Extrema for Eigenvalues of Vibrating Systems PDF Download
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Author: Dallas O. Banks
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
The results of two areas of research are reported. The first concerns bounds for the eigenvalues of vibrating strings. The second concerns bounds for eigenvalues of a positive symmetric definite matrix A relative to a nonnegative matrix B, i.e., the values of lambda such that the system of equations (A-lambda x B)x =0 has a nontrivial solution. The results in this case are the analog of results found earlier by the investigator for the eigenvalues of a vibrating string.
Author: Dallas O. Banks
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
The results of two areas of research are reported. The first concerns bounds for the eigenvalues of vibrating strings. The second concerns bounds for eigenvalues of a positive symmetric definite matrix A relative to a nonnegative matrix B, i.e., the values of lambda such that the system of equations (A-lambda x B)x =0 has a nontrivial solution. The results in this case are the analog of results found earlier by the investigator for the eigenvalues of a vibrating string.
Author: Rodney D. Gentry
Publisher:
ISBN:
Category :
Languages : en
Pages : 128
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Book Description
Author: G.M.L. Gladwell
Publisher: Springer Science & Business Media
ISBN: 9401511780
Category : Technology & Engineering
Languages : en
Pages : 272
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Book Description
The last thing one settles in writing a book is what one should put in first. Pascal's Pensees Classical vibration theory is concerned, in large part, with the infinitesimal (i. e. , linear) undamped free vibration of various discrete or continuous bodies. One of the basic problems in this theory is the determination of the natural frequencies (eigen frequencies or simply eigenvalues) and normal modes of the vibrating body. A body which is modelled as a discrete system' of rigid masses, rigid rods, massless springs, etc. , will be governed by an ordinary matrix differential equation in time t. It will have a finite number of eigenvalues, and the normal modes will be vectors, called eigenvectors. A body which is modelled as a continuous system will be governed by a partial differential equation in time and one or more spatial variables. It will have an infinite number of eigenvalues, and the normal modes will be functions (eigen functions) of the space variables. In the context of this classical theory, inverse problems are concerned with the construction of a model of a given type; e. g. , a mass-spring system, a string, etc. , which has given eigenvalues and/or eigenvectors or eigenfunctions; i. e. , given spec tral data. In general, if some such spectral data is given, there can be no system, a unique system, or many systems, having these properties.
Author: Peter Lancaster
Publisher: Elsevier
ISBN: 1483150968
Category : Science
Languages : en
Pages : 211
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Book Description
Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 570
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Book Description
Author:
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ISBN:
Category : Industrial arts
Languages : en
Pages : 1118
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Book Description
Author: Turgut Cakiraga
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 490
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Book Description
Author: Dallas Odell Banks
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 572
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Book Description
Author: Singiresu S. Rao
Publisher: John Wiley & Sons
ISBN: 1119424143
Category : Technology & Engineering
Languages : en
Pages : 816
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Book Description
A revised and up-to-date guide to advanced vibration analysis written by a noted expert The revised and updated second edition of Vibration of Continuous Systems offers a guide to all aspects of vibration of continuous systems including: derivation of equations of motion, exact and approximate solutions and computational aspects. The author—a noted expert in the field—reviews all possible types of continuous structural members and systems including strings, shafts, beams, membranes, plates, shells, three-dimensional bodies, and composite structural members. Designed to be a useful aid in the understanding of the vibration of continuous systems, the book contains exact analytical solutions, approximate analytical solutions, and numerical solutions. All the methods are presented in clear and simple terms and the second edition offers a more detailed explanation of the fundamentals and basic concepts. Vibration of Continuous Systems revised second edition: Contains new chapters on Vibration of three-dimensional solid bodies; Vibration of composite structures; and Numerical solution using the finite element method Reviews the fundamental concepts in clear and concise language Includes newly formatted content that is streamlined for effectiveness Offers many new illustrative examples and problems Presents answers to selected problems Written for professors, students of mechanics of vibration courses, and researchers, the revised second edition of Vibration of Continuous Systems offers an authoritative guide filled with illustrative examples of the theory, computational details, and applications of vibration of continuous systems.
