Name: finding forces with virtual work in linked bodies
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 6 s
Channel: JoVE

Le principe du travail virtuel peut être appliqué à des machines avec plusieurs corps rigides connectés sous charges pour résoudre les problèmes qui y sont liés.
Considérons un étau à genouillère, où une force est appliquée à son point médian, ce qui entraîne une force de réaction exercée par le bloc de bois sur l’étau.
Dans le diagramme à corps libre, le frottement est négligé et un déplacement virtuel positif est considéré.
Choisissez un système d’axes de coordonnées et définissez les incréments positifs et négatifs.
Les forces de réaction au point gauche et la force normale ne fonctionnent pas pendant ce déplacement.
Par conséquent, seul le travail virtuel effectué par les forces appliquées et de réaction doit être calculé.
En exprimant les coordonnées en fonction de l’angle thêta et en les dérivant, le travail virtuel total des deux forces peut être déterminé.
En mettant l’ensemble du travail virtuel à zéro, on obtient l’équation de la force de réaction exercée par le bloc de bois sur l’étau.

<ol>
	<li>Hibbeler, R.C. (2016). Mécanique du génie : Statique. Quatorzième édition, New Jersey : Pearson. Section 11.1, p. 586 et 587.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. et Self, B.P. (2016). Mécanique vectorielle pour les ingénieurs. Onzième édition, New York : McGraw-Hill Education. p. 578 et 579.</li>
</ol>

travail virtuel pour un système de corps rigides connectés

Le travail virtuel est une méthode puissante utilisée pour résoudre des problèmes impliquant plusieurs corps rigides connectés. Lorsque le système est à l'équilibre, le travail virtuel est nul. Cela permet le calcul des forces résultantes lorsque le système subit un déplacement virtuel. Lorsque l'on tente d'analyser un tel système, il faut d'abord utiliser un diagramme des corps libres, où une coordonnée indépendante représente la configuration des liens, et marquer sa position défléchie résultant du déplacement virtuel positif. Ensuite, mesurer les coordonnées de position à partir d'un point fixe sur le diagramme des corps libres et les diriger vers les forces qui effectuent le travail. Cela permet d'exprimer chaque déplacement virtuel en fonction de la coordonnée indépendante. La prochaine étape consiste à écrire l'équation du travail virtuel, ce qui facilite la détermination des forces et des moments résultants. Il est également important de noter ici que si une force ou un couple agit dans la direction du déplacement virtuel positif, alors leur travail est déterminé comme un travail virtuel positif ; sinon, c'est un travail virtuel négatif. Le principal avantage de l'utilisation de cette méthode est qu'elle peut être utilisée pour résoudre des problèmes impliquant un système de plusieurs corps rigides connectés. Chacun de ces systèmes est dit avoir un seul degré de liberté car l'arrangement des liens peut être entièrement spécifié en n'utilisant qu'une seule coordonnée. Cela simplifie considérablement les calculs complexes et permet de mieux comprendre comment différentes variables sont liées les unes aux autres dans des systèmes complexes. En fin de compte, l'évaluation analytique des problèmes d'équilibre impliquant plusieurs corps rigides connectés peut être effectuée efficacement avec le travail virtuel, permettant non seulement des réponses précises mais aussi une meilleure compréhension de leur fonctionnement interne.

Travail virtuel pour un système de corps rigides connectés

Le travail virtuel est une méthode puissante utilisée pour résoudre des problèmes impliquant plusieurs corps rigides connectés. Lorsque le système est en équilibre, le travail virtuel est ...

virtual-work-for-a-system-of-connected-rigid-bodies

Education

Enseignement

JoVE Core

Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Virtual Work

Travail virtuel

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Virtual Work for a System of Connected Rigid Bodies

finding forces with virtual work in linked bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero.

To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin.

Next, measure position coordinates from a fixed point on the diagram. Direct those coordinates toward the forces that do work. This lets each virtual displacement be written in terms of the independent coordinate. After that, write the virtual work equation to determine the resulting forces and moments.

The sign of the work depends on the direction of motion. If a force or couple moment acts along the positive virtual displacement, the work is positive. If it acts opposite that direction, the work is negative.

This method is especially helpful for systems with several connected rigid bodies because they often have only one degree of freedom. That means the full link arrangement can be described by one coordinate. Virtual work simplifies the calculations and also shows how the variables in the system are related.

Finding Forces with Virtual Work in Linked Bodies

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virtual work

Virtual Work in Force Equilibrium

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virtual work for a system of connected rigid bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

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Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

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Conservative Forces and Path-Independent Work

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key terms and concepts

Learn how virtual work is used with connected rigid bodies to find forces and moments using a free-body diagram, one coordinate, and equilibrium.

Finding Forces with Virtual Work in Linked Bodies | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Finding Forces with Virtual Work in Linked Bodies

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