Name: virtual work in force equilibrium
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 20 s
Channel: JoVE

考虑一个处于静力平衡状态的物体发生微小的虚位移或虚转动。
虚功等于虚力与位移的乘积。同样地，对于虚转动，所做的功等于力矩与虚角位移的乘积。
虚功原理指出，对于任意虚位移或虚转动，所有力和力矩所做的虚功的代数和为零。
当球发生虚拟的向下位移时，其重力做正的虚功，而法向力做负的虚功。
在平衡条件下，所有虚功的总和必须为零。
类似地，当一个有支撑的梁发生虚转动时，只有两个力做功。
支座处反作用力的分量对虚功没有贡献。
通过考虑沿 y 方向的虚位移，并应用虚功原理，可推导出虚功方程。
括号中的项表示转动平衡状态。

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	<li>希伯勒，RC（2016 年）。工程力学:静力学。第十四版，新泽西州:皮尔逊。第 11.1 节，第 583-584 页。</li>
	<li>Meriam， JL、Kraige， LG 和 Bolton， JN （2016）。工程力学:静力学和动力学。第八版，新加坡:John Wiley & Sons。第 7.2 节，第 394-395 页。</li>
	<li>比尔，FP，约翰斯顿，ER，Mazurek，DF，康威尔，PJ 和塞尔夫，BP（2016 年）。工程师的矢量力学。第十一版，纽约:麦格劳-希尔教育。第 577-578 页。</li>
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虚功原理

虚功原理指出，如果物体处于静态和动态平衡中，则对于任何给定的虚位移，所有的外力和力偶矩所做的所有虚功之和必须为零。 在静态平衡中，一个物体可以经历虚拟的运动，如位移或旋转。虚功等于力和虚拟位移在力的方向上所进行的点积。对于虚拟旋转中的力偶矩，也同样适用相同的原理。虚功旋转由力偶矩和与其相应的虚拟旋转进行相乘来确定。 为了用一个例子来说明这个概念，假设有一个球静止在平坦的表面上。画出它的全身图可以看出，当产生向下的虚位移时，重量会做正虚功，而法向力则会做负虚功。为了达到平衡，所有这些力的总和必须为零，因此可以相应地制定表示该条件的方程。 虚功的概念用来解决与粒子和刚体相关的问题。当分析受到共面力的刚体时，需要三个单独的方程，因为它们会涉及到不同类型的位移：x轴和y轴方向上的平移以及绕垂直于x-y平面的轴所进行的旋转。 总之，虚功是力学中的一个基本概念，它允许工程师和科学家在不进行物理测试的情况下来预测其中的结构和机器的行为。它是一种强大的工具，能够用来分析静态和动态系统的行为，并在工程和科学领域有着广泛的应用。

虚功原理指出，如果一个物体处于静力和动力平衡状态，那么所有外力所做的虚功之和……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Virtual Work

虚功

KEY TERMS AND CONCEPTS

关键术语与概念

virtual work in force equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement.

A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by multiplying the moment by the virtual rotation.

A simple example is a ball on a flat surface. If the ball has a downward virtual displacement, its weight does positive virtual work. The normal force does negative virtual work. The equilibrium condition then gives an equation in which the sum of these virtual works is zero.

Virtual work can be used for both particles and rigid bodies. For rigid bodies under coplanar forces, three equations are needed. They correspond to translation in the x direction, translation in the y direction, and rotation about an axis perpendicular to the x-y plane. Engineers and scientists use this method to study structures and machines without physically testing them.

Virtual Work in Force Equilibrium

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virtual work

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

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Finding Forces with Virtual Work in Linked Bodies

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Conservative Forces and Path-Independent Work

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key terms and concepts

Learn how virtual work helps test equilibrium using imagined displacement, rotation, and force balance in particles and rigid bodies.

Virtual Work in Force Equilibrium | 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

Virtual Work in Force Equilibrium

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