Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems 2 Volume Set

ISBN-13: 9789401776479 / Angielski / Miękka / 2016 / 1030 str.

Alexander F. Vakakis; Oleg V. Gendelman; Lawrence A. Bergman

Recenzje

From the reviews:

 “Two volumes of this monograph present an original approach to the problems of passive vibration control of dissipative mechanical and structural systems subjected to broadband transient inputs, including topics of targeted energy transfer (TET) and nonlinear energy sink (NES). … This monograph is intended for scientists and mechanical and civil engineers who have a general knowledge of analytical dynamics and ordinary and partial differential equations, as well as integro-differential equations.” (Jerzy Gawinecki, Zentralblatt MATH, Vol. 1170, 2009)

“This two-volume monograph addresses the problem of passive vibration control of mechanical systems in which a strongly nonlinear, passive, local attachment is used as a damper. The aim is to provide an in-depth explanation of the analytical, computational, and experimental techniques required to study targeted energy transfer. The applicability of the techniques to a wide range of areas is demonstrated. The intended audience is researchers and engineers interested in one-way energy transfer.” (IEEE Control Systems Magazine, Vol. 30, April, 2010)

Spis treści

Volume I: Preface; Abbreviations; 1 Introduction; 2 Preliminary Concepts, Methodologies and Techniques ; 2.1 Nonlinear Normal Modes (NNMs); 2.2 Energy Localization in Nonlinear Systems; 2.3 Internal Resonances, Transient and Sustained Resonance Captures; 2.4 Averaging, Multiple Scales and Complexification; 2.5 Methods of Advanced Signal Processing ; 2.5.1 NumericalWavelet Transforms; 2.5.2 Empirical Mode Decompositions and Hilbert Transforms ; 2.6 Perspectives on Hardware Development and Experiments ; 3 Nonlinear Targeted Energy Transfer in Discrete Linear Oscillators with Single-DOF Nonlinear Energy Sinks; 3.1 Configurations of Single-DOF NESs; 3.2 Numerical Evidence of TET in a SDOF Linear Oscillator with a SDOF NES ; 3.3 SDOF Linear Oscillators with SDOF NESs: Dynamics of the Underlying Hamiltonian Systems; 3.3.1 Numerical Study of Periodic Orbits (NNMs); 3.3.2 Analytic Study of Periodic Orbits (NNMs) ; 3.3.3 Numerical Study of Periodic Impulsive Orbits (IOs); 3.3.4 Analytic Study of Periodic and Quasi-Periodic IOs; 3.3.5 Topological Features of the Hamiltonian Dynamics ; 3.4 SDOF Linear Oscillators with SDOF NESs: Transient Dynamics of the Damped Systems; 3.4.1 Nonlinear Damped Transitions Represented in the FEP; 3.4.2 Dynamics of TET in the Damped System; 3.5 Multi-DOF (MDOF) Linear Oscillators with SDOF NESs: Resonance Capture Cascades and Multi-frequency TET ; 3.5.1 Two-DOF Linear Oscillator with a SDOF NES; 3.5.2 Semi-Infinite Chain of Linear Oscillators with an End SDOF NES ; 4 Targeted Energy Transfer in Discrete Linear Oscillators with Multi-DOF NESs; 4.1 Multi-Degree-of-Freedom(MDOF) NESs; 4.1.1 An AlternativeWay for Passive Multi-frequency Nonlinear Energy Transfers ; 4.1.2 Numerical Evidence of TET in MDOF NESs; 4.2 The Dynamics of the Underlying Hamiltonian System; 4.2.1 System I: NES with O(1) Mass ; 4.2.2 System II: NES with O(e) Mass ; 4.2.3 Asymptotic Analysis of Nonlinear Resonant Orbits ; 4.2.4 Analysis of Resonant Periodic Orbits ; 4.3 TRCs and TET in the Damped and Forced System; 4.3.1 Numerical Wavelet Transforms; 4.3.2 Damped Transitions on the Hamiltonian FEP; 4.4 Concluding Remarksl Index. Volume 2: 5 Targeted Energy Transfer in Linear Continuous Systems with Singlean Multi-DOF NESs; 5.1 Beam of Finite Length with SDOF NES; 5.1.1 Formulation of the Problem and Computational Procedure ; 5.1.2 Parametric Study of TET ; 5.2 Rod of Finite Length with SDOF NES ; 5.2.1 Formulation of the Problem, Computational Procedure and Post-Processing Algorithms ; 5.2.2 Computational Study of TET ; 5.2.3 Damped Transitions on the Hamiltonian FEP; 5.3 Rod of Semi-Infinite Length with SDOF NES; 5.3.1 Reduction to Integro-differential Form; 5.3.2 Numerical Study of Damped Transitions; 5.3.3 Analytical Study; 5.4 Rod of Finite Length with MDOF NES; 5.4.1 Formulation of the Problem and FEPs ; 5.4.2 Computational Study of TET ; 5.4.3 Multi-Modal Damped Transitions and Multi-Scale Analysis;5.5 Plate with SDOF and MDOF NESs; 5.5.1 Case of a SDOF NES; 5.5.2 Case of Multiple SDOF NESs ; 5.5.3 Case of a MDOF NES; 5.5.4 Comparative Study with Linear Tuned Mass Damper ; 6 Targeted Energy Transfer in Systems with Periodic Excitations ; 6.1 Steady State Responses and Generic Bifurcations ; 6.1.1 Analysis of Steady State Motions ; 6.1.2 Numerical Verification of the Analytical Results ; 6.2 Strongly Modulated Responses (SMRs); 6.2.1 General Formulation and Invariant Manifold Approach; 6.2.2 Reduction to One-DimensionalMaps and Existence Conditions for SMRs; 6.2.3 Numerical Simulations; 6.3 NESs as Strongly Nonlinear Absorbers for Vibration Isolation; 6.3.1 Co-existent Response Regimes; 6.3.2 Efficiency and Broadband Features of the Vibration Isolation; 6.3.3 Passive Self-tuning Capacity of the NES ; 7 NESs with Non-Smooth Stiffness Characteristics ; 7.1 Systems with Multiple NESs Possessing Clear

Blurb

This monograph is the first in the new area of targeted nonlinear energy transfer in mechanical and structural systems. This concept was initially discovered by the two leading authors in 1999, and was further developed exclusively by the entire author group in the last 6 years. Since then, additional groups of researchers in the USA, Russia, UK and France have started working on this concept and applying it. It is estimated that in the years to come, the concept of targeted nonlinear energy transfer will be considered and applied by numerous groups ofresearchers and practitioners internationally. This monograph presents theoretical methods, computational results and experimental demonstrations of this concept applied to discrete and continuous coupled nonlinear oscillators. Moreover, it demonstrates the wide applicability of targeted nonlinear energy transfer to a wide range of problems, including:
- Vibration and shock isolation in mechanical systems
- Seismic mitigation
- Aeroelastic and structural instability suppression
- Drilling operations
- Packaging devices
This is a groundbreaking and unique volume, providing new design paradigms in a variety of fields.