Nonlinear Dynamics of Continuous Elastic Systems

There are many monographs in the existing literature devoted to the static and dynamic behavior of plates and shells. Plates and shells are enco- tered often in engineering applications being integralparts of a wide range of constructions such as machines vehicles airplanes rockets ships bridges buildings and containers to name a few. In addition to the usual requi- ments posedby engineersrelatedtolightweightness su?cientrigidityor?- ibility and robust stability properties there is an additional class ofapriori dynamicalpropertiesrequiredbymodernengineeringapplicationswheren- homogeneity and non-uniformity of structural components is often the norm incertainapplications. Inaddition strictoperationalrequirementsinmodern engineering applications towards higher speeds lighter construction robust andreliableperformance dictatessmallermarginsoferrorordeviationsfrom prescribed performances in adverse or uncertain forcing environments. This in turn requires the development of new analytical and computational tools capable of addressing challenging and not very well developed topics such as nonlinearities a?ecting the system performance the e?ects of unmodeled dynamics on the stability of operation and the role of uncertainties in the systemparametersonthestructuralresponse. Asaresult thereisanongoing e?ort to address such issues leading to the development of new analytical and computational tools some of which are discussed in this monograph. The monograph follows an approach based on an integrated treatment of analysis and computation. Such a hybrid approach coupled with computer algebra can lead to results that cannot be obtained by other standard th- ries in the eld. We show that in a wide class of problems only a carefully prepared numerical experiment followed by purely mathematical conside- tionscan?nallyleadtothesoughtresults. Thenumerousanalyticalconstr- tions are illustrated by examples of application and computational results.