Static and dynamic aspects of the principle of virtual work

IF 1.9 3区工程技术 Q3 MECHANICS Meccanica Pub Date : 2024-10-30 DOI:10.1007/s11012-024-01897-w

Elżbieta Jarzębowska, Wiesław Grzesikiewicz, Michał Makowski, Artur Zbiciak, Katarzyna Rutczyńska-Wdowiak

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Abstract

The paper presents a detailed analysis of the principle of virtual work in its statics and dynamics aspects. Special attention is paid to not exact formulation and interpretation of mechanical system motion equations based upon this principle, what is presented quite often in text books. The general form of the principle of virtual work and variational formulations of the problems in statics are presented and analyzed. Additionally, the dynamic implications of the principle of virtual work and dynamics problem formulation of a system subjected to scleronomic constraints are detailed. The basis for the formulation is the dynamic implication of the principle of virtual work that specifies the relation between the constraint reactions and the body accelerations. This relation takes the form of the variation inequality. As the result, the Gauss principle which determines the body acceleration vector is presented. Furthermore, a description of impact formulation, based upon the Carnot model, caused by the constraints is provided. The theoretical development is illustrated with examples of applications of the principle of virtual work.

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静态和动态方面的虚功原理

本文从静力学和动力学两个方面详细分析了虚功原理。特别注意的是基于这一原理的机械系统运动方程的不精确公式和解释，这在教科书中经常出现。给出并分析了虚功原理的一般形式和静力学问题的变分形式。此外，还详细介绍了虚功原理的动力学含义以及受刚性约束的系统的动力学问题的表述。该公式的基础是虚功原理的动力学含义，该原理规定了约束反应与物体加速度之间的关系。这种关系表现为变差不等式的形式。在此基础上，提出了确定物体加速度矢量的高斯原理。此外，还提供了基于卡诺模型的由约束引起的影响公式的描述。用虚功原理的应用实例说明了理论的发展。

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来源期刊

Meccanica 物理-力学

CiteScore

4.70

自引率

3.70%

发文量

151

审稿时长

7 months

期刊介绍： Meccanica focuses on the methodological framework shared by mechanical scientists when addressing theoretical or applied problems. Original papers address various aspects of mechanical and mathematical modeling, of solution, as well as of analysis of system behavior. The journal explores fundamental and applications issues in established areas of mechanics research as well as in emerging fields; contemporary research on general mechanics, solid and structural mechanics, fluid mechanics, and mechanics of machines; interdisciplinary fields between mechanics and other mathematical and engineering sciences; interaction of mechanics with dynamical systems, advanced materials, control and computation; electromechanics; biomechanics. Articles include full length papers; topical overviews; brief notes; discussions and comments on published papers; book reviews; and an international calendar of conferences. Meccanica, the official journal of the Italian Association of Theoretical and Applied Mechanics, was established in 1966.