Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems

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ISBN-13:
9781402091308
Einband:
eBook
Seiten:
1030
Autor:
Alexander F. Vakakis
Serie:
156, Solid Mechanics and Its Applications
eBook Typ:
PDF
eBook Format:
eBook
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:

This monograph presents theoretical methods, computational results and experimental demonstrations of this concept applied to discrete and continuous coupled nonlinear oscillators. It demonstrates the wide applicability of targeted nonlinear energy transfer.
"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 of researchers 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: (1) Vibration and shock isolation in mechanical systems; (2) Seismic mitigation; (3) Aeroelastic and structural instability suppression; (4) Drilling operations; (5) Packaging devices.

This is a groundbreaking and unique volume, providing new design paradigms in a variety of fields."
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 Clearance Nonlinearities;7.1.1 Problem Description ; 7.1.2 Numerical Results;7.2 Vibro-Impact (VI) NESs as Shock Absorbers; 7.2.1 Passive TET to VI NESs; 7.2.2 Shock Isolation ; 7.3 SDOF Linear Oscillator with a VI NES;7.3.1 Periodic Orbits for Elastic Vibro-Impacts Represented on the FEP ; 7.3.2 Vibro-Impact Transitions in the Dissipative Case: VI TET ; 8 Experimental Verification of Targeted Energy Transfer; 8.1 TET to Ungrounded SDOF NES (Configuration II); 8.1.1 System Identification ; 8.1.2 Experimental Measurements;8.2 TET to Grounded SDOF NES (Configuration I);8.2.1 Experimental Fixture; 8.2.2 Results and Discussion ; 8.3 Experimental Demonstration of 1:1 TRCs Leading to TET; 8.3.1 Experimental Fixture; 8.3.2 Experimental TRCs ; 8.4 Steady State TET under Harmonic Excitation ; 8.4.1 System Configuration and Theoretical Analysis 8.4.2 Experimental Study ; 9 Suppression of Aeroelastic Instabilities through Passive Targeted Energy Transfer ; 9.1 Suppression of Limit-Cycle Oscillations in the van der Pol Oscillator; 9.1.1 VDP Oscillator and NES Configurations; 9.1.2 Transient Dynamics ; 9.1.3 Steady State Dynamics and Bifurcation Analysis ; 9.1.4 Summary of Results; 9.2 Triggering Mechanism for Aeroelastic Instability of an In-FlowWing ; 9.2.1 The Two-DOF Aeroelastic Model ; 9.2.2 Slow Flow Dynamics; 9.2.3 LCO Triggering Mechanism ;9.2.4 Concluding Remarks; 9.3 Suppressing Aeroelastic Instability of an In-FlowWing Using a SDOF NES ; 9.3.1 Preliminary Numerical Study ;9.3.2 Study of LCO Suppression Mechanisms; 9.3.3 Robustness of LCO Suppression; 9.3.4 Concluding Remarks; 9.4 Experimental Validation of TET-Based, Passive LCO Suppression; 9.4.1 Experimental Apparatus and Procedures; 9.4.2 Results and Discussion; 9.5 Suppressing Aeroelastic Instability of an In-FlowWing Using a MDOF NES ; 9.5.1 Revisiting the SDOF NES Design;9.5.2 Configuration of a Wing with an Attached MDOF NES ; 9.5.3 Robustness of LCO Suppression - Bifurcation Analysis; 9.6 Preliminary Results on LCO Suppression in a Wing in Unsteady Flow; 10 Seismic Mitigation by Targeted Energy Transfer ; 10.1 The Two-DOF Linear Primary System with VI NES; 10.1.1 System Description; 10.1.2 Simulation and Optimization; 10.1.3 Computational Results; 10.2 Scaled Three-Story Steel Frame Structure with NESs; 10.2.1 Characterization of the Three-Story Linear Frame Structure; 10.2.2 Simulation and Optimization of the Frame-Single VI NES System ; 10.2.3 Simulation and Optimization of the Frame-VI NES-Smooth NES System; 10.3 Experimental Verification; 10.3.1 System Incorporating the Single-VI NES; 10.3.2 System Incorporating Both VI and Smooth NESs; 10.4 Observations, Summary and Conclusions; 11 Suppression of Instabilities in Drilling Operations through Targeted Energy Transfer ; 11.1 Problem Description ; 11.2 Instability in the Drill-String Model; 11.3 Suppression of Friction-Induced Limit Cycles by TET ; 11.3.1 Addition of an NES to the Drill-String System; 11.3.2 Parametric Study for Determining the NES Parameters; 11.4 Detailed Analysis of the Drill-String with NES Attached; 11.4.1 NES Efficacy ; 11.4.2 Robustness of LCO Suppression; 11.4.3 Transient Resonance Captures; 11.5 Concluding Remarks; 12 Postscript ; Index .
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 of researchers 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: (1) Vibration and shock isolation in mechanical systems; (2) Seismic mitigation; (3) Aeroelastic and structural instability suppression; (4) Drilling operations; (5) Packaging devices.

This is a groundbreaking and unique volume, providing new design paradigms in a variety of fields.

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