Session: 07-19-01: Symposium on the Anniversary of the Timoshenko-Ehrenfest Beam Model and Other Refined Theories and Vibrations of Continuous Systems

Paper Number: 145739

145739 - Dynamic Modelling of a Controlled Orthotropic Plate: Analytic and Data-Driven Approaches in the Frequency Domain 

This talk is devoted to the mathematical modelling of a vibrating orthotropic plate equipped with a laminated piezosensor, under the influence of a lumped force actuation. We employ the Kirchhoff plate theory to derive the corresponding partial differential equation, assuming free boundary conditions. Analytical solutions for this boundary value problem are explored in the form of series expansions, using products of Krylov functions. Utilizing Galerkin’s method, this mathematical model is transformed into an infinite-dimensional control system characterized by modal coordinates. The transfer function of such a system is explicitly evaluated in the single-input single-output case. The computation of coefficients for finite-dimensional approximate systems is formalized in an algorithm with an arbitrary number of degrees of freedom.

The input-output behavior of truncated finite-dimensional models is compared with the results from the data-driven identification of the transfer function, conducted for the experimental setup at the Department of Engineering “Enzo Ferrari” of the University of Modena and Reggio Emilia. Our numerical study confirms acceptable agreement of the input-output responses for the analytic and data-driven models over the given frequency range.

Presenting Author: Alexander Zuyev Max Planck Institute for Dynamics of Complex Technical Systems

Presenting Author Biography: Alexander Zuyev received his Diploma with Honors in Mathematics from Donetsk National University in 1997 and a PhD degree in 2000 from the Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine (IAMM NASU). He was a postdoctoral researcher at the Abdus Salam International Centre for Theoretical Physics under the aegis of UNESCO and IAEA in Trieste and received the Alexander von Humboldt Research Fellowship at TU Ilmenau and the University of Stuttgart. Since his habilitation in 2008, he has been working as a Leading Researcher and Head of the Department of Applied Mechanics of IAMM NASU. In 2021, Prof. Zuyev was elected as a Corresponding Member of the National Academy of Sciences of Ukraine. Alexander Zuyev is currently a Senior Scientist at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Germany.

Authors:

Alexander Zuyev Max Planck Institute for Dynamics of Complex Technical Systems
Francesco Pellicano Università di Modena e Reggio Emilia
Antonio Zippo Università di Modena e Reggio Emilia
Giovanni Iarriccio Università di Modena e Reggio Emilia