Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1969"
210 citations
154 citations
106 citations
TL;DR: In this article, a theory describing the response of a beam under an arbitrary number of moving masses is developed, based on the Fourier technique and shows that, for a simply supported beam, the resonance frequency is lower with no corresponding decrease in maximum amplitude when the inertia is considered.
Abstract: A theory describing the response of a beam under an arbitrary number of moving masses is developed. The theory is based on the Fourier technique and shows that, for a simply supported beam, the resonance frequency is lower with no corresponding decrease in maximum amplitude when the inertia is considered.
95 citations
74 citations
TL;DR: The type of transformation required in mechanics elucidates a fundamental difference between electric circuits and mechanical systems, including the use of co-energy expressions for ideal devices which, although conservative, store no energy.
Abstract: In the description of physical systems, most of the transformations of variables turn out to be power conserving. In addition, the characteristics of many ideal devices such as electrical transformers, gears, levers, and linkages may be represented as power-conserving transformations. This paper discusses such transformations both in terms of equations and bond graph elements, and discusses applications in vibrations, electrical machine theory, and analytical mechanics. The type of transformation required in mechanics elucidates a fundamental difference between electric circuits and mechanical systems. The physical interpretation of the transformations leads to nontraditional system formulations including the use of co-energy expressions for ideal devices which, although conservative, store no energy.
70 citations
TL;DR: In this paper, a general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems.
Abstract: A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.
53 citations
TL;DR: In this article, the convergence properties of the Davidon-fletcher-powell and conjugate gradient methods were analyzed for non-quadratic cost functions and it was shown that the convergence of these methods is quadratically convergent when applied to a quadratic cost function.
Abstract: Iterative procedures that are quadratically convergent are seeing increasing application to many types of extremization problems. Three of these procedures are analyzed and their underlying theoretical similarities are pointed out. It is shown that the Davidon- Fletcher-Powell, conjugate gradient, and gradient partan methods provide identical results when applied to a quadratic cost function. This occurs because each procedure generates the same set of mutually conjugate vectors and is the basic reason for their quadratic convergence property. A slight modification to the conjugate gradient procedure proposed by Fletcher and Reeves is seen to yield a procedure that exhibits the principal property of the Davidon-Fletcher-Powell method when applied to nonquadratic cost functions. This modified conjugate gradient procedure involves a significantly smaller amount of computation than either the Davidon-Fletcher-Powell or gradient partan methods while retaining the basic properties influencing convergence of the Davidon-Fletcher-Powell procedure.
47 citations
40 citations
TL;DR: In this paper, the authors proposed a method for the evaluation of responses of linear networks with distributed or mixed lumped-distributed elements, which does not require the knowledge of the poles of the function under consideration.
Abstract: Transient responses of linear networks with distributed or mixed lumped-distributed elements are difficult to evaluate because of the infinite number of poles. The method presented here is easily applicable for any kind of transfer function, including feedback systems, and does not require the knowledge of the poles of the function under consideration. It can be used for the evaluation of responses of lumped-element networks. Errors of the results can be estimated by using two successive numerical approximations.
32 citations
TL;DR: In this article, the surface instability of an isotropic incompressible highly elastic half-infinite medium is considered, generated by uniformly distributed compressive loads parallel to the bounding plane of the medium and acting in two perpendicular directions.
Abstract: Surface instability of an isotropic incompressible highly elastic half-infinite medium is considered, generated by uniformly distributed compressive loads parallel to the bounding plane of the medium and acting in two perpendicular directions. Using the theory of Green, Rivlin, and Shield of small deformations superposed on a large deformation, asystem of four governing equations is derived. Solution of the system is sought which provides a state of deformation decaying rapidly with an increasing distance from the surface of the medium. Fulfillment of the boundary conditions leads to a characteristic equation for the critical combination of stretches. The results obtained in two limit cases agree with those given by Biot and Green and Zerna. Graphs display the dependence of the critical stretch λ 1 on the stretch λ 3 , in the perpendicular direction, and the wave number ratio.
TL;DR: In this article, the application of Fourier transform methods in elasticity problems is discussed and two different, possible methods of approach and their limitations for the solution of the above problem are presented.
Abstract: The application of Fourier transform methods in elasticity problems is discussed. An example of a half-space with the external load extending to infinity is chosen to illustrate the problem that Fourier transforms cannot be obtained in a strict mathematical sense. Two different, possible methods of approach and their limitations for the solution of the above problem are presented.
IBM1
TL;DR: In this paper, the indeterminate state of the empirical law of electrodynamic action between two current elements is reviewed and a form of the law fully consistent with experiment can be deduced from simple Newtonian dynamics.
Abstract: The indeterminate state of the empirical law of electrodynamic action between two current elements is reviewed. It is shown that a form of the law fully consistent with experiment can be deduced from simple Newtonian dynamics. This law points to anomalies to be expected in electrodynamic interactions between electric particles of unequal charge-mass ratio. This result may account for certain hitherto unexplained anomalies in electric discharge phenomena.
TL;DR: In this paper, a method for the analysis of natural frequencies of elastic beams having randomly varying characteristics is presented, which may be due to material inhomogeneities or geometrical imperfections.
Abstract: Based upon a lumped-parameter model approach followed by a passage to the limit, a method is presented for the analysis of natural frequencies of elastic beams having randomly varying characteristics. The randomness may be due to material inhomogeneities or geometrical imperfections. Statistical properties of the transverse vibrational frequencies of a simply supported elastic beam are derived assuming that the beam stiffness varies with position in a random manner.
TL;DR: In this paper, the behavior of a thin simply supported circular plate when subject to a dynamic transverse load uniformly distributed over a central circular region was determined, where the load is brought on suddenly, held constant for a period of time, and then suddenly removed.
Abstract: The object of this paper is to determine the behavior of a thin simply supported circular plate when subject to a dynamic transverse load uniformly distributed over a central circular region. The plate is made of a rigid-ideally plastic material that obeys Tresca's yield condition and the associated flow rule. The load is brought on suddenly, held constant for a period of time, and then suddenly removed.
IBM1
TL;DR: In this paper, an algorithm is developed for drawing straight-line planar graphs which are isomorphic to a convex polyhedron and simple (i.e., a connected graph with no self-loops or multiple branches).
Abstract: An algorithm is developed for drawing straight-line planar graphs which are isomorphic to a convex polyhedron and simple (i.e. a connected graph with no self-loops or multiple branches). The construction of such graphs is outlined in three stages. Stage 1 determines all the independent cycles of the graph plus one dependent cycle by Goldstein's algorithm. Stage 2 orders the cycles in such a way that they may be drawn in sequence with a given cycle as external. Stage 3 constructs the graph by successively assigning coordinates to the vertices which were placed in order according to the result of Stage 2. An iterative procedure is used for shifting the coordinates to eliminate crossings of edges. Results show that practically all these planar connected graphs up to 22 cycles can be drawn provided that the longest cycle is chosen as the external one. In addition, in the event of failure of the iteration procedure for graphs with a large number of cycles, a heuristic decision involving man-machine interaction is introduced to adjust the partially completed straight-line graph.
TL;DR: The Flow Variation Algorithm (FVA) as discussed by the authors was proposed to find the smallest disconnecting set in graphs with up to ninety vertices and eight hundred branches by reducing the number of steps needed to calculate τ s,t once τ s′,t has been found.
Abstract: A problem of interest in flow networks is that of finding the smallest disconnecting set. Let s, s′, and t be three distinct arbitrary vertices in a directed graph and let τ s,t be the value of the smallest s-t-cut. A method is given for significantly reducing the number of steps needed to calculate τ s,t once τ s′,t has been found by the Ford—Fulkerson labelling algorithm. This new method, called the Flow Variation Algorithm , has been successfully used in finding the smallest disconnecting sets in graphs with up to ninety vertices and eight hundred branches.
TL;DR: In this article, the authors considered the dynamical instabilities of a thin disc under the influence of Coriolis and centrifugal forces and represented the solutions by a pair of simultaneous integral equations whose kernels are Green's functions.
Abstract: Consideration is given to the dynamical instabilities of a thin disc under the influence of Coriolis and centrifugal forces. The solutions are represented by a pair of simultaneous integral equations whose kernels are Green's functions. They are expanded in terms of the eigenfunctions of the kernels in order to obtain the secular equation. An appropriate eigenfunction approximation to the secular equation reveals that there is a range of dynamical instabilities in which the oscillational frequency becomes complex. Numerical results are presented to substantiate the linearized theory.
TL;DR: Tuneable adjustable solid state bandwidth filter using N path system for low pass to bandpass filter transformation as discussed by the authors, which can be used for both low pass and bandpass filtering.
Abstract: Tuneable adjustable solid state bandwidth filter using N path system for low pass to bandpass filter transformation