Wave propagation of structures solved by reduced models through Lie symmetries

• Grant number: 18/21734-6
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: January 07, 2019
• End date: February 24, 2019
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: Samuel da Silva
• Grantee: Afonso Willian Nunes
• Supervisor: Jean-Mathieu Mencik
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil
• Institution abroad: Institut National des Sciences Appliquées Centre Val de Loire, Blois (INSA Centre Val de Loire), France
• Associated to the scholarship: 16/22473-6 - Applications of Lie symmetries in beams theory, BP.IC

Abstract

We propose in this study plan to reduce the order of a two-dimensional (2D) wave propagation problem using hidden invariants identified by Lie symmetries. Once this procedure is performed, the initial boundary value problem of 2D wave propagation is transformed into an equivalent ordinary differential equation (EDO) that can be easily discretized using finite element method. The biggest advantage of this proposal is to obtain low order FEM model in a different and nonconvetional way. The present project intends to investigate different boundaries conditions and geometry to gain some insight into possible future industrial applications, and to propose highly efficient model reduction techniques. (AU)