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 resu

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape centsn, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape centsn. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1

The papers in this volume address advanced nonlinear topics in the general areas of vibration mitigation and system identification, such as, methods of analysis of strongly nonlinear dyanmical systems; techniques and methodologies for interpreting complex, multi-frequency transitions in damped nonlinear responses; new approaches for passive vibration mitigation based on nonlinear targeted energy transfer (TET) and the associated concept of nonlinear energy sink (NES); and an overview and assessment of current nonlinear system identification techniques.

This research monograph provides a brief overview of the authors' research in the area of ordered granular media over the last decade. The exposition covers one-dimensional homogeneous and dimer chains in great detail incorporating novel analytical tools and experimental results supporting the analytical and numerical studies. The proposed analytical tools have since been successfully implemented in studying two-dimensional dimers, granular dimers on on-site perturbations, solitary waves in Toda lattices to name a few. The second part of the monograph dwells on weakly coupled homogeneous granular chains from analytical, numerical and experimental perspective exploring the interesting phenomenon of Landau-Zener tunneling in granular media. The final part of the monograph provides a brief introduction to locally resonant acoustic metamaterials incorporating internal rotators and the resulting energy channeling mechanism in unit-cells and in one- and two-dimensional lattices. The monograph provides a comprehensive overview of the research in this interesting domain. However, this exposition is not all exhaustive with regard to equally exciting research by other researchers across the globe, but we provide an exhaustive list of references for the interested readers to further explore in this direction.

The papers in this volume address advanced nonlinear topics in the general areas of vibration mitigation and system identification, such as, methods of analysis of strongly nonlinear dyanmical systems; techniques and methodologies for interpreting complex, multi-frequency transitions in damped nonlinear responses; new approaches for passive vibration mitigation based on nonlinear targeted energy transfer (TET) and the associated concept of nonlinear energy sink (NES); and an overview and assessment of current nonlinear system identification techniques.

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape centsn, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape centsn. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1

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 resu