Rheological SLS model. Dynamic parameters of the mechanical systems with viscous damping. Part 1: amplitude factor

Perpetual points have been defined recently and their role in the dynamics of mechanical systems is ongoing research. In this article, the nature of perpetual points in natural dissipative mechanical systems with viscous damping, but excepting any externally applied load, is examined. In linear dissipative systems, a theorem and its inverse are proven stating that the perpetual points exist if the stiffness and damping matrices are positive semi-definite and they coincide with the rigid body motions. In nonlinear dissipative natural mechanical systems with viscous damping excepting any external load, the existence of perpetual points that are associated with rigid body motions is shown. Also, an additional type of perpetual points due to the added dissipation is shown that exists, and this type of perpetual points, at least in principle can be used for identification of dissipation in nonlinear mechanical systems. Further work is needed to understand the nature of this additional type of perpetual points. In all the examined examples the perpetual points when they exist, they are not just a few points, but they are forming manifolds in state space, the Perpetual Manifolds, and their geometric characteristics worth further investigation. The findings of this article are applied in all mechanical systems with no gyroscopic effects on their motion, e.g. cars, airplanes, trucks, rockets, robots, etc. and can be used as part of the elementary studies for basic design of all mechanical systems. This work paves the way for new design processes targeting stable rigid body motions eliminating any vibrations in mechanical systems.

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Paper 13: The Dynamics of Valve Mechanisms

Proceedings of the Institution of Mechanical Engineers Conference Proceedings ◽

10.1243/pime_conf_1967_182_366_02 ◽

1967 ◽

Vol 182 (12) ◽

pp. 129-136

Author(s):

D. E. G. Crutcher

Keyword(s):

Theoretical Analysis ◽

Computer Program ◽

Coulomb Friction ◽

Dynamic Behaviour ◽

Viscous Damping ◽

Dynamic Parameters ◽

Valve Mechanism ◽

Single Degree Of Freedom ◽

Single Degree ◽

Single Mass

The paper deals with a computer program that has been developed to study the dynamic behaviour of poppet valve mechanisms. A theoretical analysis is performed on a single mass, single degree of freedom system subjected to internal and external viscous damping and Coulomb friction, representing a valve mechanism with flexible overhead linkage. Measurements have been made on engines so that computed and experimental results could be compared in order to test the program. The effect on performance of varying the dynamic parameters of valve mechanisms is investigated with the computer program.

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The Identification of Nonlinear Systems UsingCt-KtPlane Coordinates

Mathematical Problems in Engineering ◽

10.1155/2014/497872 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13

Author(s):

Ming-Fei Chen ◽

Dyi-Cheng Chen ◽

Chung-Heng Yang ◽

Shih-Feng Tseng

Keyword(s):

Nonlinear System ◽

Nonlinear Systems ◽

Dynamic Behavior ◽

Pulse Response ◽

Displacement Velocity ◽

Viscous Damping ◽

Dynamic Parameters ◽

Coordinate Plane ◽

Aerostatic Bearing ◽

System A

In order to instantaneously distinguish theCt(coefficient of viscous damping) andKt(coefficient of stiffness), which are both functions of time in an M.C.K. nonlinear system, a new identification method is proposed in this paper. The graphs of theCt-Ktare analyzed and the dynamic behavior of M.C.K. systems in aCt-Ktcoordinate plane is discussed. This method calculates two adjacent sampling data, the displacement, velocity, and acceleration (which are obtained from the responses of a pulse response experiment) and then distinguishesCtandKtof an instantaneous system. Finally, this method is used to identify the aerostatic bearing dynamic parameters,CandK.

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New Methodology for Inertial Identification of Low Mobility Mechanisms Considering Dynamic Contribution

International Journal of Automotive and Mechanical Engineering ◽

10.15282/ijame.16.4.2019.11.0545 ◽

2019 ◽

Vol 16 (4) ◽

pp. 7341-7363

Author(s):

L. A. M. Calderón ◽

C. A. R. Piedrahita

Keyword(s):

Dynamic Behaviour ◽

Mechanical Systems ◽

Control Problems ◽

Dynamic Parameters ◽

Symbolic Model ◽

Front Suspension ◽

Inertial Parameters ◽

Closed Chain ◽

Electrical Vehicle ◽

And Control

Knowledge of dynamic parameters of mechanical systems is required in different applications, particularly in the simulation and control problems. In this paper, the standard identification methods are discussed and a new methodology for identification of inertial parameters is raised when the closed chain has low mobility. The methodology includes formulating a symbolic model based on the transfer of inertial properties and a reduction using dynamic contribution indices based on CAD approximations. The new method is applied to the front suspension of an electrical vehicle. After applying the procedure, a model with few parameters that allows accurately reproducing the dynamic behaviour of the system is obtained. A novel methodology has been developed that allows the identification of dynamic parameters in low mobility mechanical systems.

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Lyapunov Stability of a Fractionally Damped Oscillator with Linear (Anti-)Damping

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0381 ◽

2020 ◽

Vol 21 (5) ◽

pp. 425-442 ◽

Cited By ~ 1

Author(s):

Matthias Hinze ◽

André Schmidt ◽

Remco I. Leine

Keyword(s):

Asymptotic Stability ◽

Lyapunov Stability ◽

Lyapunov Functional ◽

Mechanical Energy ◽

Mechanical Systems ◽

Viscous Damping ◽

Nonlinear Stability Analysis ◽

Fractional Damping ◽

Stick Slip ◽

Total Mechanical Energy

AbstractIn this paper, we develop a Lyapunov stability framework for fractionally damped mechanical systems. In particular, we study the asymptotic stability of a linear single degree-of-freedom oscillator with viscous and fractional damping. We prove that the total mechanical energy, including the stored energy in the fractional element, is a Lyapunov functional with which one can prove stability of the equilibrium. Furthermore, we develop a strict Lyapunov functional for asymptotic stability, thereby opening the way to a nonlinear stability analysis beyond an eigenvalue analysis. A key result of the paper is a Lyapunov stability condition for systems having negative viscous damping but a sufficient amount of positive fractional damping. This result forms the stepping stone to the study of Hopf bifurcations in fractionally damped mechanical systems. The theory is demonstrated on a stick-slip oscillator with Stribeck friction law leading to an effective negative viscous damping.

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A Relationship Between Defective Systems and Unit-Rank Modification of Classical Damping

Journal of Vibration and Acoustics ◽

10.1115/1.568458 ◽

1999 ◽

Vol 122 (2) ◽

pp. 180-183 ◽

Cited By ~ 10

Author(s):

Uwe Prells ◽

Michael I. Friswell

Keyword(s):

Mathematical Modeling ◽

Mechanical Systems ◽

Viscous Damping ◽

Common Assumption ◽

Damping Matrix ◽

Linearly Independent ◽

Rank One ◽

Strong Motivation ◽

Repeated Eigenvalue

A common assumption within the mathematical modeling of vibrating elastomechanical system is that the damping matrix can be diagonalized by the modal matrix of the undamped model. These damping models are sometimes called “classical” or “proportional.” Moreover it is well known that in case of a repeated eigenvalue of multiplicity m, there may not exist a full sub-basis of m linearly independent eigenvectors. These systems are generally termed “defective.” This technical brief addresses a relation between a unit-rank modification of a classical damping matrix and defective systems. It is demonstrated that if a rank-one modification of the damping matrix leads to a repeated eigenvalue, which is not an eigenvalue of the unmodified system, then the modified system is defective. Therefore defective systems are much more common in mechanical systems with general viscous damping than previously thought, and this conclusion should provide strong motivation for more detailed study of defective systems. [S0739-3717(00)00602-4]

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