Inverse Problems for Mechanical Systems

This book explores the crucial role of inverse problems across various fields of applied science and technology. By examining physical phenomena governed by mathematical physics, it addresses the challenge of determining unknown parameters and developing non-destructive methods for systems of solid and structural mechanics. It delves into the inherent mathematical complexities of inverse problems and presents innovative strategies for overcoming these issues. Aimed at doctoral students and researchers in civil and mechanical engineering, mathematical physics, and applied mathematics, the book provides a solid theoretical foundation and equips readers with the necessary mathematical and computational tools to tackle diverse inverse problems.

Provides a comprehensive coverage of cutting-edge techniques of inverse problems in mechanics of solids and structures Examines complex inverse problems with probabilistic and deep learning-based methods Integrates theoretical frameworks, mathematical tools and computational strategies

Autorentext

Alexandre Kawano earned a PhD in Engineering from Yokohama National University, Japan, and a PhD in Applied Mathematics from the Institute of Mathematics and Statistics at University of São Paulo, Brazil. He serves as associate professor at the Department of Mechatronics Engineering at USP. His research interests focus on Mathematical Inverse Problems applied to structural engineering. In particular, he is concerned with inverse problems involving combination of structural elements such as rods, beams and plates.

Antonino Morassi is full professor of Mechanics of Solids and Structures at the University of Udine, Italy. He serves as associate editor of the Journal of Vibration and Control. His most recent research interests concern the modelling of complex vibrating systems, such as nanobeams and spider orb-webs, and the identification of their mechanical properties by dynamic non-destructive measurements.

Inhalt

Eigenvalue Assignment by the Receptance Method: Structural Modification and Active Control.- Model Updating: Sensitivity Method and Bayesian Inference.- Diffusion Models in Mechanics.- Generalized Functions and Their Applications to Direct and Inverse Vibration Problems.- Inverse Problems in Imaging Using Resonant Contrast Agents.- Almost Periodic Distributions and the Spherical Mean Method to Solve Inverse Source Problems.- Inverse Problems for Nanostructures.