Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses.
This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems.
Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinearities introduced by pendulum motion may change the system dynamics, and entail a rapid increase of the oscillations of both the structure and the pendulum, leading to full pendulum rotation or chaotic dynamics. To magnetorheological damping is proposed.
Nonlinear mechanics has to be used to explain undesired response in slender footbridges, such as that occurred in the famous event of the London Millenium Bridge. The observed phenomena can be explained by an analytical nonlinear discrete-time model.
Shape memory alloys (SMAs) exhibit very interesting nonlinear thermo-mechanical properties such as shape memory effect and superelasticity. SMA elements integrated within composite beams or plates can be used for active modification of structure properties e.g. by affecting their natural frequencies.
Finite amplitude, resonant, forced dynamics of sagged, horizontal or inclined, elastic cables have recently undergone meaningful research advances concerned with modelling, analysis, response, and nonlinear/nonregular phenomena. A variety of features of nonlinear multimodal interaction in different resonance conditions are comparatively addressed.
Non-smooth systems are very common in engineering practice. Three mechanical engineering problems are presented: (i) a vibro-impact system in the form of a moling device, (ii) the influence of the opening and closing of a fatigue crack on the host system dynamics, and (iii) nonlinear interactions between a rotor and snubber ring system.
This book is aimed at a wide audience of engineers and researchers working in the field of nonlinear structural vibrations and dynamics, and undergraduate and postgraduate students reading mechanical, aerospace and civil engineering.
Autoparametric Vibrations of a Nonlinear System with a Pendulum and Magnetorheological Damping, by Jerzy Warminski and Krzysztof Kecik: Introduction to Autoparametric Vibrations. - Model of the Nonlinear Oscillator with an Attached Pendulum. - Approximate Analytical Solutions and Their Stability. - Regular and Chaotic Dynamics Near the Main Parametric Resonance. - Experimental Setup of the System with Active MR Damper. - Dynamics of an Autoparametric System with MR Damper. - Influence of a Nonlinear System’s Suspension on the InstabilityRegions. - Conclusions and Remarks. - References. - On the Dynamics of Pedestrians-Induced Lateral Vibrations of Footbridges, by Stefano Lenci and Laura Marcheggiani: Introduction and Literature Review. - A Continuous-Time Model: the SAMEO Model. - A Discrete-Time Model. - Conclusions. - References. - Applications for Shape Memory Alloys in Structural and Machine Dynamics, by Matthew P. Cartmell, Arkadiusz J. Z˙ ak and Olga A. Ganilova: Review of the Literature and Introduction. - Modelling of the Shape Memory Effect. - Dynamics of Composite Beams and Plates with Integrated SMA Elements. - Applications to Flexible Rotors. - Antagonistic Actuation Control of Vibration in Plates. - Conclusions. - References. - Theoretical and Experimental Nonlinear Vibrations of Sagged Elastic Cables, by Giuseppe Rega: Introduction. - Cable Modelling and Theoretical Analysis. - Nonlinear Phenomena in Forced Dynamic Response. - Experimental Characterisation of Cable Nonlinear Dynamics. - Further Developments and Research Topics. - References. - Engineering Applications of Non-Smooth Dynamics, by Marian Wiercigroch and Ekaterina Pavlovskaia Non-Smooth Dynamical Systems in Engineering Dynamics. - Drifting Oscillator as an Effective Model of Vibro-Impact Moling. - Nonlinear Dynamics Caused by Fatigue Crack Growth. - Regular and Chaotic Dynamics of a Rotor System with a Bearing Clearance. - Conclusions. - References.