Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields : Regular and Chaotic Dynamics of Micro/Nano Beams, and Cylindrical Panels

This book is devoted to researchers and teachers, as well as graduate students, undergraduates and bachelors in engineering mechanics, nano-mechanics, nanomaterials, nanostructures and applied mathematics. It presents a collection of the latest developments in the field of nonlinear (chaotic) dynamics of mass distributed-parameter nanomechanical structures, providing a rigorous and comprehensive study of modeling nonlinear phenomena. It is written in a unique pedagogical style particularly suitable for independent study and self-education. In addition, the book achieves a good balance between Western and Eastern extensive studies of the mathematical problems of nonlinear vibrations of structural members. Front Matter ....Pages i-xxi Nanostructural Members in Various Fields: A Literature Review (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 1-23 Size-Dependent Theories of Beams, Plates and Shells (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 25-78 Lyapunov Exponents and Methods of Their Analysis (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 79-91 Reliability of Chaotic Vibrations of Euler-Bernoulli Beams with Clearance (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 93-112 Analysis of Simple Nonlinear Dynamical Systems (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 113-129 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 131-195 Mathematical Models of Functionally Graded Beams in Temperature Field (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 197-294 Thermoelastic Vibrations of Timoshenko Microbeams (Modified Couple Stress Theory) (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 295-332 Vibrations of Size-Dependent Beams Under Topologic Optimization and Temperature Field (Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko)....Pages 333-402