Chapter
1.2.3 Aperiodic or Chaotic Oscillations
1.2.4 Excitation Level Dependence
1.2.5 Stochastic Resonance
1.2.6 Harmonic Energy Diffusion
1.3 The Exploitation of Bistable Structural Dynamics
1.3.2 Vibration Energy Harvesting
1.3.3 Sensing and Detection
Chapter 2 Mathematical Modeling and Analysis of Bistable Structural Dynamics
2.1.2 Base-excited Response
2.3 A Monostable Nonlinear Oscillator
2.4 A Bistable Oscillator
2.4.1 Free Response and Stability
2.4.2 Base-excited Response
2.5 Analytical Methods for Steady-state Dynamics
2.6 Bifurcations of Bistable Systems
2.7 Multiple Degrees-of-Freedom Systems
2.8 An Electromechanical Bistable System
Chapter 3 Vibration Control
3.2 High and Adaptable Damping Using Bistable Snap-through Dynamics
3.2.1 Model Formulation of the Bistable Device
3.2.2 A Metric for Energy Dissipation Capacity
3.2.3 Numerical Analysis of the Base-excited Response
3.2.4 Energy Dissipation Features of the Dynamic Types
3.2.5 Influences Due to Change in Frequency and Initial Conditions
3.2.6 Experimental Studies
3.3 Isolating Structures Under Large Amplitude Excitations Through Activation of Low Amplitude Interwell Dynamics: Criteria for Excitation‐induced Stability
3.3.1 Governing Equation Formulation of the Bistable Oscillator
3.3.2 Stability of the Analytically Predicted Interwell Dynamics
3.3.3 Validation of the Stability Criteria Using Numerical Simulations
3.3.4 Experimental Validation of the Stability Criteria
3.4 Exploiting Excitation-induced Stability for Dual-stage Vibration Isolation
3.4.1 Governing Equation Formulation of a Bistable Dual-stage Vibration Isolator
3.4.2 Analytical Solution of the Governing Equations
3.4.3 Examining the Stability of Analytical Predictions
3.4.4 Comparison of Isolator Performance with a Counterpart Linear Design
3.4.5 Explanation of the Valley Response
3.4.6 Investigating the Design Parameter Influences
3.4.7 Influence of Initial Conditions
3.4.8 Prototype Investigations: Numerical and Experimental Validation
3.5 Dynamic Stabilization of a Vibration Suspension Platform Attached to an Excited Host Structure
3.5.1 Model Formulation of the Bistable Suspension Coupled to a Flexible Structure
3.5.2 Analytical Solution of the Governing Equations
3.5.3 Description of the Linear Suspension for Comparison
3.5.4 Analytical and Numerical Assessment of Key Suspension Dynamics
3.5.5 Excitation Condition Influences
3.5.6 Experimental Suspension System Platform
3.5.7 Experimental and Analytical Comparisons of Isolation Performance
3.6 Snap-through Dynamics for Vibration Absorption
3.6.1 Model Formulation of a Bistable Vibration Absorber
3.6.2 Analytical Investigation of Force Cancellation Performance
3.6.3 Experimental Investigation of Force Cancellation Performance
Chapter 4 Vibration Energy Harvesting
4.1.1 Experimental and Numerical Developments in Energy Harvesting with Bistable Devices
4.1.2 Analytical Developments in Energy Harvesting with Bistable Devices
4.2 Effective and Straightforward Design Guidelines for High Performance Operations
4.2.1 Analytical Formulation of Bifurcations Associated with Achieving Snap-through
4.2.2 Experimental Validation of the Analytical Premise
4.2.3 Derivation of Criteria for Sustaining High Power Generation Performance
4.2.4 Evaluation of the Criteria Accuracy
4.3 Understanding Superharmonic Energy Diffusion in Bistable Energy Harvesters
4.3.1 Bistable Energy Harvester Modeling: Electromechanical Governing Equations
4.3.2 Amplitude Response Equations
4.3.3 Selection of System Parameters for Investigation
4.3.4 Comparison to 1-Term Harmonic Balance Solution
4.3.5 Effects of Varying Excitation Amplitude
4.3.6 Superharmonic Energy Harvesting Analysis
4.3.7 Experimentally Investigating the Contribution of Total Harvested Energy by the Superharmonic Component
4.4 Optimal and Robust Energy Harvesting from Realistic Stochastic Excitations Using the Dynamics of Structures Designed Near the Elastic Stability Limit
4.4.1 Modeling of Nonlinear Energy Harvester Platform
4.4.2 Preliminary Remarks on Accuracy, Comparisons, and Experimentation
4.4.3 Noise Bandwidth and Level Influences on Ideal Designs
4.4.4 Criticality of Design at the Elastic Stability Limit
4.4.5 Impact of Asymmetry on Energy Harvesting Performance
4.5 Amplifying the Snap‐through Dynamics of a Bistable Energy Harvester Using an Appended Linear Oscillator
4.5.1 Coupled Energy Harvesting System Governing Equations
4.5.2 Analytical Formulation by the Harmonic Balance Method: 1-Term Prediction
4.5.3 Analytical Formulation by the Harmonic Balance Method: 2-Term Prediction
4.5.4 Computing the Fundamental and Superharmonic Average Power and Power Density
4.5.5 Roles of the Auxiliary Linear Oscillator
4.5.6 Roles of the Superharmonic Dynamics in the Energy Harvesting Performance
4.5.7 Experimental Investigations of the Multiharmonic Dynamics Enhancement via the Auxiliary Linear Oscillator
4.6 A Linear Dynamic Magnifier Approach to Bistable Energy Harvesting
4.6.1 Governing Equations for the Bistable Harvester with Linear Dynamic Magnifier
4.6.2 Approximate Solution by the Method of Harmonic Balance
4.6.3 Analytical and Numerical Investigations on the Roles of the Linear Dynamic Magnifier Stage
4.6.3.1 Effect of the Mass Ratio
4.6.3.2 Effect of the Frequency Ratio
4.6.3.3 Effect of the Electromechanical Coupling
4.6.4 Interpreting Frequency Response Characteristics of the Coupled Energy Harvester System
4.6.5 Experimental Validations and Investigations
4.6.5.1 Effect of Bistable Harvester Electromechanical Coupling
4.6.5.2 Effect of Bistable Harvester Mass
Chapter 5 Sensing and Detection
5.1.1 Bistable Microsystems
5.1.2 Bifurcation-based Microsystem Applications
5.2 Detecting Changes in Structures by Harnessing the Dynamics of Bistable Circuits
5.2.1 Bifurcation-based Sensing Platform Based on Bistable Circuitry
5.2.2 Bistable Circuit Model Formulation and Validation
5.2.3 Investigation of Operational Parameters Suited for Bifurcation-based Sensing
5.2.4 Experimental Study of the Proposed Bifurcation-based Sensing Approach
5.3 Improving Damage Identification Robustness to Noise and Damping Using an Integrated Bistable and Adaptive Piezoelectric Circuit
5.3.1 An Integrated Bistable and Adaptive Piezoelectric Circuitry for Bifurcation-based SHM
5.3.2 Overview of Damage Identification Using Integrated Adaptive Piezoelectric Circuitry
5.3.3 Verification of Bifurcation-based Detection of Frequency Shifts
5.3.4 Improving the Accuracy of BB Frequency Shift Detection Through a Greater Number of Evaluations
5.3.5 Investigation of Noise Influences for a Mildly Damped Structure
5.3.6 Investigation of Noise Influences for a More Highly Damped Structure
5.4 Passive Microscale Mass Detection and Progressive Quantification by Exploiting the Bifurcations and Resonant Dynamics of a Two DOF Bistable Sensor
5.4.1 Sensor Architecture and Operational Principle Overview
5.4.2 Experimental Proof-of-concept Sensor Architecture
5.4.3 Model Formulation of the Sensor Architecture
5.4.4 Experimental Validation of the Model Formulation and Numerical Examinations of System Operation
5.4.5 Examination of Passive Quantification of Mass Adsorption via Sequential Activation of Bifurcations
5.4.6 Experimental Comparison of Bifurcation Triggering and Fundamental Mode Natural Frequency Reduction as Consistent Detection Metrics
5.4.7 Stochastic Modeling and Noise Sensitivities
5.4.8 Operational Parameter Influences for Passive Sensing Strategy
5.4.9 Sensor Embodiments and Fabrication Strategies
Chapter 6 Emerging Themes and Future Directions
6.1.2 Vibration Energy Harvesting
6.1.3 Sensing and Detection
6.2 Challenges and Future Outlooks
6.2.1 Theoretical Characterization of the Emerging Bistable and Multistable Structural/Material System Concepts
6.2.2 Application Relevance and Readiness
Harnessing Bistable Structural Dynamics
：For Vibration Control, Energy Harvesting and Sensing
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