Nonlinear targeted energy transfer in mechanical and structural systems

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Nonlinear targeted energy transfer in mechanical and structural systems

A.F. Vakakis ... [et al.]

（Solid mechanics and its applications, v. 156）

Springer, c2008

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内容説明・目次

内容説明

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, where it can be captured and dis- pated, provides a powerful strategy for vibration control and the opens the pos- bility for a wide range of applications of TET, such as, vibration and shock i- lation, passive energy harvesting, aeroelastic instability (?utter) suppression, se- mic mitigation, vortex shedding control, enhanced reliability designs (for ex- ple in power grids) and others. The monograph is intended to provide a thorough explanation of the analytical, computational and experimental methods needed to formulate and study TET in mechanical and structural systems. Several prac- cal engineering applications are examined in detail, and experimental veri?cation and validation of the theoretical predictions are provided as well. The authors also suggest a number of possible future applications where application of TET seems promising. The authors are indebted to a number of sponsoring agencies.

目次

  • 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

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