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Matrix Methods in Elasto Mechanics
01 Jan 1963-
About: The article was published on 1963-01-01 and is currently open access. It has received 175 citations till now. The article focuses on the topics: Matrix method.
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TL;DR: In this paper, three types of linear feedback control schemes are considered: joint angle and velocity feedback with (GRC) and without (IJC) cross joint feedback, and feedback of flexible state variables (FFC).
Abstract: The control of the flexible motion in a plane of two pinned beams is addressed with application to remote manipulators. Three types of linear feedback control schemes are considered: joint angle and velocity feedback with (GRC) and without (IJC) cross joint feedback, and feedback of flexible state variables (FFC). Two models of the distributed flexibility are presented along with some results obtained from them. The relative merit of the three control schemes is discussed.
395 citations
TL;DR: In this article, the dispersion function for Rayleigh waves in layered elastic media is calculated using the matrix method. But, the problem of high-frequency limitation is not addressed in this paper.
Abstract: Summary
Progress in the matrix method for the calculation of the seismic surface wave dispersion function for a layered elastic media started with the beginning of the electronic digital computer age.
The use of Thomson–Haskell formulation, Knopoff's method or any other published method has had the persistent problem of loss of precision at high frequencies. The severity of the high-frequency limitation problem varies among the approaches but exists in all of them.
In this paper we present a novel method to determine the dispersion function for Rayleigh waves in layered elastic media. In this method there is no limitation on the value of the frequency.
154 citations
31 Oct 2000
TL;DR: The matrix method can calculate a compliance matrix with less nodes of matrix than conventional finite element method and is well applicable to a flexure mechanism with circular notched hinges as the authors' micro parallel mechanism because it is approximate to the Rahmen structure.
Abstract: We apply the matrix method to kinematic analysis of our translational 3-DOF micro parallel mechanism for an instance of general flexure mechanisms. The matrix method has been well developed in architecture to analyze a frame structure. We found that this method is well applicable to such a flexure mechanism with circular notched hinges as our micro parallel mechanism because it is approximate to the Rahmen structure. Our matrix method can calculate a compliance matrix with less nodes of matrix than conventional finite element method. First, the compliance matrices of a circular notched hinge and some other beams are defined and the coordinate transformations of compliance matrix are introduced. Next, an analysis of our micro parallel mechanism is demonstrated.
123 citations
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01 Jan 1984
TL;DR: In this article, a structural network is taken to be an assemblage of slender structural members (beams, cables, rods) connected to each other at structural junctions.
Abstract: A structural network is taken to be an assemblage of slender structural members (beams, cables, rods) connected to each other at structural junctions. The junctions may include flexible bodies which, in this work, are restricted to those whose dynamics are described by a finite set of ordinary differential equations. Elastic disturbances in such a network are calculated in terms of propagation concepts. Members are described in the frequency domain by the propagation coefficients of their intrinsic wave-modes, junctions by frequency-dependent wave-mode reflection and transmission coefficients, grouped in the junction scattering matrix. Component impulse responses are calculated by a combination of analysis and application of the fast Fourier transform algorithm. Network time responses are synthesized by convolution of component impulse responses. A consistent analytical framework is constructed within which descriptions of various member types and junctions can be accommodated. The analysis is set up for computer implementation. Computational examples are used to demonstrate the techniques.
114 citations
TL;DR: In this paper, a complete review of the principal methods developed for Love and Rayleigh-wave dispersion of free modes in plane-layered perfectly elastic, isotropic earth models and puts to rest controversies that have arisen with regard to computational stability.
Abstract: SUMMARY
The theory of Love- and Rayleigh-wave dispersion for plane-layered earth models has undergone a number of developments since the initial work of Thomson and Haskell. Most of these were concerned with computational difficulties associated with numerical overflow and loss of precision at high frequencies in the original Thomson-Haskell formalism. Several seemingly distinct approaches have been followed, including the delta matrix, reduced delta matrix, Schwab-Knopoff, fast Schwab-Knopoff, Kennett's Reflection-Transmission Matrix and Abo-Zena methods. This paper analyses all these methods in detail and finds explicit transformations connecting them. It is shown that they are essentially equivalent and, contrary to some claims made, each solves the loss of precision problem equally well. This is demonstrated both theoretically and computationally. By extracting the best computational features of the various methods, we develop a new algorithm (sec Appendix A5), called the fast delta matrix algorithm. To date, this is the simplest and most efficient algorithm for surface-wave dispersion computations (see Fig. 4).
The theory given in this paper provides a complete review of the principal methods developed for Love- and Rayleigh-wave dispersion of free modes in plane-layered perfectly elastic, isotropic earth models and puts to rest controversies that have arisen with regard to computational stability.
111 citations