On Georg Duffing, some of the equations named after him and associated phenomena

by Prof. Ivana Kovacic (Department of Mechanics, Faculty of Technical Sciences, Novi Sad, Serbia)

Wednesday 15 Dec 2010, 18:00 → 19:00 Europe/Belgrade

301 F (Mathematical Institute)

The classical Duffing Equation is one of the most important equations in the theory of nonlinear dynamics, which models a harmonically excited single-degree-of-freedom oscillator with a linear-plus-cubic restoring force. This equation is named after Georg Duffing, a German engineer, who published a comprehensive book ‘Forced oscillations with variable natural frequency and their technical significance’ in 1918. Since then there has been a tremendous amount of work done on this equation and its various forms, including the development of different methods and the use of these methods to investigate the rich dynamic behaviour and associated phenomena of different and disparate оscillatory systems modelled by them.

The first objective of this lecture is to give a historical background to Duffing’s work and life, as not much is known and published about him. The story behind this is very interesting, because Georg Duffing was not an academic; he was an engineer, who carried out academic work in his spare time. The second objective is to compare and illustrate some of the characteristic nonlinear phenomena, including multi-valued amplitudefrequency response, hysteresis and the occurrence of jumps in the classical Duffing Oscillator and the one that contains pure cubic nonlinearity and is also under the action of a constant force.

The lecture is also to announce the appearance of the book The Duffing Equation: Nonlinear Oscillators and their Behaviour
http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470715499.html
which brings together the results of a wealth of disseminated research literature on the Duffing Equation.

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Klasična Dufingova jednačina, koja modelira kretanje oscilatora sa jednim stepenom slobode, restitucionom silom koja sadrži linearni i kubni geometrijski član i pod dejstvom je harmonijske prinude, predstavlja jednu od najvažnijih jednačina u teoriji nelinearne dinamike. Jednačina je dobila ime po Georgu Dufingu, nemačkom inženjeru, koji je 1918. godine publikovao sadržajnu knjigu „Prinudne oscilacije sa promenljivom sopstvenom frekvencijom i njihov tehnički značaj”. Nakon toga, sprovedeno je obilje istraživanja vezanog za ovu jednačinu i njene oblike, razvijeni su brojni metodi za njihovo rešavanje, kao i ispitivanje dinamičkog ponašanja i fenomena koji se javljaju u različitim oscilatornim sistemima koje one modeluju.

Ovo predavanje ima za cilj da najpre da istorijsku pregled Dufingovog života i rada, s obzirom da o ovome nema mnogo dostupnih informacija. Istorijska pozadina je veoma interesantna, jer Georg Dufing nije imao univerzitetsku karijeru, već je bio inženjer koji je svoja istraživanja sprovodio u slobodno vreme. Osim toga, dodatni cilj predavanja je poređenje i ilustracija nekih nelinearnih fenomena, kao što su amplitudno-frekventne karakteristike sa višestrukim stacionarnim rešenjima, histerezisno ponašanje i pojava skoka amplitude kod klasičnog Dufingovog oscilatora i onog koji ima čisto kubnu nelinearnost i pod dodatnim je dejstvom konstante sile.

Predavanje je i povod da se najavi izlazak monografije "Dufingova jednačina: nelinearni oscilatori i njihovo ponašanje"
http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470715499.html
koja sadrži bogatstvo prikupljenih rezultata koji se tiču Dufingove jednačine.