Uniqueness in the determination of loads in multi-span beams and plates

Author(s)

Kawano, Alexandre ^[1] ; Morassi, Antonino ^[2]

Affiliation

^[1] Univ Sao Paulo, Escola Politecn, Sao Paulo - Brazil

^[2] Univ Udine, Polytech Dept Engn & Architecture, Udine - Italy

• Document type: Journal article
• Source: EUROPEAN JOURNAL OF APPLIED MATHEMATICS; v. 30, n. 1, p. 176-195, FEB 2019.
• Web of Science Citations: 0

Abstract

Most of the results available on the inverse problem of determining loads acting on elastic beams or plates under transverse vibration refer to single beam or single plate. In this paper, we consider the determination of sources in multi-span systems obtained by connecting either two Euler-Bernoulli elastic beams or two rectangular Kirchhoff-Love elastic plates. The material of the structure is assumed to be homogeneous and isotropic. The transverse load is of the form g(t)f(x), where g(t) is a known function of time and f(x) is the unknown term depending on the position variable x. Under slight a priori assumptions, we prove a uniqueness result for f(x) in terms of observations of the dynamic response taken at interior points of the structure in an arbitrary small interval of time. A numerical implementation of the method is included to show the possible application of the results in the practical identification of the source term. (AU)

• FAPESP's process: 17/07189-2 - Dynamic behavior of spider orb-webs and related inverse problems
• Grantee: Alexandre Kawano
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 17/06452-1 - Uniqueness in the identification of sources in spider webs, Euler-Bernoulli continuous beams and in Germain-Lagrange plates
• Grantee: Alexandre Kawano
• Support Opportunities: Regular Research Grants