Random oscillations of nonlinear systems with distributed Parameter

The article analyzes random vibrations of nonlinear mechanical systems with distributed parameters. The motion of such systems is described by nonlinear partial differential equations with corresponding initial and boundary conditions. In our case, the system as a whole is limited, so any motion can be considered as the sum of the natural oscillations of the system, i.e. in the form of an expansion of the boundary value problem in terms of own functions. The use of the theory of random processes in the calculation of mechanical systems is a prerequisite for the creation of sound design methods and the creation of effective vibration protection devices, these methods allow us to investigate dynamic processes, to determine the probabilistic characteristics of displacements of points of the system and their first two derivatives. In the work established these conditions are met, they provide effective vibration protection of the system under study with wide changes in the pass band of the frequencies of the random vibration effect, and the frequency of the disturbing force is much greater than the natural frequency of the system as a whole, in addition, with an increase in the damping capacity of the elastic-damping link of the system, the intensity of the random process significantly decreases, which in turn leads to a sharp decrease in the dynamic coefficient of the system.

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Features of the damping capacity of Mn – Cu alloys

MATEC Web of Conferences ◽

10.1051/matecconf/202134401012 ◽

2021 ◽

Vol 344 ◽

pp. 01012

Author(s):

Sergey Naumov ◽

Svetlana Ginne

Keyword(s):

Sharp Decrease ◽

Alloying Elements ◽

Damping Capacity ◽

Natural Ageing ◽

Cu Alloys ◽

The Stability

Data on the damping capacity of Mn – Cu alloys are adduced. The results of studying the influence of alloying elements, natural ageing at temperatures of 293 K, 273 K and 263 K on the stability of the damping capacity of Mn – Cu alloys are presented. The high damping capacity of Mn – Cu alloys decreases by 4 ... 6 times during natural ageing at 293 K, remains during 1,7 years of natural ageing at 273 K and 263 K. The analysis of factors that should be considered responsible for a sharp decrease in the damping capacity of Mn – Cu alloys during natural ageing is submitted.

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Methods for Determinning Critical Values of Nonconservative Loads in Problems of Stability of Mechanical Systems

Proceedings of Higher Educational Institutions Маchine Building ◽

10.18698/0536-1044-2019-10-3-13 ◽

2019 ◽

pp. 3-13 ◽

Cited By ~ 1

Author(s):

V.P. Radin ◽

V.P. Chirkov ◽

A.V. Shchugorev ◽

V.N. Shchugorev

Keyword(s):

Complex Function ◽

Mechanical Systems ◽

Critical Values ◽

The Finite Element Method ◽

Natural Oscillations ◽

Flowing Liquid ◽

Stability Problems ◽

Distributed Parameters ◽

The Stability ◽

Systems With Distributed Parameters

Methods for determining critical values of nonconservative loads in stability problems of mechanical systems with distributed parameters are considered in this work. Based on a dynamic approach to stability problems, the method of direct integration of the linearized equation of perturbed motion is proposed, and the problem of determining critical loads is reduced to the problem of minimizing a complex function of several variables. As a second method, the method of decomposition of the solution of the equation of perturbed motion in the forms of natural oscillations is presented. The fundamentals of the application of the finite element method to the problems of stability under the action of non-conservative loads are also described. The methods are illustrated on classical problems: the stability of the cantilever rod under the action of potential and tracking forces and the stability of the pipeline section with flowing liquid. The accuracy and convergence of the latter two methods are analyzed depending on the number of members in the series and the number of finite elements.

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Vibration Protection of Mechanical Systems Consisting of Solid And Deformable Bodies

European Journal of Engineering Research and Science ◽

10.24018/ejers.2018.3.9.860 ◽

2018 ◽

Vol 3 (9) ◽

pp. 18

Author(s):

Ismail Ibrahimovich Safarov ◽

Teshaev Muhsin Khudoyberdiyevich

Keyword(s):

Finite Number ◽

Degrees Of Freedom ◽

Mechanical Systems ◽

Numerical Results ◽

Constructive Method ◽

Vibration Protection ◽

Deformable Bodies ◽

Reaction Forces ◽

Active Vibration ◽

Servo Constraints

In this paper active vibration protection of mechanical systems consisting of solid and deformable bodies is considered. To actively control the oscillations of dissipative mechanical systems, a constructive method is used to determine the structure of the reaction forces of servo constraints. As an example, we consider the system with a finite number of degrees of freedom. Numerical results for various harmonic are also given.

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Natural Oscillations of Viscoelastic Lamellar Mechanical Systems with Point Communications

Applied Mathematics ◽

10.4236/am.2014.519289 ◽

2014 ◽

Vol 05 (19) ◽

pp. 3018-3025 ◽

Cited By ~ 1

Author(s):

Safarov Ismail Ibrahimovich ◽

Teshaev Muhsin Hudoyberdievich ◽

Madjidov Maqsud

Keyword(s):

Mechanical Systems ◽

Natural Oscillations

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Receptances in Mechanical Systems

Journal of the Royal Aeronautical Society ◽

10.1017/s036839310009862x ◽

1954 ◽

Vol 58 (520) ◽

pp. 305-305 ◽

Cited By ~ 1

Author(s):

W. J. Duncan ◽

M. A. Biot ◽

D. C. Johnson ◽

R. E. D. Bishop

Keyword(s):

Mechanical Systems ◽

Oscillatory System ◽

Disturbing Force ◽

The Cross

We wish to propose that the word “receptance” should be used instead of “admittance” as applied to mechanical systems (see R. and M. 2,000, 1947). By this, we mean that if a generalised disturbing force Fseiωt is applied at the sth generalised co-ordinate qs of a linear oscillatory system, then the response at the rth generalised co-ordinate is given byqs = αrsFseiωtwhere αrs is the “Cross-receptance” between qr and qs. If r = s, then αrs would be the “direct receptance” at qs.

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Entrainment of central pattern generators to natural oscillations of collocated mechanical systems

2008 47th IEEE Conference on Decision and Control ◽

10.1109/cdc.2008.4739198 ◽

2008 ◽

Cited By ~ 3

Author(s):

Y. Futakata ◽

T. Iwasaki

Keyword(s):

Central Pattern Generators ◽

Mechanical Systems ◽

Natural Oscillations ◽

Pattern Generators

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Design of Passive Reconfigurable Manipulation Assistive Aids

Volume 2B: 27th Design Automation Conference ◽

10.1115/detc2001/dac-21087 ◽

2001 ◽

Author(s):

Xichun Nie ◽

Venkat Krovi

Keyword(s):

Task Performance ◽

Degrees Of Freedom ◽

Structural Parameters ◽

Mechanical Systems ◽

Degree Of Freedom ◽

Mechanical Constraints ◽

The Creation

Abstract Multi-jointed mechanical systems typically possess excess degrees-of-freedom, which often are neither required nor used in performing typical manipulation tasks. These excessive degrees of freedom then need to be reduced by application of constraints, either actively by suitable control or passively in hardware, prior to task performance. Our interest is in creating articulated manipulation assistive aids, which combine the motion flexibility due to the multiple articulations with the simplicity of reduced degree-of-freedom control and actuation due to the presence of hardware mechanical constraints. Specifically we investigate the process of design and prototyping of such reduced-degree-of-freedom manipulators to closely approximate desired planar paths. We then examine design enhancements to permit easy reconfiguration for different sets of paths. Finally, special attention is paid to the creation of a prototype with the ability to be reconfigured for multiple sets of paths, by a controlled variation of the principal structural parameters.

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The Study on Disturbing Force of Dynamic Mechanical Systems Using Kalman Filter Techniques

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.705.371 ◽

2013 ◽

Vol 705 ◽

pp. 371-377

Author(s):

Zhang Jing

Keyword(s):

Kalman Filter ◽

Mechanical Systems ◽

Dynamic Structure ◽

Estimation Accuracy ◽

Complex Dynamic ◽

Model Quality ◽

Disturbing Force ◽

Dynamic Mechanical ◽

Multiple Sensors ◽

Mems Sensor

According to the approach presented in this paper, the disturbing force of dynamic mechanical systems can be estimated using Kalman Filter techniques. It has been shown how multiple sensors can be included to improve the estimation accuracy and how the algorithm responds to changing parameters and model inaccuracies. Finally, the approach has been experimentally verified with a MEMS-sensor and a more complex dynamic structure of a milling machine with active magnetic guides. Future enhancements may especially regard the model side, since the estimation accuracy is directly determined by the model quality.

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Study of a Stripper Header for Grain Harvesting as a Vibrating System

Engineering Technologies and Systems ◽

10.15507/2658-4123.031.202103.403-413 ◽

2021 ◽

Vol 31 (3) ◽

pp. 403-413

Author(s):

Vladimir Yu. Savin

Keyword(s):

Differential Equation ◽

Mathematical Description ◽

Elastic Element ◽

Lagrange Equation ◽

Oscillatory System ◽

Angular Frequency ◽

Forced Oscillations ◽

Disturbing Force ◽

Vibration Effect ◽

Generalized Force

Introduction. Grain losses caused by stripping defects are the main problem to be solved in designing a stripper header. To reduce these losses, a design of a stripper header with a vibration drive is proposed. This device combines the processes of stripping grain crops and the vibration effect of the stripping fingers upon the ears of plants. The most important stage of the mathematical description of these processes is composing the differential equation of the stripping fingers motion. Materials and Methods. A computational-graphic diagram of an oscillatory system with one degree of freedom is proposed. To compose the differential equation of the stripping fingers motion, a method based on the application of the Lagrange equation was used. The oscillations of the system under studying arise from the motion of a point in the system according to a given law. The problem of kinematic excitation is reduced to the problem of force perturbation. This stage of the study was carried out without taking into account the resistance forces. Results. An equation for motion of stripping fingers making vibrational reciprocating movements is obtained. It is proposed to select the elastic element in the design scheme and consider a more general case of the stripping fingers movement. In this case, the movement of the stripping fingers is considered to be difficult. A characteristic feature of the mathematical description is the presence of a generalized force of potential forces. The differential equation of motion of a comb in the presence of an elastic element and the solution of this equation are composed. Discussion and Conclusion. Forced oscillations of a system without resistance, excited by a harmonic disturbing force, are harmonic oscillations with constant amplitude. On close values of the angular frequency of vibration of the drive output link and the root of the ratio of the stiffness coefficient of the elastic element to the stripping fingers mass, the case of resonance takes place. The system parameters must be selected so as to avoid this negative phenomenon.

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