Wave Propagation Approach for Structural Vibration

Foreword
Preface
Introduction
Contents
About the Author
Symbols
1 The Basic Theory of Structure–Borne Noise
	1.1 The Vibration Modes of Beams
		1.1.1 Basic Equations
		1.1.2 MATLAB Examples
	1.2 The Vibration Modes of Plates
		1.2.1 Basic Equations
		1.2.2 Calculation Examples for Plates
		1.2.3 The Natural Frequencies of Plates
	1.3 Sound Pressure, Sound Power, and Sound Radiation Efficiency
		1.3.1 Far-Field Sound Pressure
		1.3.2 The Wave Number Transform Solution
		1.3.3 Volume Velocity and Sound Pressure
	1.4 Sound Power and Sound Radiation Efficiency
		1.4.1 Basic Equations for the Radiation Mode Theory
		1.4.2 Examples of Beam and Plate Structures
		1.4.3 Radiation Efficiency in Terms of Radiation Modes
		1.4.4 Radiation Efficiency in Terms of Structural Modes
		1.4.5 Examples of the Calculation of Radiation Efficiency
	References
2 Basic Theory of WPA
	2.1 Challenges and Evolution of Analytical Method
	2.2 Mathematical Description of WPA
		2.2.1 Development History of WPA
		2.2.2 Characteristic Function Expressed by Exponential Function
		2.2.3 Coefficients of Response Function of Point Harmonic Force
		2.2.4 Coefficients of Point Harmonic Bending Moment Response Function
		2.2.5 Boundary Conditions
		2.2.6 Analytical Reconstruction of Finite Beam
	2.3 WPA for Analysis of Finite Simple Structures
		2.3.1 WPA Expressions of Displacement, Shear Force, and Bending Moment
		2.3.2 S–S Beam
		2.3.3 C–C Beam
		2.3.4 C-F Beam
		2.3.5 Comparison Between WPA and Classical Analytical Method
	2.4 Traceability and Characteristic Analysis of WPA
		2.4.1 Traceability of WPA
		2.4.2 Characteristics of WPA
	2.5 Introduction to the Various “Parameters” in WPA
		2.5.1 WPA and Mechanism Analysis
	2.6 Shortcomings of WPA
	2.7 Summary
	References
3 Analysis of Plate Structure Using WPA Method
	3.1 Introduction
	3.2 Bending Vibration and Wave of Uniform Plate
	3.3 Response of Infinite Plate Under Harmonic Force (Moment)
		3.3.1 Response of an Infinite Plate Under Harmonic Force
		3.3.2 Response of Infinite Plate Under Harmonic Moment
	3.4 Wave Propagation in Infinite Plate at the Vertical Incidence of Bending Wave in Discontinuous Interface
		3.4.1 Plate Simply Supported at the Middle
		3.4.2 Plate Simply Supported at One End
		3.4.3 Plate Firmly Supported at One End
		3.4.4 Plate Free at One End
	3.5 Wave Propagation When Bending Wave of Infinite Plate Is Incident on Discontinuous Interface
	3.6 Forced Vibration of a Rectangular Plate with Both Ends Simply Supported
	3.7 Analytical Solution Example for Vibration of a Plate Using WPA
	3.8 WPA Method for Solving Structure Power Flow of Plate
	3.9 Summary
	References
4 WPA for Analyzing Complex Beam Structures
	4.1 Research History and Methods of Complex Beam Structures
	4.2 WPA Analysis of Elastic Coupled Beams
		4.2.1 Establishment of WPA Expression
		4.2.2 Boundary Conditions and Consistency Conditions
		4.2.3 Vibration Response of Elastic Coupled Beam
	4.3 Finite Arbitrary Multi-Supported Elastic Beam
		4.3.1 Mechanical Model and WPA Expression
		4.3.2 WPA Superposition Under Multi-Harmonic Force Excitation
	4.4 Dynamic Response and Stress of Four-Supported Mast
		4.4.1 Mechanical Model and WPA Expression
		4.4.2 Analysis of Dynamic Stress of Four-Supported Mast
	4.5 Periodic and Quasi-Periodic Structures
		4.5.1 Properties of Periodic Structure
		4.5.2 Properties of Quasi-Periodic Structure
	4.6 Energy Transmission Loss Due to Flexible Tubes
		4.6.1 Establishment of WPA Expression
		4.6.2 Boundary Conditions and Consistency Conditions
		4.6.3 Analysis of Dynamic Characteristics of Pipe Sections with Flexible Tubes
	4.7 “Double-Stage Vibration Isolation” Device for Pipeline
		4.7.1 Establishment of WPA Expression
		4.7.2 Boundary Conditions and Consistency Conditions
	4.8 Summary
	References
5 WPA for Analyzing Hybrid Dynamic Systems
	5.1 Hybrid Power Systems
	5.2 The Continuous Elastic Beam System with Lumped Mass
		5.2.1 The Mechanical Model and Derivation of the WPA Formula
		5.2.2 The Dynamic Characteristics of the Multi-support Mast with a Heavy End
	5.3 The Analysis of the Dynamic Characteristics of Multi-supported Beams with Dynamic Vibration Absorbers
		5.3.1 The General Equation of WPA
		5.3.2 Dynamic Flow Expression
		5.3.3 Calculation and Discussion
		5.3.4 Summary of the Analysis
	5.4 The Analysis of Mast Retrofitting with TMD Using the WPA Method
		5.4.1 The Physical Model
		5.4.2 Calculation Example
	5.5 Summary
	References
6 WPA for Calculating Response Under Distributed Force Excitation
	6.1 Introduction
	6.2 Mechanical Model and Formula Deduction
	6.3 Simple Cantilever Beam Structure
	6.4 Comparison Between Examples of WAP Method and Classical Analytical Method
	6.5 Summary
	References
7 Discrete Distributed Tuned Mass Damper
	7.1 Introduction
	7.2 The Velocity Impedance of MTMD
	7.3 The Vibration Absorption Characteristics of MTMD
	7.4 Analysis, Calculation, and Discussion
		7.4.1 The Basic Parameter Analysis
		7.4.2 The Comparison Between MTMD and TMD
		7.4.3 The Comparison in Under/Over-Tuned States
		7.4.4 Influence of the Mass Ratio
	7.5 The Actual Vibration Elimination Effect
	7.6 Summary
	References
8 Analysis of Raft Using WPA Method
	8.1 Single-Stage and Double-Stage Vibration Isolation
		8.1.1 Vibration Isolation System Model and Basic Transmission Characteristics
		8.1.2 Influence of Mass Ratio
	8.2 Raft Vibration Isolation System
		8.2.1 History of Raft Research
		8.2.2 Definition, Modeling, and Basic Characteristics of Rafts
		8.2.3 Physical Modeling and Coordination Conditions
		8.2.4 Analysis of Basic Transfer Characteristics
	8.3 System Thinking and Consideration of Rafts
		8.3.1 Raft Application Paradox
		8.3.2 Definition of Emergence
		8.3.3 Several Inferences
		8.3.4 Large Raft and Small Raft
	8.4 Analysis of Rafts Using the WPA Method
		8.4.1 Internal Coupling Force Acting on the Raft
		8.4.2 Vibration Displacement of the Raft Beam
		8.4.3 Boundary Conditions and Compatibility Conditions
		8.4.4 WPA Expression of Vibration Isolation Effect of Raft
	8.5 “Mass Effect” Analysis of Raft
		8.5.1 Basic Parameters
		8.5.2 Comparative Study of Rigid Installation of Equipment
		8.5.3 Impact of Equipment Location on the Effect of Vibration Isolation
	8.6 “Mixing Effect” Analysis of Rafts
		8.6.1 Offset of Two Structural Waves
		8.6.2 Offset of Multisource Structural Waves
		8.6.3 External and Internal Mixing Effects
		8.6.4 Equal-Master Rafts and Master-Slave Rafts
		8.6.5 Impact of Raft Frame Damping
	8.7 “Tuning Effect” of Rafts
	8.8 WPA Analysis and Test
		8.8.1 Raft Test Device
		8.8.2 Analysis of Test Results
	8.9 Summary
	References
9 Vibration Power Flow and Experimental Investigation
	9.1 Basic Theory of Vibration Power Flow
		9.1.1 Research Review of Power Flow
		9.1.2 Basic Characteristics of Power Flow
		9.1.3 Development and Focus of Power Flow
		9.1.4 Input Power
		9.1.5 Transmitted Power
	9.2 Power Flow Test of Structure
		9.2.1 Summary of Test and Measurement Research
		9.2.2 Input Power Measurement
		9.2.3 Transmitted Power Measurement
	9.3 Testing and Measurement
		9.3.1 Test Structure and Parameters
		9.3.2 Test Procedure
		9.3.3 Input Power Measurement
		9.3.4 Transmitted Power Measurement
	9.4 Control Power Measurement Accuracy
	9.5 Summary
	References
Afterword
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