distance this certainly improves the interests in ski jumping among athletes and spectators the comparison between the take off techniques of the best jumpers showed that even though the more marked upper body movement creates higher air resistance it does not necessarily result in shorter jumping distance if the exposure time to high air resistance is not too long a comparison between the first and second round jumps of the same jumpers showed that the final results in this competition were at least partly affected by the wind conditions

transverse vibrations of non homogeneous orthotropic rectangular plates of variable thickness a spline technique an analysis and numerical results are presented for free transverse vibrations of non homogeneous orthotropic rectangular plates of non uniform thickness and resting on an elastic foundation of winkler type on the basis of classical plate theory the non homogeneity of the plate material is assumed to arise due to the exponential variation in young s moduli and density along one direction following levy approach i e the two parallel edges are simply supported the fourth order differential equation governing the motion of such plates of exponentially varying thickness in one direction has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges effect of the non homogeneity and elastic foundation together with other plate parameters such as orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for specified plates for all the three boundary conditions

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

nonlinear vibration of functionally graded circular cylindrical shells based on improved donnell equations abstract in the present work the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents governing equations are derived using improved donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration one term approximate solution is assumed to satisfy simply supported boundary conditions the galerkin method the volmir s assumption and fourth order runge kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies nonlinear frequency amplitude relation and nonlinear dynamic responses numerical results show the effects of characteristics of functionally graded materials pre loaded axial compression and dimensional ratios on the dynamical behavior of shells the proposed results are validated by comparing with those in the literature

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

block transformations of one dimensional deterministic cellular automaton rules given a one dimensional cellular automaton rule f a block transform of f is a rule tbf such that there exists between the limit sets of both rules a bijection that replaces each site value x in a configuration belonging to the limit set of f with a string xb xx x of length b in the corresponding configuration belonging to the limit set of tbf if f is totalistic there exists a unique totalistic block transform and a large number of nontotalistic block transforms tbf if f is not totalistic there are no totalistic block transforms but there still exists a large number of non totalistic block transforms their number increases very rapidly with the block size b and the range of f the range of tbf may be any integer greater than or equal to rb many block transforms are studied the evolution according to rule tbf towards its limit set is discussed in terms of the annihilation of defects these defects are often simply related to the defects characterizing the evolution according to rule f

chaos and diffusion in deterministic cellular automata abstract it is shown that some of the deterministic one dimensional cellular automata studied recently by wolfram exhibit a kind of spontaneous symmetry breaking the associated kinks bloch walls perform annihilating diffusive walks for infinite lattices and large times in addition close analogies between these automata and strange attractors are exhibited by mapping the automata onto dynamical systems defined by iterations of the unit square

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

3d vibration analysis of solid and hollow circular cylinders via chebyshev ritz method a general approach is presented for solving the free vibration of solid and hollow circular cylinders the analysis procedure is based on the small strain linear and exact elasticity theory by taking the chebyshev polynomial series multiplied by a boundary function to satisfy the geometric boundary conditions as the admissible functions the ritz method is applied to derive the frequency equation of the cylinder according to the axisymmetric geometrical property of a circular cylinder the vibration modes are divided into three distinct categories axisymmetric vibration torsional vibration and circumferential vibration moreover for a cylinder with the same boundary conditions at the two ends the vibration modes can be further divided into antisymmetric and symmetric ones in the length direction convergence and comparison studies demonstrate the high accuracy and small computational cost of the present method a significant advantage over other ritz solutions is that the present method can guarantee stable numerical operation even when a large number of terms of admissible functions are used not only the lower order but also the higher order frequencies can be obtained by using a few terms of the chebyshev polynomials finally the first several frequencies of circular cylinders with different boundary conditions with respect to various parameters such as the length radius ratio and the inside outside radius ratio are given 2003 elsevier science b v all rights reserved

free and forced vibrations of hollow elastic cylinders of finite length an analytical model of axisymmetric vibrations of hollow elastic circular cylinders with arbitrary boundary conditions is presented free vibrations of cylinders with free or fixed boundaries and forced vibrations of cylinders with specified non uniform displacement or stress on the boundaries are considered three series solutions are used and each term in each series is an exact solution to the exact governing equations of motion the terms in the expressions for components of displacement and stress are products of bessel and sinusoidal functions and are orthogonal to each other complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two respectively it is therefore possible to satisfy arbitrary boundary conditions it is shown that just two terms in each series are sufficient to determine several resonance frequencies of cylinders with certain specified boundary conditions the error is less than 1 numerical results are also presented for forced vibration of hollow steel cylinders of length 10 mm and outer diameter 10 mm with specified normal displacement or stress excellent agreement with finite element results is obtained at all frequencies up to 1 mhz convergence of the series is also discussed

analytical modelling of flexural vibration of arbitrary flat plates by the boundary forming approach abstract the approach described in this paper provides the flexural vibration response of a finite plate of arbitrary shape and arbitrary boundary conditions in terms of the known analytical response of an infinite plate the solution is obtained by superposing to the infinite plate two excitations an original and a secondary excitation the latter which is continuously distributed outside the contour line bounding the original plate has the role of creating at this line the boundary conditions proper to the targeted original plate the plate displacement is obtained in terms of continuous analytical functions which in turn enable comprehensive analysis of the dynamic variables such as stress energy density and energy flow the key advantage of the approach is the possibility to assess the computation error the accuracy of the method has been analysed indirectly by comparison with known modal solutions of rectangular plates and directly by assessing the boundary error the potential of the method is demonstrated using an example of a plate of complex shape and non homogeneous boundary conditions

thermodynamics of systems of finite sequences it is proposed that the hamming distance between bit strings plays the role of interaction energy the statistical sum and thermodynamic functions are calculated for the canonical ensemble of bit sequences the method is illustrated with an ensemble of two sequence systems which evolve according to cellular automata rules

vibrations of rectangular plates with arbitrary non uniform elastic edge restraints abstract arbitrary non uniform elastic edge restraints represent the most general class of boundary conditions for plate problems and are encountered in many real world applications the vibrations of plates with this kind of boundary conditions however are rarely studied in the literature perhaps because there is a lack of suitable analytical or numerical techniques in this investigation a general analytical method is derived for the vibration analysis of rectangular plates with elastic edge restraints of varying stiffness both rotational and translational restraints can be arbitrarily applied to an edge and their stiffness distributions are generally described in terms of a set of invariants cosine functions the displacement solution is sought simply as a linear combination of several one and two dimensional fourier cosine series expansions all the unknown fourier coefficients are treated equally as a set of independent generalized coordinates and solved directly from the rayleigh ritz formulation unlike the existing techniques the current method does not require any special procedures or schemes to deal with different boundary conditions a few classical problems involving non uniform rotational restraints are first solved and used to check the current solution against some of the existing techniques the modal results are also presented for plates with more complicated boundary conditions in which an edge is no longer completely restrained in the translational direction the accuracy and reliability of the current method are repeatedly demonstrated through all these examples

accurate vibration frequencies of circular cylinders from three dimensional analysis a three dimensional 3 d method of analysis developed in a companion paper a w leissa and j so j acoust soc am 98 2122 2135 1995 is used to obtain free vibration frequencies of completely free elastic cylinders extensive accurate data are presented for the first 20 frequencies of each circumferential wave number 0 5 for free free cylinders having length to diameter ratios l d of 1 1 5 2 3 and 5 with a poisson s ratio of 0 3 an additional study for l d 1 over the full range 0 0 5 possible for isotropic materials shows that poisson s ratio effects can be quite important the first known values of frequencies from 3 d analysis of cylinders having one end fixed with all other boundaries free are also presented in considerable detail for free free cylinders comparisons are made with less accurate 3 d results published previously by other researchers

optimization of the ritz method to calculate axisymmetric natural vibration frequencies of cylinders a straightforward accurate technique is presented for calculating natural frequencies for axisymmetric vibration of cylinders of any aspect ratio the ritz variational method is applied by using algebraic polynomials in the form of power series in the axial and radial coordinates the adequate choice of the maximum exponents for each coordinate is important factor in order to achieve better accuracy compatible with an admissible time of calculation a computational model is developed that provides the optimum selection of exponents by following an automatic iterative process this leads to a precise calculation of frequencies in a minimum time of calculation the method is tested by comparing numerical and experimental results and a good agreement is obtained the common hypothesis on the number of terms in the radial and axial coordinates is not sufficiently justified as is proved

three dimensional vibrations of cylindrical elastic solids with v notches and sharp radial cracks abstract this paper provides free vibration data for cylindrical elastic solids specifically thick circular plates and cylinders with v notches and sharp radial cracks for which no extensive previously published database is known to exist bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick v notched plate under transverse vibratory motion and three dimensional 3 d normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a v notched cylindrical elastic solid under 3 d free vibration a theoretical analysis is done in this work utilizing a variational ritz procedure including these essential singularity effects the procedure incorporates a complete set of admissible algebraic trigonometric polynomials in conjunction with an admissible set of edge functions that explicitly model the 3 d stress singularities which exist along a reentrant terminus edge i e 180 of the v notch the first set of polynomials guarantees convergence to exact frequencies as sufficient terms are retained the second set of edge functions in addition to representing the corner stress singularities substantially accelerates the convergence of frequency solutions this is demonstrated through extensive convergence studies that have been carried out by the investigators numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various v notch angles and depths the relative depth of the v notch is defined as 1 c a and the notch angle is defined as 360 for a very small notch angle 1 or less the notch may be regarded as a sharp radial crack accurate four significant figure frequencies are presented for a wide spectrum of notch angles 360 depths 1 c a and thickness ratios a h for plates and h a for cylinders an extended database of frequencies for completely free thick sectorial semi circular and segmented plates and cylinders are also reported herein as interesting special cases a generalization of the elasticity based ritz analysis and findings applicable here is an arbitrarily shaped v notched cylindrical solid being a surface traced out by a family of generatrix which pass through the circumference of an arbitrarily shaped v notched directrix curve r several of which are described for future investigations and close extensions of this work

eigenfunction analysis of radially polarized piezoelectric cylindrical shells of finite length an eigenfunction approach is presented to determine the response of radially polarized piezoelectric cylindrical shells of finite length to electrical excitation the equations of motion of the piezoelectric cylinder are first derived by using the membrane approximation then they are solved by expressing the displacement distribution as the sum of the static solution and a weighted sum of a complete set of functions the eigenfunctions of the short circuited cylinder the static solution is necessary to exactly satisfy the boundary conditions of the electrically excited cylinder moreover in some cases the series solution does not converge to the correct displacement distribution when some other terms instead of the static solution are used to satisfy the boundary conditions the weights or displacement coefficients are determined by using the orthogonal property of the eigenfunctions finally the input electrical admittance is determined by using the equation of state and the displacement distribution analyses of cylinders with various boundary conditions are presented to illustrate the approach numerical results are used to show that the series solutions converge very rapidly to the closed form solutions

vibration of rectangular plates by reduction of the plate partial differential equation into simultaneous ordinary differential equations the extended kantorovich approach is modified to determine the optimum separable solutions of the partial differential equation describing the plate vibrations in the modificiation the variational method is used to reduce the partial differential equation into two simultaneous ordinary differential equations which are solved exactly in terms of four unknown modal parameters four algebraic equations necessary for the solution of these unknown parameters are then derived from the ordinary differential equations and their boundary conditions

exact series model of langevin transducers with internal losses an exact series method is presented to analyze classical langevin transducers with arbitrary boundary conditions the transducers consist of an axially polarized piezoelectric solid cylinder sandwiched between two elastic solid cylinders all three cylinders are of the same diameter the length to diameter ratio is arbitrary complex piezoelectric and elastic coefficients are used to model internal losses solutions to the exact linearized governing equations for each cylinder include four series each term in each series is an exact solution to the governing equations bessel and trigonometric functions that form complete and orthogonal sets in the radial and axial directions respectively are used in the series asymmetric transducers and boundary conditions are modeled by using axially symmetric and anti symmetric sets of functions all interface and boundary conditions are satisfied in a weighted average sense the computed input electrical admittance displacement and stress in transducers are pres

1 f fluctuation in the game of life abstract the fourier power spectra are examined for the game of life and its variants the results show that only the game of life exhibits fluctuation by means of observing patterns and measuring entropy and difference pattern spreading rate we conclude that the game of life only belongs to wolfram s class iv cellular automata which are thought to be capable of supporting universal computation this predicts a connection between fluctuation and computational universality

harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells abstract a meshfree approach the harmonic reproducing kernel particle method is proposed for the free vibration analysis of rotating cylindrical shells the reproducing kernel particle estimation is employed in hybridized form with harmonic functions to approximate the two dimensional displacement field this is the first instance in which a meshless technique has been adopted for rotating shell dynamics this technique provides ease of enforcing various types of boundary conditions and concurrently is able to capture the traveling modes the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotation are all taken into account in the present formulation this study examines in detail the effects of different boundary conditions on the frequency characteristics of rotating shells the present results wherever possible are verified by comparison against results available in the open literature in general close agreement between the authors results and those of others has been found further results presented here in selective parametric studies may be used as benchmarks for future related works

free vibration analysis of circular cylindrical shells abstract a general analytical method is presented for evaluating the free vibration characteristics of a circular cylindrical shell with classical boundary conditions of any type the solution is obtained through a direct solution procedure in which sanders shell equations are used with the axial modal displacements represented as simple fourier series expressions stokes transformation is exploited to obtain correct series expressions for the derivatives of the fourier series an explicit expression of the exact frequency equation can be obtained for any kind of boundary conditions the accuracy of the method is checked against available data the method is used to find the modal characteristics of the thermal liner model of the u s fast test reactor ftp the numerical results obtained are compared with finite element method solutions

an exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports abstract an analytical method is developed for the vibration analysis of rectangular plates with elastically restrained edges the displacement solution is expressed as a two dimensional fourier series supplemented with several one dimensional fourier series mathematically such a series expansion is capable of representing any function including the exact displacement solution whose third order partial derivatives are required to be continuous over the area of the plate since the discontinuities or jumps potentially related to the partial derivatives at the edges when they are periodically extended onto the entire x y plane as implied by a two dimensional fourier series expansion have been explicitly absorbed by the supplementary terms all the series expansions for up to the fourth order derivatives can be directly obtained through term by term differentiations of the displacement series thus an exact solution can be obtained by letting the series simultaneously satisfy the governing differential equation and the boundary conditions on a point wise basis because the series solution has to be truncated numerically the exact solution should be understood as a solution with arbitrary precision several numerical examples are presented to illustrate the excellent accuracy of the current solution the proposed method can be directly extended to other more complicated boundary conditions involving non uniform elastic restraints point supports partial supports and their combinations

analysis of solid elastic cylinders with internal losses using complete sets of functions abstract a method to determine the response of a solid elastic isotropic cylinder with internal losses and arbitrary length to radius ratio to excitations acting on its surface is presented the method is based on the use of complete sets of functions and the response to arbitrary excitations can be analysed it is illustrated for axisymmetric excitations that are anti symmetric with respect to the plane midway between the ends of the cylinder excitations that are symmetric have been considered earlier d d ebenezer et al forced vibrations of solid elastic cylinders journal of sound and vibration 282 2005 991 1007 all components of displacement and stress are expressed as a sum of two infinite series that contain terms that are complete in the axial and radial direction respectively therefore arbitrary boundary conditions can be satisfied in lossless cylinders for each chosen set there are difficulties at those frequencies at which certain functions become zero some other complete set of functions can be used at these frequencies however this difficulty does not arise for cylinders with losses two different sets are used to compute the resonance frequencies of lossless cylinders the responses of cylinders with internal losses to uniform and concentrated excitations on the flat and curved surfaces are also presented to illustrate the approach they are in good agreement with results obtained using atila a finite element software package

comparisons of vibration frequencies for rods and beams from one dimensional and three dimensional analyses a method of three dimensional 3 d analysis is developed for the free vibration frequencies and mode shapes of solid circular cylinders of elastic material the method assumes for the three displacement components a fourier series in the circumferential direction and algebraic polynomials in the radial r and axial z directions all types of boundary conditions and arbitrary length to diameter ratios l d may be accommodated extensive convergence studies show that frequencies which are exact to five or six significant figures may be obtained for cylinders with free free ends and that three or four figure accuracy is achievable for fixed free ends these accurate frequencies are compared with ones determined from known elementary and improved 1 d theories for longitudinal torsional and bending modes for various l d ratios thereby establishing the ranges of accuracy of the 1 d analyses for circular cross sections

orthotropic influence on frequency characteristics of a rotating composite laminated conical shell by the generalized differential quadrature method by using the generalized differential quadrature gdq method this paper presents the influence of orthotropic material on the frequency characteristics for a rotating thin truncated circular symmetrical cross ply laminated composite conical shell with simply supported boundary conditions at both edges the present analysis includes the effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation frequency characteristics is obtained for various orthotropic parameters the orthotropic influences of material on the frequency characteristics are also discussed for different cone angles to validate the accuracy and efficiency of present analysis by the gdq method comparisons are made with those available in open literature very good agreements are achieved

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

axisymmetric free vibrations of finite anisotropic cylinders abstract a technique is presented for obtaining estimates for the natural frequencies of axisymmetric free vibration for anisotropic cylinders of finite length the weak forms of the governing differential equations are solved by using the ritz method with terms of power series in the co ordinate directions as the approximating functions the dimensions of the cylinder are arbitrary and a wide range of geometries can be considered the solution technique is applied to the example problems of an isotropic cylinder and a cylinder composed of a material with hexagonal symmetry the method gives natural frequencies and mode shapes that are in excellent agreement with existing solutions the condition of traction free faces of the cylinder is also accurately satisfied

upper bound on the products of particle interactions in cellular automata abstract particle like objects are observed to propagate and interact in many spatially extended dynamical systems for one of the simplest classes of such systems one dimensional cellular automata we establish a rigorous upper bound on the number of distinct products that these interactions can generate the upper bound is controlled by the structural complexity of the interacting particles a quantity which is defined here and which measures the amount of spatio temporal information that a particle stores along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata thereby elucidating why that approach is of general utility the upper bound is tested against several relatively complex domain particle cellular automata and found to be tight

vibration characteristics of thin rotating cylindrical shells with various boundary conditions abstract an analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of fourier series expansion method based on sanders shell equations the governing equations of motion which take into account the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotating are derived the displacement field is expressed as a product of fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements stokes transformation is employed to derive the derivatives of the fourier series expressions then through the process of formula derivation an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type once the frequency equation has been determined the frequencies are calculated numerically to validate the present analysis comparisons between the results of the present method and previous studies are performed and very good agreement is achieved finally the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries and the results are presented

analysis of axially polarized piezoelectric cylinders with arbitrary boundary conditions on flat surfaces a method to analyze axially polarized piezoelectric ceramic cylinders with arbitrary length to radius ratio and arbitrary boundary conditions on the flat surfaces is presented the method is based on the use of functions that individually exactly satisfy the axisymmetric equations of motion and the gauss electrostatic conditions the axial and radial components of displacement and the potential are expressed as weighted sums of these functions the functions form complete sets in the radial direction and arbitrary boundary conditions can therefore be satisfied on the flat surfaces on the curved surface certain uniform boundary conditions can be exactly satisfied the weights are easily determined by using the orthogonal property of the functions the input electrical admittance is a function of only the average boundary conditions and is very easily determined several special cases and numerical results are presented for electrically and mechanically excited cylinders to illustrate the method the se

flow over a ski jumper in flight prediction of the aerodynamic force and flight posture with higher lift to drag ratio large eddy simulations less are performed to study the flow characteristics around two flight posture models of ski jumping these models are constructed by three dimensionally scanning two national team ski jumpers taking flight postures the drag and lift forces on each component of a ski jumper and skis head with helmet and goggle body arms legs and skis and their lift to drag ratios are obtained for the two posture models the drag forces on the body legs and skis are larger than those on the arms and head with helmet and goggle but the lift forces on the body and skis are larger than their drag forces resulting in high lift to drag ratios on the body and skis and low lift to drag ratio on the legs we construct simple geometric models such as the circular cylinder sphere and thin rectangular plate predicting the drag and lift forces on each component of a ski jumper and skis and validate them with those obtained from les using these geometric models we perform a parametric study on the position angles of flight posture for higher total lift to drag ratio the flight postures obtained increase the total lift to drag ratios by 35 and 21 from those of two base postures respectively finally less are performed for the postures obtained and show the increases in the total lift to drag ratios by 21 and 16 respectively indicating the adequacy of using the simple geometric models for finding a flight posture of ski jumping having a higher lift to drag ratio at low cost

two dimensional cellular automata a largely phenomenological study of two dimensional cellular automata is reported qualitative classes of behavior similar to those in one dimensional cellular automata are found growth from simple seeds in two dimensiona cellular automata can produce patterns with complicated boundaries characterized by a variety of growth dimensions evolution from disordered states can give domains with boundaries that execute effectively continuous motions some global properties of cellular automata can be described by entropies and lyapunov exponents others are undecidable

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section in this paper the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non extensible membranes the three dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations which relate the frequencies of elastic waves to their wavenumbers numerical results for waveguides with various boundary conditions are presented to illustrate the approach analysis of the dispersion spectra is carried out and cutoff frequencies are obtained and characterized mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed the main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed the results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder

vibration of orthotropic plates discussion on the completeness of the solutions used in direct methods fil rosales marta beatriz consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet bahia blanca argentina universidad nacional del sur departamento de ingenieria argentina

free vibrations of beams with general boundary conditions a simple and unified approach is presented for the vibration analysis of a generally supported beam the flexural displacement of the beam is sought as the linear combination of a fourier series and an auxiliary polynomial function the polynomial function is introduced to take all the relevant discontinuities with the original displacement and its derivatives at the boundaries and the fourier series now simply represents a residual or conditioned displacement that has at least three continuous derivatives as a result not only is it always possible to expand the displacement in a fourier series for beams with any boundary conditions but also the solution converges at a much faster speed the reliability and robustness of the proposed technique are demonstrated through numerical examples

comments on accurate vibration frequencies of circular cylinders from three dimensional analysis j acoust soc am 98 2136 2141 1995 leissa and so presented accurate frequencies for solid cylinders using the rayleigh ritz method for both a completely traction free solid cylinder and a solid cylinder which is fixed at one end they compared their frequencies for the traction free case with my series solution in their tables vi and vii the comparison does not demonstrate the accuracy which can be achieved with the series solution a table demonstrating the convergence of the series solution is presented in this comment discrepancies were found between the rayleigh ritz solutions and the converged series solution for some of the frequencies in table vi further discrepancies were found in some of the other results all discrepancies are tabulated for the traction free case

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

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

computational mechanics of cellular automata an example abstract we illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space time behavior of elementary one dimensional cellular automaton rule 54 the dominant regular domain of the cellular automation is identified and a domain filter is constructed to locate and classify defects in the domain the primary particles are identified and a range of interparticle interactions is studied the deterministic equation of motion of the filtered space time behavior is derived filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher level defects particle interactions and secondary domains we define the emergence time at which the space time behavior condenses into configurations consisting only of domains particles and particle interactions taken together these techniques serve as the basis for the investigation of pattern evolution and self organization in this representative system

three dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels abstract the free vibration problem of a homogeneous isotropic thick cylindrical shell or panel subjected to a certain type of simply supported edge boundary conditions is considered for this problem the governing equations of three dimensional linear elasticity are employed and solved by using a new iterative approach which in practice leads to the prediction of the exact frequencies of vibration in the particular case of a flat plate or a complete shell excellent agreement is achieved between results based on the present approach and corresponding results based on other exact analyses available in the literature for certain cylindrical panel geometries comparisons are also made between corresponding numerical results based on the present analysis and certain two dimensional shell theories

forced vibrations of solid elastic cylinders abstract a method is presented to determine the vibration response of a solid elastic isotropic cylinder with arbitrary length to radius ratio when subject to arbitrary distribution of axisymmetric excitation on its surfaces in this method the axial and radial components of displacement are expressed as a sum of two infinite series each term in both the series is an exact solution to the governing equations of motion and has a coefficient that is used to satisfy boundary conditions one series contains bessel functions that form a complete set in the radial direction and the other contains trigonometric functions that form a complete set in the axial direction the components of stress are also expressed in terms of complete sets of functions by using the expression for displacement the coefficients in the series are determined by using the orthogonal properties of the functions to satisfy the boundary conditions in a mean square error sense numerical results are presented to illustrate the broadband responses of cylinders to uniform and concentrated loads on the flat and curved surfaces they are in good agreement with results obtained using atila a commercial finite element software

comments on comparisons of vibration frequencies for rods and beams from one dimensional and three dimensional analyses j acoust soc am 98 2122 2135 1995 leissa and so use accurate solutions generated by the rayleigh ritz procedure as a basis of comparison for the one dimensional theories for longitudinal torsional and bending vibrations of rods and beams they considered both the free free and fixed free cases in the past i have considered similar comparisons for the free free case based on a series solution a comparison of my series solution with the authors rayleigh ritz solution showed some disagreements those disagreements are tabulated the authors did not use the best shear coefficient in their comparison nor did they compare the pickett solution which they reference comparisons using timoshenko s shear coefficient and pickett s solution are also presented in this comment

transformations of one dimensional cellular automation rules by translation invariant local surjective mappings abstract if m is a noninvertible translation invariant local surjective mapping it is shown that some local one dimensional deterministic cellular automaton rules f have a transform by m defined by m m f when it exists is local and its wolfram s class is the same as f the evolution of a cellular automaton according to rule is simply related to the evolution according to rule f in the case of class 3 rules the evolution to the attractor may often be viewed as particle like structures evolving in a regular background if the structure of these particles and their interactions for a rule f are known then the structure and interactions of the transformed particles for rule are also known if m is a nontrivial invertible translation invariant local surjective mapping always exists but it is in general site and time dependent

wind and fairness in ski jumping a computer modelling analysis wind is closely associated with the discussion of fairness in ski jumping to counter act its influence on the jump length the international ski federation fis has introduced a wind compensation approach we applied three differently accurate computer models of the flight phase with wind m1 m2 and m3 to study the jump length effects of various wind scenarios the previously used model m1 is accurate for wind blowing in direction of the flight path but inaccuracies are to be expected for wind directions deviating from the tangent to the flight path m2 considers the change of airflow direction but it does not consider the associated change in the angle of attack of the skis which additionally modifies drag and lift area time functions m3 predicts the length effect for all wind directions within the plane of the flight trajectory without any mathematical simplification prediction errors of m3 are determined only by the quality of the input data wind velocity drag and lift area functions take off velocity and weight for comparing the three models drag and lift area functions of an optimized reference jump were used results obtained with m2 which is much easier to handle than m3 did not deviate noticeably when compared to predictions of the reference model m3 therefore we suggest to use m2 in future applications a comparison of m2 predictions with the fis wind compensation system showed substantial discrepancies for instance in the first flight phase tailwind can increase jump length and headwind can decrease it this is opposite of what had been anticipated before and is not considered in the current wind compensation system in ski jumping

elastic waves in piezoceramic cylinders of sector cross section abstract the propagation of elastic waves in piezoceramic cylindrical waveguides of circular cross sections with sector cut is investigated on the basis of the linear theory of electroelasticity dispersion functions are obtained from boundary conditions in an analytical form of functional determinants for each value of the generalized wave number a selected set of numerical results including real imaginary and complex branches of full dispersion spectrums with various symmetry of wave movements is presented to describe the essential characteristics of the waves leading effects of spectrums transformation by change of waveguide s angular measure are enlightened and wave asymptotic behavior is analyzed the variation of the cross section is considered as a mechanism to control the dispersion characteristics of waveguides

finite solid circular cylinders subjected to arbitrary surface load part i analytic solution abstract this paper presents a general framework for obtaining analytic solutions for finite elastic isotropic solid cylinders subjected to arbitrary surface load the method of solution uses the displacement function approach to uncouple the equations of equilibrium the most general solution forms for the two displacement functions for solid cylinders are proposed in terms of infinite series with z and dependencies in terms of trigonometric and hyperbolic functions and with r dependency in terms of bessel and modified bessel functions of the first kind of fractional order all possible combinations of odd and even dependencies of and z are included and the curved boundary loads are expanded into double fourier series expansion while the end boundary loads are expanded into fourier bessel expansion it is showed analytically that only one set of the end boundary conditions needs to be satisfied a system of simultaneous equations for the unknown constants is given independent of the type of the boundary loads this new approach provides the most general theory for the stress analysis of elastic isotropic solid circular cylinders of finite length application of the present solution to the stress analysis for the double punch test is presented in part ii of this study

an exact series solution for calculating the eigenfrequencies of orthotropic plates with completely free boundary abstract an analysis for solving boundary value problems in structural mechanics which was proposed by wang and lin 1996 journal of sound and vibration 196 285 293 1999 journal of applied mechanics 66 380 387 1 2 has been extended to the calculation of the eigenfrequencies of an orthotropic plate under all free boundary conditions the convergence of the series solution is assured and the procedure leads to pointwise exact solutions the calculated eigenfrequencies have been verified by a different approach and indicate that the present method is simple and effective

invariant strings and pattern recognizing properties of one dimensional cellular automata a cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions it is shown that given an arbitrary string of values and an arbitrary neighborhood size representing the range of interaction a simple procedure can be used to find the rules of that neighborhood size under which the string is invariant the set of nearestneighbor rules for which invariant strings exist is completely specified as is the set of strings invariant under each such rule for any automaton rule an associated filtering rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings a result is provided defining the rule of minimum neighborhood size for which an arbitrarily chosen string is the unique invariant string the applications of filtering rules to pattern recognition problems are discussed

free vibration study of layered cylindrical shells by collocation with splines the free vibration of circular cylindrical thin shells made up of uniform layers of isotropic or specially orthotropic materials is studied using point collocation method and employing spline function approximations the equations of motion for the shell are derived by extending love s first approximation theory assuming the solution in a separable form a system of coupled differential equations in the longitudinal circumferential and transverse displacement functions is obtained these functions are approximated by bickley type splines of suitable orders the process of point collocation with suitable boundary conditions results in a generalized eigenvalue problem from which the values of a frequency parameter and the corresponding mode shapes of vibration for specified values of the other parameters are obtained two types of boundary conditions and four types of layers are considered the effect of neglecting the coupling between the flexural and extensional displacements is analysed the influences of the relative layer thickness a length parameter and a total thickness parameter on the frequencies are studied both axisymmetric and asymmetric vibrations are investigated the effect of the circumferential node number on the vibrational behaviour of the shell is also analysed

chaotic like behaviour in chains of stable nonlinear oscillators abstract irregular evolution is observed in a chain of forced duffing oscillators even when the maximum lyapunov exponent is strictly negative this phenomenon generalizes similar results previously obtained in the context of coupled map lattices the relationship with chaotic cellular automata is investigated by introducing a suitable encoding while in some parameter region the evolution of the chain of oscillators turns out to be described exactly by a deterministic cellular automaton with a finite interaction range in other regions even automata with an infinite range are unable to reproduce the observed patterms we discuss the possible connection with an information downgrade occurring during the observation process