Plenary Lecture

Non-Linear Dynamics of Interacting Structural Members

Professor J. Awrejcewicz
Department of Automation, Biomechanics and Mechatronics
Lodz University of Technology
Co-Author Professor V. A. Krysko

Abstract: We develop mathematical models of interacting structural members (beams and plates) subject to regular and noisy loads. The governing partial differential equations are reduced to a truncated system of ordinary differential equations. Spatial-temporal chaotic vibrations of a plate and two/three beams coupled only by boundary conditions are studied. Novel transition scenarios from regular to chaotic dynamics of the mentioned deterministic systems are detected, illustrated and discussed. The modifications of classical three scenarios of transition from regular vibrations to deterministic spatial-temporal chaos are proposed and validated. It is shown, among other, how the white noise lowers the threshold for transition into spatial-temporal chaotic dynamics and how it significantly reduces occurrence of periodic vibrations. It is reported that a scenario of transition into chaos of the studied mechanical interacting slender structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts of vibration kinds (control parameter planes). Furthermore, two interesting non-linear phenomena are illustrated and discussed. The first one is associated with increase of the noise intensity, which yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear). The second one deals with a loss of symmetry of the previously symmetric dynamical regime yielded by action of a small symmetrically distributed white noise.

Brief Biography of the Speaker: Graduated from the Lodz University of Technology (TUL) in 1977 (Mechanics) and from the University of Łódź in 1978 (Philosophy), Poland. He became a Full Professor in 1997. Now, he is the chairperson of Department of Automation, Biomechanics and Mechatronics, the head of the 4‐year Ph.D. Course on Mechanics, and the head of the Mechatronics Course at TUL. His research includes: Nonlinear Mechanics (analytical, numerical and experimental methods; structural and lumped mass mechanical systems; thermo‐elasticity; asymptotic methods; dynamics; bifurcation and chaos; numerical methods; non‐smooth and discontinuous systems), Mechatronics and Control (vibrations control; optimization), Biomechanics (modeling of human organs; stability of human gait; experimental and numerical methods). He has served on Editorial Boards of 65 journals, gave 73 seminars at international universities, delivered 55 plenary/keynote talks, attended 310 conferences, and served as a member of scientific committees of over 170 conferences. He spent 10 years abroad carrying out research supported by Fulbright Award for Seniors, University of California, Berkeley, 2001; T. Kosciuszko Foundation Award, University of Illinois, USA, 1999/2000; Research Centre for Advanced Science and Technology, Tokyo University, Japan, 1992; Japan Society for Promotion of Science and Technology, Tokyo University, 1990/1991; Alexander von Humboldt Foundation, University of Braunschweig, Germany, 1987‐1990, 1993; ‘TEMPRA’ Program, 1995, Région Rhône‐Alpes (ENTPE), Valeaux-en-Velin/Lyon; NATO Grant Award, Lyon, 2005; Central European University (Budapest) 2003/2004; Waikato University, Hamilton (New Zealand) 1996/1997. He was a principal investigator of 15 grants of the Committee for Scientific Research (KBN) in Poland, two TEMPRA grants (1995/1996; 2000/2001) and POLONIUM grant (1999/2001). He is a recipient of: Honorary Doctor Awards of the Bielsko-Biała Academy of Arts and Technology and the Częstochowa University of Technology; MAESTRO grant (2012-2016), Poland; Humboldt Research Award for Seniors, Germany, 2011‐2012; MASTER Grant Award, Foundation for Polish Science, 2010‐2012; GOLDEN LAMP Award (PGNiG) in technical sciences, 2006, Poland