Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9

Preface	6
Contents	8
1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes	10
1.1 Introduction	10
1.2 Device Description, Design and Optimization	11
1.2.1 Harvester	11
1.2.2 Electric Interface	12
1.2.3 Application Constraints, Vibrational Input and Energy Requirements	12
1.2.4 Device Optimization	13
1.3 Product Development	15
1.3.1 Virtual Prototype	15
1.3.2 3D Printed Prototypes	15
1.3.3 Molded Prototypes	15
1.4 Conclusions	17
References	18
2 Issues in Experimental Testing of Piezoelectric Energy Harvesters	20
2.1 Introduction	20
2.2 Analytical Model Description	21
2.3 Test Apparatus	22
2.4 Experimental Results	23
2.5 Closing Remarks	26
References	26
3 Innovative Piezoelectric Cantilever Beam Shape for Improved Energy Harvesting	27
3.1 Introduction	27
3.2 Modeling of Energy Harvesting with Different Cantilever Structures	28
3.3 Results and Discussion	28
3.3.1 Eigen-Frequency Analysis	29
3.3.2 Electrical Analysis	29
3.4 Conclusion	30
Reference	31
4 Energy Harvesting from Piezoelectric Stacks Using Impacting Beam	33
4.1 Introduction	33
4.2 Methodology	34
4.3 Analytical Expressions for Cantilever and Stopper Via Impact	34
4.4 Electromechanical Modeling of Piezoelectric Stacks	37
4.5 Experimental Validation of the Analytical Model	39
4.6 Harmonic Base Acceleration at Different Frequencies with Impact and Without Impact Conditions	40
4.7 Conclusion	43
References	45
5 Nonlinear 2-DOFs Vibration Energy Harvester Based on Magnetic Levitation	46
5.1 Introduction	46
5.2 Design and System Modeling	47
5.2.1 Proposed Device	47
5.3 Optimality Conditions and Average Power	48
5.4 Results and Discussion	49
5.4.1 Optimal Design Parameters	49
5.4.2 Bandwidth Enhancement	50
5.4.3 Normalized Power Density Enhancement	51
5.5 Conclusion	51
References	52
6 Parameter Identification of Riveted Joints Using Vibration Methods	53
6.1 Introduction	53
6.2 Methodology	54
6.3 Experimental Studies	54
6.4 Model Validation of the Continuous Plate	55
6.5 Parameter Identification of Riveted Joints	55
6.6 Discussion and Conclusions	58
References	59
7 Dynamic Ground Testing: Ground Vibration Tests Through Control Surface Excitation	60
Abbreviations	60
7.1 Introduction	60
7.2 A340-600 MSN360 Research Ground Vibration Test (2011)	61
7.3 Instrumentation	62
7.4 Excitation Signals	63
7.5 Streamlined Analysis	65
8 Adaptive Support of an Aircraft Panel	66
8.1 Introduction of Adaptive Boundary Conditions	66
8.2 Finite Element Models	67
8.3 Calculations	68
8.4 Results	69
8.5 Conclusions	70
References	71
9 Calculating the Impact Force of Supersonic Hail Stones Using SWAT-TEEM	72
9.1 Introduction	72
9.2 Force Reconstruction Theory	73
9.2.1 Formulation of SWAT (Sum of Weighted Acceleration Technique)	73
9.2.2 Formulation of SWAT-TEEM (Sum of Weighted Acceleration Technique—Time Eliminated Elastic Modes)	74
9.2.3 Condition of the Inverse in SWAT and SWAT-TEEM	75
9.3 Test Item Description	75
9.4 Characterization Test	76
9.5 Hail Impact Test	77
9.5.1 Results	79
9.6 Conclusions and Future Work	83
References	84
10 Testing and Validation of the Dynamic Inertia Measurement Method	85
Nomenclature	85
10.1 Introduction	86
10.2 DIM Background Theory	87
10.3 Previous DIM Validation Efforts on Large-Scale Test Articles	87
10.3.1 X-38 Crew Return Vehicle	88
10.3.2 Initial Iron Bird Test Article	88
10.4 Iron Bird Test Article	89
10.5 Test Plan	90
10.6 Analytic Model	90
10.7 Pendulum Swing Test	90
10.8 Dynamic Inertia Measurement Test	92
10.8.1 Equipment	92
10.8.1.1 Soft-Support System	93
10.8.1.2 3-DOF Load Cells: Soft Supports	93
10.8.1.3 6-DOF Force Sensors: Reaction Forces	93
10.8.1.4 Shakers: Excitation	93
10.8.1.5 3-DOF and 1-DOF Force Sensors: Excitation	94
10.8.1.6 Accelerometers	94
10.8.1.7 Laser Tracker System	95
10.8.2 Test Model	95
10.8.3 Test Description	96
10.9 Results	97
10.9.1 Dynamic Inertia Measurement Analysis	97
10.9.2 Comparison of Seismic and GVT T333B (PCB Piezotronics, Inc.) Accelerometers	99
10.9.3 Dynamic Inertia Measurement Results	100
10.9.4 Comparison of Results from Different Methods	101
10.10 Recommendations and Considerations	106
10.10.1 Testing Recommendations and Considerations	106
10.10.2 Processing Recommendations and Considerations	106
10.10.3 Basic Theory Recommendations and Considerations	106
10.10.4 Additional Recommendations	107
10.11 Conclusions	107
References	107
11 Estimation of Amplitude-Dependent Resonance and Damping in MEMS Shock Accelerometers	109
Nomenclature	109
11.1 Introduction	109
11.2 Analysis	110
11.3 Experiment	112
11.4 Analysis	113
11.5 Discussion	115
11.6 Summary	117
References	117
12 Development of a Mapping Function for a Low- to High-Amplitude Input	118
12.1 Introduction	118
12.2 Multi-axial Pyroshock Plate (MAPP) Set-Up	119
12.2.1 Interface	119
12.3 Background	120
12.3.1 Sub-scale Comparison Laboratory Study	120
12.4 Full-Scale Pyroshock Testing	121
12.4.1 Test Layout	121
12.5 Analysis	121
12.5.1 Time Domain	124
12.5.2 Frequency Response Function Analysis	126
12.5.3 Output Auto Power Spectra Analysis	127
12.5.4 Shock Response Spectra Analysis	128
12.6 Summary	130
References	130
13 Experimental Study of Glass Fiber Reinforced Polyester Under Repeated Impacts	131
13.1 Introduction	131
13.2 Experimental Procedures	132
13.2.1 Specimen Description	132
13.2.2 Impact Device Description	132
13.2.3 Impact Device Calibration	134
13.2.4 Repeated Impact Procedures	135
13.3 Results and Discussion	135
13.3.1 Device Calibration Results	135
13.3.2 Deflection of Composite Specimens	136
13.3.3 Impact Fatigue Trend of Composite Specimens	137
13.4 Conclusion	138
References	138
14 FE Modeling of Paperboard Material Using Sandwich Structure Method	139
14.1 Introduction	139
14.2 Finite Element Model	140
14.3 Simulation Results	141
14.4 Conclusions	142
References	142
15 Evaluation of Seismic Performance of an Excavation Support System	143
15.1 Introduction	143
15.2 Soil Properties and Site Conditions	143
15.3 Construction Phases and Numerical Modeling	144
15.4 Instrumentation System and Comparison of Results	146
15.4.1 Instrumentation	146
15.4.2 Ground and Pile Settlements	147
15.4.3 Lateral Deformations	148
15.5 Conclusion	150
References	150
16 Calculating Stress and Strain from Experimental ODS Data	151
16.1 Introduction	151
16.2 Variable Speed Rotating Machine	151
16.3 Mode Shapes of the Machine	152
16.4 ODS Expansion	152
16.5 Strain from Shape Data	154
16.6 Stress from Strain	155
16.7 Strain from Mode Shapes	156
16.8 Stress from Mode Shapes	157
16.9 Strain in the 985 & 2280 RPM ODS	158
16.10 Stress in the 985 & 2280 RPM ODS	158
16.11 Conclusions	159
References	160
17 Case Study: Modeling Generator Chassis Responses with ODS Data	162
17.1 Introduction	162
17.2 Theoretical Background	163
17.3 Experiment Setup	163
17.4 Model Setup	165
17.5 Results and Discussion	165
17.6 Concluding Remarks	167
References	168
18 Shock Calibration with Zero Shift Using a Digital Filter Technique	169
18.1 Introduction	169
18.2 Shock Calibration System	169
18.3 Experimental Results	170
18.4 Charge Amplifier and Virtual Amplifier	170
18.5 Calibration Procedure and Results	172
18.6 Conclusion	173
References	173
19 Mechanical Shock Environment Synthesis for Structural Failure Elicitation	174
19.1 Introduction	174
19.2 Theoretical Background	175
19.2.1 Shock Response Spectra (SRS) Method	175
19.2.2 Least Favorable Response	176
19.2.3 Sum of Decaying Sinusoids Method	176
19.2.4 Wavelet Method	176
19.2.5 Temporal Moments Methods	177
19.3 Test Methods	178
19.3.1 Test Article Description	178
19.3.2 Numerical Modeling and Experimental Testing	178
19.3.3 Test Hardware and Experimental Setup	180
19.4 Experimental Results	182
19.5 Conclusion	182
References	184
20 Natural Frequencies of Layered Beams Using a Continuous Variation Model	185
Nomenclature	185
20.1 Introduction	186
20.2 Modeling	186
20.3 Numerical Examples	188
20.3.1 Two-Cell Beams	188
20.3.2 Three-Cell Beams	192
20.4 FEM	194
20.5 Conclusions	194
References	198
21 Analysis of H∞ and H2 Optimal Design Scheme for an Electromagnetic Damper with Shunt Resonant Circuit	199
21.1 Introduction	199
21.2 Tuned Mass Damper (TMD)	200
21.2.1 TMD H∞ Optimisation	201
21.2.2 TMD H2 Optimisation	201
21.3 Electromagnetic Shunt Damper (EMDS)	202
21.3.1 H∞ Optimisation Design	202
21.3.2 H2 Optimisation Design	204
21.4 Theoretical Comparison of the TMD and EMDS	205
21.5 Discussion	208
References	209
22 Orbit Stability Determination of Satellites Using Harmonic Force Excitation Analysis	211
22.1 Introduction	211
22.2 Background	212
22.3 System Model	215
22.4 Analysis	215
22.5 Conclusion	219
References	220
23 Energy Harvesting Perspectives from Parametric Resonant Systems	221
23.1 Introduction	221
23.2 A Parametrically Excited Beam	222
23.3 Analytical Analysis of Energy Flows	224
23.4 Numerical Approach: Quasi-linear FEM	225
23.5 Numerical Analysis of Energy Flows	225
23.6 Experiment	227
23.7 Discussion and Further Applications	228
23.8 Conclusions	229
References	230

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