Nonlinear Dynamic Phenomena in Mechanics

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.

From the reviews:

“Aimed at engineers and researchers in structural vibrations and students in mechanical, aerospace and civil engineering, this book is relatively easy to read for those experienced in applied mathematics. Five multi-author monographs on nonlinear material and dynamic mechanical phenomena are presented. These achieve the objective of informing the audience of treatments to date.” (Angelo Campanella, Noise Control Engineering Journal, Vol. 61 (1), January-February, 2012)

• Lublin University of Technology, Lublin, Poland

  Jerzy Warminski

• Department of Architecture, Buildings and Structures, Polytechnic University of Marche, Ancona, Italy

  Stefano Lenci

• School of Engineering, University of Glasgow, Glasgow, United Kingdom

  Matthew P. Cartmell

• Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Roma, Italy

  Giuseppe Rega

• School of Engineering, Centre for Applied Dynamics Research (CADR) King’s College Research (CADR), University of Aberdeen, Aberdeen, United Kingdom

  Marian Wiercigroch

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