The Oscillation of Non-linear Mechanical Systems with Two Degrees of Freedom PDF Download
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Author: A. O. Gilchrist
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: A. O. Gilchrist
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Bernard Katz
Publisher:
ISBN:
Category : Nonlinear systems
Languages : en
Pages : 216
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Author: Frank Robert Arnold
Publisher:
ISBN:
Category : Oscillations
Languages : en
Pages : 398
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Book Description
Author: Arkadiy I. Manevich
Publisher: World Scientific
ISBN: 1860945104
Category : Science
Languages : en
Pages : 278
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Book Description
One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.
Author: David Owen Swint
Publisher:
ISBN:
Category : Nonlinear mechanics
Languages : en
Pages : 342
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Book Description
Author: Kenneth F. Paulovich
Publisher:
ISBN:
Category : Vibration
Languages : en
Pages : 154
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Book Description
Author: Roger F. Gans
Publisher: Springer
ISBN: 3319083716
Category : Technology & Engineering
Languages : en
Pages : 448
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Book Description
This essential textbook concerns analysis and control of engineering mechanisms, which includes almost any apparatus with moving parts used in daily life, from musical instruments to robots. A particular characteristic of this book is that it presents with considerable breadth and rigor both vibrations and controls. Many contemporary texts combine both of these topics in a single, one term course. This text supports the more favorable circumstance where the material is covered in a one year sequence contains enough material for a two semester sequence, but it can also be used in a single semester course combining two topics. “Mechanical Systems: A Unified Approach to Vibrations and Controls” presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text.
Author: Polina S. Landa
Publisher: Springer
ISBN: 9783642074233
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Author: Mahmoud Abd-Elfattah Moustafa
Publisher:
ISBN:
Category : Oscillations
Languages : en
Pages : 250
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Book Description
The study of nonlinear vibrations of systems having two degrees of freedom has met considerable attention during the past few years. Nonlinear symmetrical systems have received most of it. Normal mode motion of a system is defined as a periodic motion such that the masses of the system assume repeated displacements after some interval of time, called the period of oscillation. In this kind of motion there is a definite relation between the displacements of the masses which is called the modal relation. The modal line is defined as the locus of all points, in the plane representing the displacements, which set the system in normal mode motion when started from rest. This line passes through the origin of the plane. Systems vibrating in normal modes have also what is called the orthogonality property. That is, the modal relation curves intersect the total energy line orthogonally. There exists a type of normal mode which has a straight modal relation. The linear systems belong to it. In this type of mode the orthogonality property is used to determine the modal relations and this in turn enables the equations of motion to be decoupled to form two separate systems, each with a single degree of freedom. This of course simplifies analysis of the system. Generally speaking the modal relations are not straight and they could be determined easily by numerical means. For this purpose an algorithm for determining the normal mode motions was developed. The application of the orthogonality property is also useful when applied to small displacements. One striking phenomenon have more normal modes than The existence of this excess of of nonlinear systems is that they may the number of degrees of freedom. modes can be easily detected by using the orthogonality property. The stability of systems oscillating in normal modes could be studied by using Liapounovrs theorem of stability. The total energy equation of a dynamical system is a Liapounov function. The idea of the modal phase plane, which is a plot of the total energy line and the modal line, is introduced. This helps in deducing the stability of normal modes. The concepts of singularities in this plane are defined. The mathematical procedure for determining the normal modes was applied to an air spring system with two degrees of freedom. An experimental apparatus was constructed to compare the theoretical and the experimental results. This comparison showed fair agreement. The forced motion of the air spring system was studied experimentally. Over some range of the exciting frequency two resonances appeared. Each one corresponds to one normal mode. The results showed that the system eventually oscillates essentially in normal modes when the exciting frequency is equal to a natural frequency of the system.
Author: Nguyen Van Dao
Publisher: Springer Science & Business Media
ISBN: 9401141509
Category : Technology & Engineering
Languages : en
Pages : 341
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Book Description
This volume contains selected papers presented at the Symposium on "Recent Developments in Non-linear Oscillations of Mechanical Systems", held in Hanoi, Vietnam, from 2 - 5 March 1999. This Symposium was initiated and sponsored by the International Union of Theoretical and Applied Mechanics (lUI AM) and organised in conjunction with Vietnam National University, Hanoi. Ihe purpose of the Symposium was to bring together scientists active in different fields of oscillations with the aim to review the recent progress in theory of oscillations and engineering applications and to outline the prospects in its further achievements to then co-ordinate and direct research in this field to further co-operation between scientists and various scientific institutions. An International Scientific Committee was appointed by the Bureau of IUI AM with the following members: Nguyen Van Dao (Vietnam, Co-Chairman) E.J. Kreuzer (Germany, Co-Chairman) D.H. van Campen (The Netherlands) F.L. Chernousko (Russia) A.H. Nayfeh (U.S.A) Nguyen Xuan Hung (Vietnam) W.O. Schiehlen (Germany) J.M.T. Thompson (U.K) Y. Veda (Japan). This Committee selected the participants to be invited and the papers to be presented at the Symposium. As a result of this procedure, 52 active scientists from 16 countries responded to the invitation, and 42 papers were presented in lecture and poster discussion sessions.
