Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1975"
TL;DR: In this article, a clear procedure for the variational problem solution via the Walsh functions is established and an operational matrix is derived for integration use, by means of the direct method using the Walsh series.
Abstract: This paper establishes a clear procedure for the variational problem solution via the Walsh functions.technique. First the Walsh functions are introduced and their properties briefly summarized. Then an operational matrix is derived for integration use. The variational problems are solved by means of the direct method using the Walsh series. An illustrative example and a practical application to a heat conduction problem are included.
142 citations
TL;DR: In this article, the two-dimensional, plane stress problem of linear elasticity is analyzed within a state space framework, where the medium considered is homogeneous and isotropic Vlasov's mixed formulation of elasticity.
Abstract: The two-dimensional, plane stress problem of linear elasticity is analyzed within a state space framework The medium considered is homogeneous and isotropic Vlasov's mixed formulation of elasticity is used throughout The field equations are derived in closed form, thus avoiding Vlasov's intermediate infinite series solution Finally, all the properties of the transfer matrix are shown to follow directly from embedding the problem into a state space setting
111 citations
TL;DR: In this article, a numerical inversion of the Laplace transform is used to calculate the frequency domain function at pre-assigned complex points and form a weighted sum, which is then used for the integration of differential equations.
Abstract: A new method for the calculation of time responses of lumped time invariant networks is presented. It is based on the numerical inversion of the Laplace transform and involves the computation of the frequency domain function at pre-assigned complex points and forming a weighted sum. The method exactly inverts a certain number of terms of the Taylor expansion of the time response and is thus equivalent to the methods used for the integration of differential equations. This equivalence is established on two examples. The order of integration can be changed between 1 and 46 without any difficulty. Additional properties resulting from the application of the numerical Laplace transform inversion are also discussed and some novel applications indicated.
90 citations
TL;DR: In this article, the authors consider the feedback interconnection of two multi-input multi-output subsystems characterized by rational transfer functions and show that the effect of output disturbances on stability is taken into account.
Abstract: This paper considers the feedback interconnection of two multi-input multi-output subsystems characterized by rational transfer functions Ĝ1 and Ĝ functions are not assumed to be proper nor exponentially stableThe effect of output disturbances on stability is taken into account. Ten examples are given to show that instabilities may appear anywhere around the loop. Next, under a sequence of successively more restrictive assumptions, we prove four sets of necessary and sufficient conditions for the exponential stability of the system. Using coprime factorizations, we obtain four equivalent expressions for the system characteristic polynomial. Two stability tests are derived, the first one is based exclusively on transfer functions, the second is based on the characteristic polynomial. The paper ends by providing translation rules for reformulating all definitions and theorems for the discrete-time case (i.e. instead of Laplace transforms use Z-transforms, etc.).
77 citations
TL;DR: In this article, a pulsatile fully developed flow of Newtonian viscous fluid in a straight rectangular channel can be synthesized from analytic solutions of steady flow and oscillatory flow, showing dependence on a "viscous diffusion length", the square root of the kinematic viscosity divided by frequency.
Abstract: Solutions for pulsatile fully developed flow of Newtonian viscous fluid in a straight rectangular channel can be synthesized from analytic solutions of steady flow and oscillatory flow. A new steady solution is presented that is valid for all duct aspect ratios. Also new oscillatory solutions are given, showing dependence on a “viscous diffusion length”, the square root of the kinematic viscosity divided by frequency.
48 citations
TL;DR: In this paper, a wave digital filter derived from doubly terminated LC-ladder networks is proposed, which replaces each series or shunt arm element of the ladder by its equivalent digital two-port.
Abstract: This paper proposes a new wave digital filter derived from doubly terminated LC-ladder networks by replacing each series or shunt arm element of the ladder by its equivalent digital two-port. It is shown that such two-ports may be cascaded without the use of adapters defined by Fettweis ( 1 ). A number of realizations of the wave digital two-ports, which are canonic with respect to both multipliers and delays, have been obtained. Also a realization which is canonic with respect to multipliers only is given and an example considered using this realization. The sensitivity of this filter with respect to the multiplier coefficient changes due to finite word length is compared with the conventional cascaded digital filter and also the one proposed by Renner and Gupta. It is found that the proposed filter appears to be a more desirable form of implementation than the conventional cascade form and comparable to that of Renner and Gupta ( 2 ).
42 citations
40 citations
TL;DR: In this article, the second law of thermodynamics is used to describe the symmetry conditions of RS-field fields in the sense of Paynterian bondgraphs, where entropy is interpreted as a kind of thermal charge.
Abstract: Energy conversion takes place either in generalized capacitor or generalized resistor networks, that is, C- and R-fields in the sense of Paynterian bondgraphs. Entropy is interpreted as a kind of thermal charge. An electrical example is the difference of conduction and convection associated with mass flow. The generation of entropy in irreversible processes is represented by RS-fields as extension of the simple generalized resistors or R-elements. Thermoelectric power conversion is described by combined RS-fields, and Onsager's symmetry conditions for such fields are derived from the second law of thermodynamics.
30 citations
TL;DR: In this paper, the parametric resonance of an axially accelerated beam is investigated, where the beam which has encastre ends is subjected to a periodic root force as shown in Fig. 1, and regions of instability are identified for various combinations of the excitation frequency and amplitude of the axial oscillations.
Abstract: Dynamic problems of axially moving materials as exemplified by strings in textile industry and band saws, belts and chains in mechanical machinery have recently received some attention ( 1–15 ). In the present study, the parametric resonance of an axially accelerated beam is investigated. The beam which has encastre ends is subjected to a periodic root force as shown in Fig. 1 . The object of the investigation is to identify regions of instability of this system for various combinations of the excitation frequency and amplitude of the axial oscillations.
25 citations
23 citations
TL;DR: In this article, necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered, and the special case when a polynomial in that class can be factored into a finite product of single variable p.r.
Abstract: Necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered. The special case when a polynomial in that class can be factored into a finite product of single variable polynomials is investigated. A set of necessary and sufficient conditions for decomposing a multivariable p.r.f. into a sum of single variable p.r.f.'s is given. Examples to illustrate applications of sum and product separabilities of functions are given.
TL;DR: In this paper, sufficient conditions are developed for solutions to certain classes of nonlinear continuous-time systems to be located within certain a priori specified sets over a given time interval.
Abstract: Sufficient conditions are developed for solutions to certain classes of nonlinear continuous-time systems to be located within certain a priori specified sets over a given time interval. Analogous results are obtained for discrete-time systems, and in both cases such conditions are shown to be necessary under mild additional hypotheses.
TL;DR: In this paper, the general formulation of axi-symmetric plane strain problems in linear, mechanically homogeneous, isotropic and centro symmetric elastic solids of grade two is given.
Abstract: Given here is the general formulation of axi-symmetric plane strain problems in linear, mechanically homogeneous, isotropic and centrosymmetric elastic solids of grade two. The definition of a plane strain axi-symmetric state of stress is presented, and the necessary and sufficient conditions to achieve it are derived. The general axi-symmetric displacement vector is found, several problems are considered and the reduction of all results to the corresponding classical solutions is discussed.
TL;DR: In this paper, the authors considered the applications of integral equationsto the general electromagnetic problem when the applied fields are alternating and focused on a problem with cylindrical symmetry, by employing Green's third identity, the boundary value problem is turned into a pair of integral equations of the second kind.
Abstract: A classical method for solving static field problems is based on Fredholm integral equations. Here we consider the applications of integral equationsto the general electromagnetic problem when the applied fields are alternating. Attention is focused on a problem with cylindrical symmetry. By employing Green's third identity, theboundary value problem is turned into a pair of integral equations of the second kind. This set of equations can form the basis for the numerical solution of these problems.
TL;DR: In this article, both upper and lower bounds for axisymmetric flow through conical converging dies are presented, and compared to previously published work on spherical velocity fields, it is found that each type provides a lower solution over a part of the range of process variables.
Abstract: A variety of mathematical models may be used to analyse plastic deformation during a metal-forming process. One of these methods—limit analysis—places the estimate of required power between an upper bound and a lower bound. The upper and lower bound analyses are designed so that the actual power or forming stress requirement is less than that predicted by the upper bound and greater than that predicted by the lower bound. Finding a lower upper bound and a higher lower bound reduces the uncertainty of the actual power requirement. Upper and lower bounds will permit the determination of such quantities as required forces, limitations on the process, optimal die design, flow patterns, and prediction and prevention of defects. Fundamental to the development of both upper bound and lower bound solutions is the division of the body into zones. For each of the zones there is written either a velocity field (upper bound) or a stress field (lower bound). A better choice of zones and fields brings the calculated values closer to actual values. In the present work, both upper and lower bound solutions are presented for axisymmetric flow through conical converging dies. For the upper bound triangular velocity fields have been solved and compared to previously published work on spherical velocity fields. It is found that each type provides a lower solution over a part of the range of process variables. A previously published lower bound solution for axisymmetric flow is refined.
TL;DR: In this paper, a statistical multiparameter sensitivity measure, similar in spirit to that of Rosenblum and Ghausi, is presented, utilizing a second-order series approximation for the ΔH/H(x+Δx) function, is shown to converge for pass band network functions.
Abstract: In this paper a statistical multiparameter sensitivity measure, similar in spirit to that of Rosenblum and Ghausi, is presented The measure, utilizing a second-order series approximation for the ΔH/H(x+Δx) function, is shown to converge for pass band network functions, independent of the network Q In addition this independece is shown to extend considerably the region of convergence (especially for narrowband bandpass network functions) In the stopband, especially when the network function is of the narrowband (finite attenuation) band reject type, equivalent results are obtained for the ΔH/H function Finally, the ΔH/H(x+Δx) and ΔH/H sensitivity measures are shown to form a dual pair whose second-order and asymptotic behaviors conform to sound physical arguments in their respective regions of applicability (convergence)
TL;DR: In this paper, generalized inverses of the matrix A are used to derive algebraic conditions for the existence and uniqueness of a solution, and an example is presented to illustrate application of the results to circuit theory.
Abstract: A system of differential equations A( d/d t) x = Bx+f, along with the initial condition x( 0 ) = k, is considered where A and B are m x n matrices. Generalized inverses of the matrix A are used to derive algebraic conditions for the existence and uniqueness of a solution. An example is presented to illustrate application of the results to circuit theory.
TL;DR: In this article, a simplified model of the hysteresis motor is introduced and analyzed; field analysis is undertaken at hand of Maxwell's stress tensor and Poynting's theorem.
Abstract: A simplified model of the hysteresis motor is introduced and analyzed; field analysis is undertaken at hand of Maxwell's stress tensor and Poynting's theorem. The suggested approach provides deeper insight into the power interchange process between stator and rotor.
TL;DR: Statistical sensitivity measures for gain and phase functions of high Q active networks are studied and explicit formulas for the sensitivity measures of second-order active RC networks are presented.
Abstract: Statistical sensitivity measures for gain and phase functions of high Q active networks are studied. Explicit formulas for the sensitivity measures of second-order active RC networks are presented. The formulas obtained are shown to be simple and can be readily calculated for various high Q active RC filters. General formulation of the sensitivity measure for multiple-loop feedback active networks, which use high Q biquadratic active RC networks, is also given.
TL;DR: In this paper, a modified Romberg procedure for evaluating complex integrals is applied to the computation of the Schwarz-Christoffel transformation for flow in a rectangular cavity and past a rectangular bump.
Abstract: A modified Romberg procedure for evaluating complex integrals is applied to the computation of the Schwarz-Christoffel transformation. An iterative procedure proposed by Wassmuth is used to determine the constants of the transformation for flow past a polygonal boundary. The flow in a rectangular cavity and past a rectangular bump are computed.
TL;DR: Conditions under which decentralized decision making leads to the same results as centralized decision making are stated and proved.
Abstract: This paper treats the problem of amalgamating the preference orderings of individuals into an overall preference ordering for the society comprised of those individuals. A mathematical rule for doing this is known as a “social welfare function”. The imposition of five seemingly desirable conditions on the social welfare function leads to Arrow's Impossibility Theorem, which states that there is no function which satisfies these five conditions. To circumvent this problem, several proposed restrictions on the social welfare function are discussed. The concept of decentralized group decision making, in which the members of the group are arranged in a hierarchical structure, is described. Here decision making takes place within subgroups and then the subgroups are treated as individuals in the decision making process for the group as a whole. Conditions under which decentralized decision making leads to the same results as centralized decision making are stated and proved.
TL;DR: In this paper, second moment properties of a class of Markov sequences are established through a diagonal series expansion of the bivariate density function of the sequence, and an expression for the resulting density is given.
Abstract: Second moment properties of a class of Markov sequences are established through a diagonal series expansion of the bivariate density function of the sequence. It is shown that if the expansion coefficients are raised to any positive integer power, the resulting series converges to a bivariate density. An expression for the resulting density is given. This change in the coefficient sequence is shown to be related to the Chapman-Kolmogorov equation. Some second-moment properties of the Markov sequence are then derived. Also, some bandwidth properties of related pulse trains are considered.
TL;DR: In this article, the authors present the applications of the stability-equation method to the analysis and design of linear systems and present the stability conditions for control systems with a transport lag or a distributive lag.
Abstract: This paper presents the applications of the stability-equation method to the analysis and design of linear systems. Control systems with multiple inputs and outputs are considered; the absolute stability and relative stability characteristics are analyzed. Stability conditions for control systems with a transport lag or a distributive lag are presented. Finally, the stability characteristics of a system with a distributive parameter are analyzed.
TL;DR: In this paper, equations are developed for the general term of the resultant series when certain operations are carried out on a series or on several series Convenient equations are given for obtaining those factors common to a given series, and lower order factors are tabulated Several useful examples are given
Abstract: When an operation is carried out on polynomials or power series the result is usually a new power series The general term of the series is the product of a multiplier which depends on the operation being performed and another factor which is common to the power series being operated on In this paper equations are developed for the general term of the resultant series when certain operations are carried out on a series or on several series Convenient equations are given for obtaining those factors common to a given series, and the lower order factors are tabulated Several useful examples are given
TL;DR: In this paper, the impedance and admittance matrices of parallel connections without ideal transformers were derived, and necessary and sufficient conditions for equality were given, but not the inequalities themselves.
Abstract: Inequalities are derived relating the impedance and admittance matrices of parallel connections without ideal transformers to the matrices of parallel connections with ideal transformers; necessary and sufficient conditions for equality are given. Equivalent conditions for equality, but not the inequalities themselves, were previously obtained in the invertible case by Lempel and Cederbaum and by Murti and Thulasiraman.
TL;DR: In this paper, a simplified criterion for finding the limit cycle in a parameter plane is presented, and a simplified method for testing limit cycle stability is introduced, which is used for illustrating the advantages of the stability equation method.
Abstract: This paper presents the applications of the stability equation method to the analysis and design of nonlinear systems. A simplified criterion for finding the limit cycle in a parameter plane is presented, and a simplified method for testing limit cycle stability is introduced. Several examples, considered in the current literature, are used for illustrating the advantages of the method presented.