An Eigenvalue Problem for the Analysis of Variable Topology Mechanical Systems

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
József Kövecses ◽  
Josep M. Font-Llagunes
Keyword(s):  
Eigenvalue Problem ◽  
Momentum Transfer ◽  
Mechanical Systems ◽  
Time Varying ◽  
Topology Change ◽  
Impulsive Constraints ◽  
Variable Topology ◽  
Energy And Momentum

Mechanical systems with time-varying topology appear frequently in natural or human-made artificial systems. The nature of topology transitions is a key characteristic in the functioning of such systems. In this paper, we discuss a concept that can offer possibilities to gain insight and analyze topology transitions. This approach relies on the use of impulsive constraints and a formulation that makes it possible to decouple the dynamics at topology change. A key point is an eigenvalue problem that characterizes several aspects of energy and momentum transfer at the discontinuous topology transition.

Dynamics of Non-Ideal Topology Transitions in Multibody Mechanical Systems

2009 ◽  
Author(s):  
Josep M. Font-Llagunes ◽  
Jo´zsef Ko¨vecses
Keyword(s):  
Kinetic Energy ◽  
Experimental Analysis ◽  
Multibody System ◽  
Mechanical Systems ◽  
Dynamic Equations ◽  
Time Varying ◽  
Topology Change ◽  
Impulsive Constraints ◽  
Topology Changes ◽  
Ideal Topology

Mechanical systems with time-varying topology appear frequently in various applications. In this paper, topology changes that can be modeled by means of bilateral impulsive constraints are analyzed. We present a concept to project kinematic and kinetic quantities to two mutually orthogonal subspaces of the tangent space of the mechanical system. This can be used to obtain decoupled formulations of the kinetic energy and the dynamic equations at topology transition. It will be shown that the configuration of the multibody system at topology change significantly influences the projection of non-ideal forces to both subspaces. Experimental analysis, using a dual-pantograph robotic prototype interacting with a stiff environment, is presented to illustrate the material.

On Length Scales for the Radial Rotating Jet Pressure Exchange Mechanism

2008 ◽  
Author(s):  
Muhammad Umar ◽  
Charles A. Garris
Keyword(s):  
Momentum Transfer ◽  
Near Field ◽  
Exchange Process ◽  
Energy Levels ◽  
Mixing Layer ◽  
Complex Flow ◽  
Transfer Energy ◽  
Length Scales ◽  
Pressure Exchange ◽  
Energy And Momentum

The crypto-steady rotating jet pressure exchange ejector is a novel concept in turbomachinery where two fluids, at different energy levels, come in direct contact with each other to transfer energy and momentum between them through non-steady interface pressure forces. The current paper seeks to provide an insight into the complex flow phenomena occurring inside the radial flow pressure exchange ejector. The primary mechanisms controlling the process are pressure exchange and mixing. This paper will seek to discriminate between energy transfer by each respective mechanism. The energy and momentum transfer in the near field is shown to be mainly due to the pressure exchange process, as the mixing layer does not develop substantially in this region. As the radius increases, the mixing layer tends to grow and the energy and momentum transfer is governed by the mixing process. As a consequence, the length scales of the pressure exchange zone are small, thus making the pressure exchange ejector more compact in size. The paper will delineate between the two length scales. If this new concept is shown to be viable for gas compression at sufficiently high pressure ratios, then, in refrigeration applications, it would enable environmentally benign refrigerants to replace the harmful chlorofluorocarbons (CFC) and reduce the effluence of greenhouse gases. Applications in many other areas, where conventional ejectors are currently used, are also possible.

A Probabilistic Tolerance Allocation Method for Dynamic Mechanical Systems With Periodic Response and Discontinuous Forcing Functions

1995 ◽  
Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha
Keyword(s):  
Combustion Engine ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Optimization Procedure ◽  
Tolerance Allocation ◽  
Radial Clearance ◽  
Time Varying ◽  
Link Length ◽  
Design Variables ◽  
Forcing Functions

Abstract Tolerance allocation standards do not exist for mechanical systems whose response are time varying and are subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine.

Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

2019 ◽  
Vol 29 (09) ◽  
pp. 1930024
Author(s):  
Sergej Čelikovský ◽  
Volodymyr Lynnyk
Keyword(s):  
Stability Region ◽  
Inverted Pendulum ◽  
Chaotic Behavior ◽  
Mechanical Systems ◽  
Small Time ◽  
Time Varying ◽  
External Forcing ◽  
Double Support ◽  
Lateral Dynamics ◽  
Detailed Mathematical Analysis

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this article. The chaotic behavior, when being externally harmonically perturbed, is demonstrated. Two rather exceptional features are analyzed. Firstly, the unperturbed undamped hybrid inverted pendulum behaves inside a certain stability region periodically and its respective frequencies range from zero (close to the boundary of that stability region) to infinity (close to its double support equilibrium). Secondly, the constant lateral forcing less than a certain threshold does not affect the periodic behavior of the hybrid inverted pendulum and preserves its equilibrium at the origin. The latter is due to the hybrid nature of the equilibrium at the origin, which exists only in the Filippov sense. It is actually a trivial example of the so-called pseudo-equilibrium [Kuznetsov et al., 2003]. Nevertheless, such an observation holds only for constant external forcing and even arbitrary small time-varying external forcing may destabilize the origin. As a matter of fact, one can observe many, possibly even infinitely many, distinct chaotic attractors for a single system when the forcing amplitude does not exceed the mentioned threshold. Moreover, some general properties of the hybrid inverted pendulum are characterized through its topological equivalence to the classical pendulum. Extensive numerical experiments demonstrate the chaotic behavior of the harmonically perturbed hybrid inverted pendulum.

Symplectic Analysis of Wrinkles in Elastic Layers With Graded Stiffnesses

2018 ◽  
Vol 86 (1) ◽  
Author(s):  
Jianjun Sui ◽  
Junbo Chen ◽  
Xiaoxiao Zhang ◽  
Guohua Nie ◽  
Teng Zhang
Keyword(s):  
Finite Element ◽  
Hamiltonian System ◽  
Eigenvalue Problem ◽  
Time Variable ◽  
Time Varying ◽  
Thickness Direction ◽  
Varying Coefficients ◽  
Elastic Layers ◽  
Critical Strains ◽  
Graded Structures

Wrinkles in layered neo-Hookean structures were recently formulated as a Hamiltonian system by taking the thickness direction as a pseudo-time variable. This enabled an efficient and accurate numerical method to solve the eigenvalue problem for onset wrinkles. Here, we show that wrinkles in graded elastic layers can also be described as a time-varying Hamiltonian system. The connection between wrinkles and the Hamiltonian system is established through an energy method. Within the Hamiltonian framework, the eigenvalue problem of predicting wrinkles is defined by a series of ordinary differential equations with varying coefficients. By modifying the boundary conditions at the top surface, the eigenvalue problem can be efficiently and accurately solved with numerical solvers of boundary value problems. We demonstrated the accuracy of the symplectic analysis by comparing the theoretically predicted displacement eigenfunctions, critical strains, and wavelengths of wrinkles in two typical graded structures with finite element simulations.

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