Linear and Nonlinear Waves in Microstructured Solids: Homogenization and Asymptotic Approaches

ISBN-13: 9780367704131 / Angielski

Igor V. Andrianov; Vladyslav Danishevskyy; Jan Awrejcewicz

Opis

The book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics. Presenting original solutions to common issues, it builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering.

Spis treści

1. Models and Methods of Research of Elastic Waves in Nonlinear and Nonhomogeneous Materials. 2. Waves in Layered Materials: Linear Problems 3. Waves in Fibre Composites: Linear Problems 4. Longitudinal Waves in Layered Composite Material with Account of Physical and Geometrical Nonlinearity 5. Antiplane ShearWaves in Fibre Composite. Structural Nonlinearity 6. Formation of Localized NonlinearWaves in Fibre Composite Material 7. Vibration Localization in 1D Linear and Nonlinear Lattices: Discrete and Continuous Models 8. Spatial Localization of Linear Elastic Waves in Composite Materials With Defects 9. Non-Linear Vibrations of Viscoelastic Heterogeneous Solids of Finite Size: Internal Resonances and Modes Interactions 10. Nonlocal, Gradient and Local Models of Elastic Media: 1D Case 11. Regular and Chaotic Dynamics Based on Continualization and Discretization

O autorze

Igor Andrianov is Professor with 25 years of experience in Mathematics, Applied Mechanics and Mechanics of Solids. Researcher with 41 years of experience in Applied Mathematics and Mechanics of Solids. Supervisor of 18 Ph.D. students. Research interests: Asymptotic Approaches, Nonlinear Dynamics, Composite Materials, Theory of Plates and Shells. Jan Awrejcewicz is a Head of the Department of Automation, Biomechanics and Mechatronics at Lodz University of Technology, Head of Ph.D. School on 'Mechanics' (since 1996) and of graduate/postgraduate programs on Mechatronics (since 2006). He is also recipient of Doctor Honoris Causa (Honorary Professor) of Academy of Arts and Technology (Poland, Bielsko-Biala, 2014) and of Czestochowa University of Technology (Poland, Czestochowa, 2014), Kielce University of Technology (2019), National Technical University "Kharkiv Polytechnic Institute" (2019), and Gdańsk University of Technology (2019). His papers and research cover various disciplines of mechanics, material science, biomechanics, applied mathematics, automation, physics and computer oriented sciences, with main focus on nonlinear processes. Vladyslav V Danishevskyy is Professor at Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine. His research area includes mechanical and physical properties of composite materials, metamaterials and heterogeneous structures; non-linear dynamics; waves in heterogeneous media; asymptotic methods.