vibration of twisted and curved cylindrical panels with variable thickness abstract a numerical procedure with an exact strain displacement relationship of twisted and curved cylindrical panels having variable thickness derived by considering the green strain tensor on general shell theory is presented using the principle of virtual work and the rayleigh ritz method with algebraic polynomials as in plane and transverse displacement functions the accuracy and applicability of the procedure are verified by comparing the present results with previous experimental and theoretical results for several panels the effects of variation ratio of thickness in chordwise and lengthwise directions twist and curvature both in two directions aforementioned on vibrations of cylindrical panels are studied in detail and typical vibration mode shapes are plotted to demonstrate the effects

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

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

solving low density subset sum problems the subset sum problem is to decide whether or not the 0 l integer programming problem s n i l a i x i m i x i 0 or 1 has a solution where the a i and m are given positive integers this problem is np complete and the difficulty of solving it is the basis of public key cryptosystems of knapsack type an algorithm is proposed that searches for a solution when given an instance of the subset sum problem this algorithm always halts in polynomial time but does not always find a solution when one exists it converts the problem to one of finding a particular short vector v in a lattice and then uses a lattice basis reduction algorithm due to a k lenstra h w lenstra jr and l lovasz to attempt to find v the performance of the proposed algorithm is analyzed let the density d of a subset sum problem be defined by d n log 2 max i a i then for almost all problems of density d d n it is proved that the lattice basis reduction algorithm locates v extensive computational tests of the algorithm suggest that it works for densities d d c n where d c n is a cutoff value that is substantially larger than 1 n this method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below d c n as n

free vibrations of completely free doubly curved laminated composite shallow shells abstract vibrational frequencies are determined for completely free laminated plates and shallow shells having rectangular planforms the ritz method with algebraic polynomial displacement functions is used convergence studies are made and accurate results are obtained by using 192 displacement terms for spherical circular cylindrical hyperbolic paraboloidal shallow shells and 64 terms for plates results are compared with those obtained experimentally and by finite element methods it is found that the present method needs considerably fewer degrees of freedom than the finite element method to obtain the same accuracy and that the results compare well with experimental ones the effect of various parameters material number of layers fiber orientation upon the frequencies is studied

code construction and decoding algorithms for semi quantitative group testing with nonuniform thresholds we analyze a new group testing scheme termed semi quantitative group testing which may be viewed as a concatenation of an adder channel and a discrete quantizer our focus is on non uniform quantizers with arbitrary thresholds for the most general semi quantitative group testing model we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds the sequences represent extensions and generalizations of b h and certain types of super increasing and lexicographically ordered sequences and they lead to code structures amenable for efficient recursive decoding we describe the decoding methods and provide an accompanying computational complexity and performance analysis

on the equivalence of generalized differential quadrature and highest order finite difference scheme abstract it is shown in this paper that the global method of generalized differential quadrature gdq is equivalent to the highest order finite difference scheme which is the extension of low order finite difference schemes the effect of grid point distribution on the accuracy of numerical results is studied by two numerical examples the results showed that the ability to alter the grid point distribution in the gdq method is an important feature to obtain accurate numerical solutions in certain problems

newman polynomials with prescribed vanishing and integer sets with distinct subset sums we study the problem of determining the minimal degree d m of a polynomial that has all coefficients in 0 1 and a zero of multiplicity m at 1 we show that a greedy solution is optimal precisely when m 5 mirroring a result of boyd on polynomials with 1 coefficients we then examine polynomials of the form e e xe 1 where e is a set of m positive odd integers with distinct subset sums and we develop algorithms to determine the minimal degree of such a polynomial we determine that d m satisfies inequalities of the form 2m c1m d m 103 96 2m c2 last we consider the related problem of finding a set of m positive integers with distinct subset sums and minimal largest element and show that the conway guy sequence yields the optimal solution for m 9 extending some computations of lunnon

integer sets with distinct subset sums in section 1 we introduce the problem of finding minimal height sets of n natural numbers with distinct subset sums ssd and in section 2 review the well known conway guy sequence u conjectured to yield a minimal ssd set for every n we go on section 3 to prove that u certainly cannot be improved upon by any greedy sequence to verify numerically section 4 that it does yield ssd sets for n 80 and section 5 by direct search to show that these are minimal for n s 8 there is a brief interlude section 6 on the problem of decoding the subset from its sum in section 7 generalizations of u are constructed which are asymptotically smaller defining the limit ratio of a sequence w to be a 1imn wn 2l the atkinson negro santoro sequence v known to give ssd sets has a 0 6334 conwayguy conjectured to has a 0 4703 and our best generalization has a 0 4419 we also section 8 discuss when such sequences have the same a and section 9 how a may efficiently be computed to high accuracy 1 the distinct subset sum problem a well known problem in combinatorial number theory 2 pp 64 65 involves the construction for given n of a set p pi i 1 n of natural numbers possessing the property we shall call subset sum distinctness or ssd for short that is l l f pi p e pi s t c l n i s i t or distinct subsets of p have distinct sums evidently choosing pi 21 satisfies 1 1 the interest lies in how much the maximum element pn can be reduced below 2n 1 in order to explore the ssd property it is convenient to consider a more general concept we say that x has a representation by p with length k and signature 1 when for some s and t as before 1 2 x e pe po ies iet where s n t 0 si it k isi iti 1 that is x is the difference of two disjoint subset sums of which the first has 1 terms more than the second and the two together have k terms alternatively n 1 3 x eip i l received june 23 1986 revised october 20 1986 1980 mathematics subject classification 1985 revision primary 11b13 05 04 05a99 11j13 94a60 65b05

differential quadrature approach for delamination buckling analysis of composites with shear deformation the differential quadrature method dqm is used to analyze the one dimensional buckling of a laminated composite beam plate having an across the width delamination located at an arbitrary depth and an arbitrary location along its span a beam theory with shear deformation is used in formulating the problem several case studies are conducted to examine the buckling response of laminates hosting such a delamination using dqm the system of equilibrium equations and the boundary conditions are transformed into a system of linear algebraic eigenvalue equations that are solved by a standard eigensolver the influences of several parameters that affect the buckling strength of such laminates are investigated the investigated parameters are the shear deformation factor the length of the delamination and the through the thickness and longitudinal positions of the delamination the results verify the accuracy and efficiency of dqm

non linear free periodic vibrations of open cylindrical shallow shells this paper is concerned with the non linear free periodic vibrations of thin open cylindrical and shallow shells vibrating in the geometrically non linear regime a multi degree of freedom model with hierarchical basis functions is adopted and the principle of the virtual work is used to define the time domain equations of motion these equations are transformed into the frequency domain by the harmonic balance method and are finally solved by an arc length continuation method shells of different thicknesses and of different curvature radius are analysed and the variation of the non linear natural frequencies of these shells with the vibration amplitude are investigated in some detail the variation of the mode shapes with the vibration amplitude is demonstrated it is found that both softening and hardening spring effects occur and that the number of couplings between vibration modes is rather large in undamped shells

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

stabilization pole placement and regular implementability in this paper we study control by interconnection of linear differential systems we give necessary and sufficient conditions for regular implementability of a given linear differential system we formulate the problems of stabilization and pole placement as problems of finding a suitable regularly implementable sub behavior of the manifest plant behavior the problem formulations and their resolutions are completely representation free and specified only in terms of the system dynamics control is viewed as regular interconnection a controller is a system that constrains the plant behavior through a distinguished set of variables namely the control variables the issue of implementation of a controller in the feedback configuration and its relation to regularity of interconnection is addressed freedom of disturbances in a plant and regular interconnection with a controller also turn out to be inter related

arbitrary precision frequencies of a free rectangular thin plate abstract a variational method developed by the authors and named whole element method wem is used to find the arbitrary precision frequencies of a rectangular thin plate within the germain lagrange theory having its four borders free of constraint wem consists is proposing an adequate functional and a sequence representing the plate transversal displacementw x y such a sequence is made of a linear combination of functions belonging to a complete set inl2 the sequence and not each co ordinate function is required to satisfy the essential or geometric conditions the sequence generation is systematic and no analysis of the classical natural modes of the plate is needed in particular trigonometric functions which a priori belong to a complete set in the domain are used in the present analysis the solving equations involving very simple sums arise from the minimization of the functional wem is based on theorems which show the ultimate exactness of the eigenvalues and the uniform convergence of the essential functions of the problem to the authors knowledge this problem has no classical solution

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

a constructive solution to interconnection and decomposition problems with multidimensional behaviors by a multidimensional behavior we mean the solution space of a linear constant coefficient system of partial difference or differential equations within the behavioral framework a natural concept of interconnection has been introduced by j c willems the regular interconnection problem can be formulated as follows given a behavior the plant find if possible another behavior a controller such that their interconnection is not redundant and is equal to a certain desired behavior we give a constructive solution to this problem which is in terms of polynomial matrix equations that can be solved using the theory of grobner bases we also study a dual problem concerning the existence of direct sum decompositions of multidimensional behaviors finally we present a unified framework for studying both problems as special cases of constructing relative complements in the lattice of behaviors

vibrations of completely free shallow shells of rectangular planform abstract although much has been written about the free vibrations of rectangular plates having completely free boundaries very little has appeared for the case when the plates have curvature i e shallow shells a solution of the problem is presented here for shells having arbitrary but constant curvature the ritz method is used with displacement functions assumed in the form of polynomials convergence studies were made to determine the number of terms required for reasonable solution accuracy numerical results were obtained for the frequencies and mode shapes of three types of shells circular cylindrical spherical and hyperbolic paraboidal and these are compared with those of a flat plate

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

numerical study of grid distribution effect on accuracy of dq analysis of beams and plates by error estimation of derivative approximation the accuracy of global methods such as the differential quadrature dq approach is usually sensitive to the grid point distribution this paper is to numerically study the effect of grid point distribution on the accuracy of dq solution for beams and plates it was found that the stretching of grid towards the boundary can improve the accuracy of dq solution especially for coarse meshes the optimal grid point distribution corresponding to optimal stretching parameter depends on the order of derivatives in the boundary condition and the number of grid points used the optimal grid distribution may not be from the roots of orthogonal polynomials this differs somewhat from the conventional analysis this paper also proposes a simple and effective formulation for stretching the grid towards the boundary the error distribution of derivative approximation is also studied and used to analyze the effect of grid point distribution on accuracy of numerical solutions copyright 2001 john wiley sons ltd

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

on interconnections control and feedback the purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context we start with an extensive physical example which serves to illustrate that the familiar input output feedback loop structure is not as universal as we have been taught to believe this leads to a formulation of control problems in terms of interconnections subsequently we study interconnections of linear time invariant systems from this vantage point let us mention two of the results obtained the first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant provided the plant is not autonomous the second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law these results yield pole placement and stabilization of controllable plants as a special case these ideas are finally applied to the stabilization of a nonlinear system around an operating point

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

strong controlled invariance of behavioural nd systems abstractin this paper we give a stronger version of the notion of behavioral controlled invariance introduced in pereira rocha 2017 in the context of regular partial interconnections in such interconnections the variables are divided into two sets the variables to be controlled and the variables on which it is allowed to enforce restrictions control variables moreover regularity means that the restrictions of the controller do not overlap with the ones already implied by the laws of the original behavior a complete characterization of strong controlled invariance for nd behaviors is derived making use of a special controller behavior known as the canonical controller

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables