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Normal Modes and Localization in Nonlinear Systems
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 wit...
Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems
This monograph evolved over a period of nine years from a series of papers and presentations addressing the subject of passive vibration control of mechanical s- tems subjected to broadband, transient inputs. The unifying theme is Targeted - ergy Transfer – TET, which represents a new and unique approach to the passive control problem, in which a strongly nonlinear, fully passive, local attachment, the Nonlinear Energy Sink – NES, is employed to drastically alter the dynamics of the primary system to which it is attached. The intrinsic capacity of the properly - signed NES to promote rapid localization of externally applied (narrowband) - bration or (broadband) shock energy to itself, wh...
Advanced Nonlinear Strategies for Vibration Mitigation and System Identification
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.
Proceedings of the Third World Conference on Structural Control
Organized by the International Association for Structural Control(IASC), and sponsored by the European Association for the Controlof Structures (EACS), the recent world conference on structuralcontrol (3WCSC) brought together engineers, scientists, architects,builders and other practitioners interested in the general fieldsof active, hybrid and passive vibration control, health monitoringand damage detection, intelligent/smart materials and systems.Applications included buildings, bridges, space structures andcivil infrastructures under the action of dynamic environments(earthquake, wind, traffic...) and man-made loads. It provideda valuable forum for the discussion of the most pressing conc...
Nonlinear Dynamics of Continuous Elastic Systems
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.
Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media
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 phenome...
The Mechanics of Jointed Structures
This book introduces the challenges inherent in jointed structures and guides researchers to the still-open, pressing challenges that need to be solved to advance this critical field. The authors cover multiple facets of interfacial mechanics that pertain to jointed structures: tribological modeling and measurements of the interface surfaces, constitutive modeling of joints, numerical reduction techniques for structures with joints, and uncertainty quantification and propagation for these structures. Thus, the key subspecialties addressed are model reduction for nonlinear systems, uncertainty quantification, constitutive modeling of joints, and measurements of interfacial mechanics propertie...
Wave Propagation in Linear and Nonlinear Periodic Media
Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media. The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.
Nonlinear Dynamics, Volume 1
Nonlinear Dynamics, Volume 1. Proceedings of the 33rd IMAC, A Conference and Exposition on Balancing Simulation and Testing, 2015, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Oscillations Nonlinear Simulation Using Harmonic Balance Nonlinear Modal Analysis Nonlinear System Identification Nonlinear Modeling & Simulation Nonlinearity in Practice Nonlinear Systems Round Robin on Nonlinear System Identification.
