HAMILTON'S PRINCIPLE FOR EXTERNAL VISCOUS FLUID–STRUCTURE INTERACTION

• Published in: Journal of sound and vibration Vol. 238; no. 1; pp. 113 - 145
• Main Authors: BENAROYA, H., WEI, T.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 16.11.2000; Elsevier
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Fluid-structure interactions; Equations of motion; Experimental study; Dynamics; External flows; Analytical method; Variational principle; Variational calculus; Fluid models; Hamiltonian mechanics; Modelling; Viscous fluids; Hamilton principle
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2000.3152

Hamilton's principle is extended so as to be able to model external flow–structure interaction. This is accomplished by using Reynold's Transport theorem. In this form Hamilton's principle is hybrid in the sense that it has an analytical part as well as a part that depends on experimentally derived functions. Examples are presented. The discussion on implications and extensions is extensive. In this work, a general theory is developed for the case where the configuration is not prescribed at the end times of the variational principle. This leads to a single governing equation of motion. This limitation can be removed by prescribing the end times, as usually done. This is outlined in the present paper, and will be the subject of a future paper. A detailed discussion is also presented of the experimental work performed in parallel with and in support of the theoretical developments. As a true fluid-structural model, it is necessary to fully couple the dynamics. This has been the foundation of our formulation.