vibration analysis of high speed rotating conical shell with arbitrary boundary conditions based on the energy method an analytical model for the vibration characteristics of high speed rotating conical shell with arbitrary boundary is constructed effects of centrifugal and coriolis accelerations as well as initial hoop tension due to rotating are all taken into account a set of translational and rotational artificial springs to simulate the elastic constraints imposed on the conical shell edges under the framework each of the displacement components of the conical shell is invariantly described by a modified fourier series which is composed of a standard fourier series and closed form auxiliary functions all the expansion coefficients are determined by using the familiar rayleigh ritz procedure as the generalized coordinates to validate the present analysis a series of comparisons between the present results and those available in the open literature are carried out and very good agreements are obtained on this basis some numerical results are given to illustrate the effects of rota

the efficiency factors of particular effects in designs with orthogonal factorial structure on etudie le confounding partiel qui n est pas necessairement orthogonal aux blocs on relie le facteur d efficacite d une interaction ou d un effet principaux aux nombres de chemins d un certain type dans le graphe de concurrence des traitements

the structure of quasi multipliers of c algebras let a be a c algebra and a its enveloping w algebra let lm a be the left multipliers of a rm a the right multipliers of a and qm a the quasi multipliers of a a question was raised by akemann and pedersen 1 whether qm a lm a rm a mckennon 20 gave a nonseparable counterexample l brown 6 shows the answer is negative for stable separable c algebras also in this paper we mainly consider a unitial c algebras we give a criterion for qm a lm a rm a in the case that a is stable we give a necessary and sufficient condition for qm a lm a rm a we also give answers for other c algebras

general balance and treatment permutations abstract many equi replicate designs whether ordinary block designs or multi stratum designs have a structure which is left unchanged by a group g of permutations of the treatments this group g is often used in the construction of the design a survey of the properties of such designs is given and useful necessary conditions on g are found for such a design to be generally balanced if g is abelian then the necessary conditions are satisfied in this case explicit formulas for the efficiency factors are given

analysis of rotating laminated cylindrical shells by different thin shell theories abstract the natural frequencies of the forward and backward modes of thin rotating laminated cylindrical shells are determined by using four common thin shell theories namely donnell s flugge s love s and sanders the objective is to present a unified analysis formulated with the use of tracers so that it can be reduced to any of the four shell theories by giving appropriate values to the tracers for simplicity results are presented only for the case of simply supported simply supported boundary conditions which can be satisfied by expressing the displacement fields in terms of the products of sine and cosine functions numerical results presented are the non dimensional frequency parameters of the forward and backward travelling modes for rotating cylindrical shells and the non dimensional frequency parameters for non rotating cylindrical shells the present analysis is verified by comparing the numerical results with those in the literature and very good agreement is obtained

construction of block designs using mathematical programming summary the construction of optimal or nearly optimal block designs using the a optimality criterion is formulated as a non linear 0 1 programme an approach which ignores the 0 1 constraint is suggested and its feasibility is examined by constructing block designs using the non linear programming computer package minos

circuits and efficiency in incomplete block designs summary this paper explains why numbers of circuits in the variety concurrence graph of a design provide an attractive measure of its efficiency it is conjectured that the search for designs with an optimal value of the harmonic mean efficiency factor can be restricted to those with minimal numbers of circuits of shorter lengths this conjecture is seen to be highly plausible to be a natural generalization of a conjecture that is already widely accepted and to offer significant savings in the construction of efficient designs

influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell the influence of boundary conditions on the frequency characteristics of a rotating conical shell is studied using the galerkin method the results obtained include the relationships between the frequency parameter and circumferential wavenumber and between the frequency parameter and rotating velocity at various cone angles under different boundary conditions the variation of the frequency characteristics at various vibrational modes is also shown in order to validate the present analysis several comparisons of the numerical results with those published are made one comparison is for an infinitely long rotating cylindrical shell other comparisons are for the non rotating conical shells as is expected these comparisons show very good agreement

triangles and efficiency factors summary we show that the number of triangles in the variety concurrence graph of a regulargraph design can be used to derive upper bounds on the harmonic mean efficiency factor the best alpha lattice designs and the best cyclic designs have efficiency factors very close to the bounds our investigation gives insight into the structure of such designs we see also that a certain type of regular graph group divisible design has a minimal number of triangles

construction of optimal block designs by computer this article describes an effective algorithm for constructing optimal or near optimal incomplete block designs with up to 100 treatments the algorithm is found to perform well when evaluated against 874 optimal or near optimal incomplete block designs in the literature examples that motivated the development of the algorithm are given

conjectures for optimal block designs summary in the study and construction of optimal block designs over the past 20 years a number of conjectures have been repeatedly stated and used the purpose of this note is to bring together some of these conjectures although known to those actively engaged in research in design it is hoped that this note will stimulate other statisticians and mathematicians to give their attention to these unsolved problems

fundamental approximate identities and quasi multipliers of simple af c algebras abstract we study c algebras with fundamental approximate identities as a generalization of stable c algebras and show that the only separable simple af c algebras for which the quasi multipliers equal the left plus right multipliers are unital or elementary

on circuits and optimality conjectures for block designs on montre que la conjecture 5 de john et williams 1982 implique une condition forte sur les nombres de circuits dans le graphe de concurrence d un plan binaire a optimal

support algebras of σ unital c algebras and their quasi multipliers we study certain dense hereditary subalgebras of n unital c algebras and their relations with the pedersen ideals the quasi multipliers of the dense hereditary subalgebras are also studied

upper bounds for average efficiency factors of two factor interactions summary an upper bound is derived for the average efficiency factor of a two factor interaction when an experiment is arranged as an incomplete block design attention is restricted to designs which have orthogonal factorial structure and which allow one or both main effects to be estimated with full efficiency it is shown that several designs may be compared simultaneously using a graphical interpretation of the bound an incomplete block design may be assessed by comparison of its average efficiency factor with a theoretical upper bound see for example williams patterson and john 1976 when the design is to be used for a factorial experiment lewis and dean 1980 show that a design with a high average efficiency factor does not necessarily have high factorial efficiency factors upper bounds for factorial efficiency factors have not received much attention in the literature the main effect efficiency factors can be compared directly with the usual average efficiency factor upper bounds but there are no simple formulae for upper bounds for the interaction efficiency factors in this paper we consider two factor interactions in the cases that one or both of the corresponding main effects achieve full efficiency many of the designs listed in the literature satisfy one of these restrictions we also restrict attention to experiments arranged in designs which have orthogonal factorial structure in order to avoid problems of adjusting the interaction estimates for those of the main effects 2 preliminaries let d v k b r denote the set of connected binary incomplete block designs having v treat ment labels each replicated r times and b blocks each of size k k v let i be a v x v identity matrix and let the v x b matrix nd be the incidence matrix of the design d d v k b r then assuming the usual additive model ad ri ndnd ik is the intra block matrix with generalized inverse q2d the covariance matrix of the vector of block adjusted treatment effects s is then qd a2 where o2 is the common variance of the residuals consider an n factor experiment with v ml x m2 x x mn treatment combinations arranged in design d in an unpublished manuscript j a john shows that when d is a generalized cyclic design results on the efficiency of the interaction between factors i and j may be obtained by considering the interaction in the sub design d l of d where di is formed from d by deleting from the treatment combinations all digits except those in positions i and j the present authors have extended this result to the whole class of incomplete block designs d v k b r see appendix therefore without loss of generality we restrict attention to the subclass of designs d v k b r where v mi x m1 and r r v iv we need only consider binary designs when k v since it is known that the average efficiency factor of a binary design is higher than that of a corresponding non binary design

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

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

a criterion for the construction of optimal neighbour designs on donne une methode a deux etapes ou le plan de blocs incomplets resolvable efficace peut etre utilise comme point de depart pour la construction d un plan de voisinage efficace

optimal semi latin squares with side six and block size two an n x n k semi latin square is like an n n latin square except that there are k letters in each cell each of the nk letters occurs once in each row and once in each column designs for experiments are assessed according to the statistical concept of efficiency factor a high efficiency factor corresponds to low variances of within block estimators there are four widely used measures of the efficiency factor of a design for each any design which maximizes the value of the efficiency factor among a given class of designs is said to be optimal in that class previous theory gives optimal semi latin squares for various values of k for all values of n except for n 6 in this paper we therefore examine 6 x 6 2 semi latin squares we restrict attention to those semi latin squares whose quotient block designs are regular graph designs because a plausible and widely believed conjecture is that optimal regular graph designs are optimal overall for each of the four measures of efficiency factor we find the optimal 6 6 2 semi latin square among regular graph semi latin squares of that size

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

vibration of finite length rotating cylindrical shells abstract the flugge type basic equations for a finite lenght rotating cylindrical shell including the effect of the initial tensions due to the rotation are employed and by galerkin s method frequency analyses of travelling waves are presented for three kinds of boundary conditions i e both ends a clamped b simply supported without axial constraint and c simply supported with axial constraint in all these cases it is found that the dependence of the frequencies upon the rotational speed is insignificantly affected by the boundary conditions and thus can be represented by the simple relation for a thin rotating ring provided that the frequencies and rotating speeds are normalized by the natural frequencies of a non rotating cylindrical shell