A Variational Principle for the Linear Coupled Thermoelastodynamic Analysis of Mechanism Systems

1984 ◽  
Vol 106 (3) ◽  
pp. 291-296 ◽  
Author(s):  
C. K. Sung ◽  
B. S. Thompson ◽  
J. J. McGrath
Keyword(s):  
Variational Principle ◽  
Thermal Loading ◽  
Equations Of Motion ◽  
Problem Definition ◽  
Connecting Rod ◽  
Thermoelastic Response ◽  
Flexible Mechanism ◽  
Anisotropic Elastic ◽  
Definition Of ◽  
Approximate Equations

A variational principle is presented which provides the basis for developing the equations governing the coupled thermoelastic response of planar flexible mechanism systems subjected to both mechanical and thermal loading. These systems are modeled as chains of continua with anisotropic elastic constitutive equations. By permitting arbitrary independent variations of the system parameters for each link, approximate equations of motion and boundary conditions may be systematically constructed. As an illustrative example, the derivation of the problem definition of a flexible connecting rod of a slider crank mechanism subjected to thermal shock is presented.

A Variational Principle for the Elastodynamic Motion of Planar Linkages

1976 ◽  
Vol 98 (4) ◽  
pp. 1306-1312 ◽  
Author(s):  
B. S. Thompson ◽  
A. D. S. Barr
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Problem Definition ◽  
Compatibility Conditions ◽  
Elastic Deformations ◽  
Rigid Body Motions ◽  
Planar Linkages ◽  
Crank Mechanism ◽  
Approximate Equations ◽  
Motion Boundary

A variational principle is presented that may be used for setting up the equations describing the elastodynamic motion of planar linkages in which all the members are considered to be flexible. These systems are modeled as a set of continua in which elastic deformations are superimposed on gross rigid-body motions. Displacement continuity at pin joints, or any other special constraints that are peculiar to the linkage being analyzed, are incorporated by the use of Lagrange multipliers. By permitting independent variations of the stress, strain, displacement, and velocity parameters for each link approximate equations of motion, boundary and compatibility conditions for the complete mechanism may be systematically constructed. As an illustrative example, the derivation of the problem definition for a flexible slider-crank mechanism is given.

A Variational Principle for the Hygrothermoelastodynamic Analysis of Mechanism Systems

1987 ◽  
Vol 109 (3) ◽  
pp. 294-300 ◽  
Author(s):  
C. K. Sung ◽  
B. S. Thompson
Keyword(s):  
High Speed ◽  
High Performance ◽  
Fibrous Composite ◽  
Equations Of Motion ◽  
Problem Definition ◽  
Theoretical Development ◽  
Connecting Rod ◽  
Rigid Body Motions ◽  
Crank Mechanism ◽  
Approximate Equations

A variational theorem is presented that may be employed for systematically establishing the equations governing the dynamic response of flexible planar linkage mechanisms simultaneously subjected to both mechanical and hygrothermal loadings. This theoretical development is motivated by recent research advocating that high-speed mechanisms should be fabricated in polymeric fibrous composite materials in order to achieve high-performance characteristics. The constitutive behavior of some of these materials is, however, dependent upon the ambient environmental conditions, and hence mathematical models must be developed in order to predict the response of mechanism systems fabricated with these materials. This class of mechanism systems is modeled herein as a set of continua in which elastic deformations are superimposed upon gross rigid-body motions. By permitting arbitrary independent variations of the system parameters for each link, approximate equations of motion, energy balance, mass balance, and boundary conditions may be systematically constructed. As an illustrative example, the derivation of a problem definition for the flexible connecting-rod of a slider-crank mechanism subjected to hygrothermal loading is presented.

Modal Loss Factor Predication in Flexible Mechanism Systems With Constrain Viscoelastic Layers

1998 ◽  
Author(s):  
Zhang Xianmin ◽  
Liu Jike
Keyword(s):  
Equations Of Motion ◽  
Sandwich Beam ◽  
Viscoelastic Layer ◽  
Treatment Technique ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Frame Element ◽  
Modal Damping ◽  
Flexible Mechanism ◽  
Viscoelastic Layers

Abstract Control of dynamic vibration is critical to the operational success of many flexible mechanism systems. This paper addresses the problem of vibration control of such mechanisms through passive damping, using constrained layer damping treatment technique. A new type of shape function for three layer frame element containing a viscoelastic layer is developed. The equations of motion of the damped flexible mechanism are derived. Modal loss factors of this kind mechanisms are predicated from undamped normal mode by means of the modal strain energy method. Comparisons between the results obtained by this paper and the results obtained by exact solution of the governing equations for a well known sandwich beam demonstrate that the method presented in this paper is correct and reliable. Application of this method in predication of modal damping ratios for damped mechanisms is discussed. It is believed that the method of this paper hold the greatest potential for optimal design of damped flexible mechanism systems.

Calculation and study of the failure of the connecting-rod small end based on thermoelastic plasticity

2016 ◽  
Vol 231 (11) ◽  
pp. 1489-1499
Author(s):  
Guohua Chen ◽  
Ridong Liao ◽  
Xue Jiang
Keyword(s):  
Contact Force ◽  
Wall Thickness ◽  
Loading Condition ◽  
Thermal Loading ◽  
Operating Temperature ◽  
Thermomechanical Coupling ◽  
Plasticity Model ◽  
High Power Density ◽  
Connecting Rod ◽  
Interference Fit

In this study, the mechanisms that cause bush loosening and rotation failure were studied on the connecting-rod small end of a high-power-density engine. Using the thermoelastic plasticity model and the thermomechanical coupling method, the stress field and the assembly contact force of the connecting-rod small end were predicted by considering four different loading conditions: first, the initial loading condition; second, the thermal loading condition; third, the mechanical loading condition; fourth, the unloading condition. This process showed the effects of the initial interference fit, the operating temperature and the wall thickness of the bush on the assembly contact force. It was found that, first, a large interference leads to a small assembly contact force after unloading, second, a higher operating temperature significantly reduces the assembly contact force and, third, the wall thickness of the bush has little influence on the assembly contact force. In conclusion, a high operating temperature is the main cause of bush loosening and rotation. This conclusion was validated by the experimental results. On the basis of this study, it is suggested that the operating temperature is limited in order to maintain the reliability of the connecting-rod small end.

scholarly journals The effective mass problem for the Landau-Pekar equations

2021 ◽  
Author(s):  
Dario Feliciangeli ◽  
Simone Rademacher ◽  
Robert Seiringer
Keyword(s):  
Variational Principle ◽  
Effective Mass ◽  
Initial Velocity ◽  
Energy Functional ◽  
Mass Problem ◽  
Definition Of

Abstract We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

Dynamical systems: Approximate Lagrangians and Noether symmetries

2019 ◽  
Vol 16 (10) ◽  
pp. 1950160 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Kinetic Energy ◽  
Equations Of Motion ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Second Order Equations

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

On the symplectically invariant variational principle and generating functions

1990 ◽  
Vol 431 (1883) ◽  
pp. 403-417 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Generating Function ◽  
Generating Functions ◽  
Geometric Approach ◽  
Canonical Transformations ◽  
Weyl Transform ◽  
Analogous Relation ◽  
Definition Of ◽  
Symplectic Invariance

The generating function for canonical transformations derived by Marinov has the important property of symplectic invariance (i. e. under linear canonical transformations). However, a more geometric approach to the rederivation of this function from the variational principle reveals that it is not free from caustic singularities after all. These singularities can be avoided without breaking the symplectic invariance by the definition of a complementary generating function bearing an analogous relation to the Woodward ambiguity function in telecommunications theory as that tying Marinov’s function to the Wigner function and the Weyl transform in quantum mechanics. Marinov’s function is specially apt to describe canonical transformations close to the identity, but breaks down for reflections through a point in phase space, easily described by the new generating function.

A Reverse Glue Approach to Automated Construction of Multi-Piece Molds

2003 ◽  
Author(s):  
Yong Chen ◽  
David W. Rosen
Keyword(s):  
Design Process ◽  
Problem Definition ◽  
Mold Cavity ◽  
Mold Design ◽  
Difficult Time ◽  
Construction Step ◽  
Efficiency And Effectiveness ◽  
Definition Of ◽  
Face Generation ◽  
Construction Algorithms

Mold design can be a difficult, time-consuming process. Determining how to split a mold cavity into multiple mold pieces (e.g., core, cavity) manually can be a tedious process. This paper focuses on the mold construction step of the automated mold design process. By investigating glue operations and its relations with parting faces, an approach based on reverse glue operation is presented. The key of the reverse glue operation is to generate parting faces. A problem definition of parting face generation for a region is provided. Correspondingly, three face generating criteria are identified. Based on the parting lines of a region, our algorithms to generate the parting faces are presented. Our mold construction algorithms for two-piece molds and multi-piece molds are also presented with brief discussions. Some industrial examples are provided which illustrate the efficiency and effectiveness of our approach. We tested our mold designs by fabricating stereolithography mold inserts (a rapid tooling method) and molding parts.

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