On the bifurcation and stability of the steady-state motions of complex mechanical systems

1973 ◽  
Vol 37 (3) ◽  
pp. 371-382 ◽  
Author(s):  
V.M. Morozov ◽  
V.N. Rubanovskii ◽  
V.V. Rumiantsev ◽  
V.A. Samsonov
Keyword(s):  
Steady State ◽  
Mechanical Systems ◽  
Complex Mechanical Systems ◽  
Bifurcation And Stability

scholarly journals Degrading systems availability analysis: analytical semi-Markov approach

2021 ◽  
Vol 23 (1) ◽  
pp. 195-208
Author(s):  
Varun Kumar ◽  
Girish Kumar ◽  
Rajesh Kumar Singh ◽  
Umang Soni
Keyword(s):  
Steady State ◽  
Degradation Mechanism ◽  
Continuous Process ◽  
Mechanical Systems ◽  
Embedded Markov Chain ◽  
Steady State Probability ◽  
Opportunistic Maintenance ◽  
System Availability ◽  
Availability Analysis ◽  
Complex Mechanical Systems

This paper deals with modeling and analysis of complex mechanical systems that deteriorate with age. As systems age, the questions on their availability and reliability start to surface. The system is believed to suffer from internal stochastic degradation mechanism that is described as a gradual and continuous process of performance deterioration. Therefore, it becomes difficult for maintenance engineer to model such system. Semi-Markov approach is proposed to analyze the degradation of complex mechanical systems. It involves constructing states corresponding to the system functionality status and constructing kernel matrix between the states. The construction of the transition matrix takes the failure rate and repair rate into account. Once the steady-state probability of the embedded Markov chain is computed, one can compute the steady-state solution and finally, the system availability. System models based on perfect repair without opportunistic and with opportunistic maintenance have been developed and the benefits of opportunistic maintenance are quantified in terms of increased system availability. The proposed methodology is demonstrated for a two-stage reciprocating air compressor with intercooler in between, system in series configuration.

scholarly journals REACTANCES AND SUSCEPTANCES OF MECHANICAL SYSTEMS

2021 ◽  
pp. 64-75
Author(s):  
I.P. Popov ◽  
Keyword(s):  
Steady State ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Harmonic Force ◽  
Parallel Connection ◽  
Electrical Circuits ◽  
Major Interest ◽  
Inert Body ◽  
Complex Mechanical Systems ◽  
External Harmonic Force

The classical solution to the problems associated with calculating the velocities and reactions of elements of complex mechanical systems under harmonic force consists in the compilation and integration of systems of differential equations and is rather cumbersome and time-consuming. In most cases, a steady state is of major interest. The purpose of this study is to develop essentially compact methods for calculating systems under steady-state conditions. The problem is solved by the methods which are typically used to calculate electrical circuits. Representation of harmonic quantities as rotating vectors in a complex plane and the operations with their complex amplitudes can greatly facilitate the calculation of arbitrarily complex mechanical systems under harmonic effects in the steady state. In the proposed method, a key role is played by mechanical reactance, resistance, and impedance for the parallel connection of consumers of mechanical power, as well as susceptance, conductance, and admittance for the serial one. At force resonance, the total reactance of the mechanical system is zero. This means that the system does not exhibit reactive resistance to the external harmonic force. At velocity resonance, the total susceptibility of the mechanical system is zero. This means that the system has infinitely high resistance to the external harmonic force. As a result, the stock of the source of harmonic force is stationary, although the inert body and the elastic element oscillate.

Energy Method for Determining Dynamic Characteristics of Mechanisms

1949 ◽  
Vol 16 (3) ◽  
pp. 283-288
Author(s):  
B. E. Quinn
Keyword(s):  
Dynamic Characteristics ◽  
Energy Method ◽  
Mechanical Systems ◽  
Direct Approach ◽  
Graphical Methods ◽  
Applied Forces ◽  
Complex Mechanical Systems

Abstract Two types of problems are dealt with in the paper which are involved in the design of mechanisms required to have specified dynamic characteristics: (1) Determination of applied forces required to produce specified dynamic characteristics. (2) Determination of the dynamic characteristics which will result from the application of known forces. While graphical methods may be used in the solution of type (1) problems involving more or less complex mechanical systems, they do not afford a direct approach to type (2) problems. The energy method which will be outlined can be applied in either case, although this paper will be primarily concerned with the determination of the dynamic characteristics which result when a known force is applied to a given mechanism.

A Form Verification System for the Conceptual Design of Complex Mechanical Systems

1993 ◽  
Author(s):  
Jonathan S. Colton ◽  
Mark P. Ouellette
Keyword(s):  
Conceptual Design ◽  
Process Model ◽  
Mechanical Systems ◽  
Data Representation ◽  
Design System ◽  
Complex Data ◽  
Graphical Display ◽  
Design Environment ◽  
Blackboard System ◽  
Complex Mechanical Systems

Abstract This paper presents a summary of research into the development and implementation of a domain independent, computer-based model for the conceptual design of complex mechanical systems (Ouellette, 1992). The creation of such a design model includes the integration of four major concepts: (1) The use of a graphical display for visualizing the conceptual design attributes; (2) The proper representation of the complex data and diverse knowledge required to design the system; (3) The integration of quality design methods into the conceptual design; and (4) The modeling of the conceptual design process as a mapping between functions and forms. Using the design of an automobile as a case study, a design environment was created which consisted of a distributed problem solving paradigm and a parametric graphical display. The requirements of the design problem with respect to data representation and design processing were evaluated and a process model was specified. The resulting vehicle design system consists of a tight integration between a blackboard system and a parametric design system. The completed system allows a designer to view graphical representations of the candidate conceptual designs that the blackboard system generates.

NONLINEAR MODELING OF COMPLEX MECHANICAL SYSTEMS

1994 ◽  
Vol 04 (03) ◽  
pp. 521-551 ◽  
Author(s):  
MARTIN LESSER
Keyword(s):  
Nonlinear Models ◽  
Nonlinear Modeling ◽  
Mechanical Systems ◽  
Computer Software ◽  
Nonholonomic Systems ◽  
Reference List ◽  
Spacecraft Design ◽  
Vehicle Technology ◽  
Configuration Manifold ◽  
Complex Mechanical Systems

This article provides an introduction to a technique for formulating nonlinear models of mechanical systems composed of interconnected and constrained rigid body systems such as those encountered in vehicle technology, biomechanics, spacecraft design and robotics. The approach is based on an algorithm developed by Kane to treat nonholonomic systems, for example systems with rolling constraints. The algorithm is interpreted geometrically in terms of tangent vectors to the instantaneous configuration manifold embedded in the space of nonconstrained motions for the system. The level and style of the presentation is intended to be understood by scientifically literate readers with minimal knowledge in mechanics beyond the introductory level. Examples also show how computer algebra can be used to reduce the effort required for treating complex systems. An annotated reference list, which includes a discussion of computer software, is also provided.

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