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.

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This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different materials with diverse dynamical characteristics and complicated boundary conditions. New theoretical and numerical approaches for analyzing the dynamics of such continua are presented, such as the method of added masses and the method of proper orthogonal decomposition. The presented hybrid approach leads to results that cannot be obtained by other standard theories in the field. The demonstrated methods are illustrated by numerous examples of application.

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