Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems

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 .