Spectral Density Multi-Field Energy Theory in Structural Dynamics
Methods and Applications
- 1st Edition - August 1, 2026
- Latest edition
- Author: Zhao-Dong Xu
- Language: English
Spectral Density Multi-Field Energy Theory in Structural Dynamics: Methods and Applications introduces a powerful analytical framework for advancing structural dynamics and disast… Read more
Spectral Density Multi-Field Energy Theory in Structural Dynamics: Methods and Applications introduces a powerful analytical framework for advancing structural dynamics and disaster prevention, presenting a novel, spectral density, multi-field energy theory that addresses these challenges through an energy-based lens. The book covers theoretical derivation in-depth while also exploring applications such as damage identification in large-span spatial structures, catastrophe modeling, macro strain energy methods, and energy flow analysis. Real-world case studies demonstrate its effectiveness in structural health monitoring, disaster chain analysis, and dynamic response evaluation under intricate excitation conditions.
This book provides researchers, engineers, and postgraduate students in civil, mechanical, and aerospace engineering with a clear and practical framework for tackling complex dynamic structural problems, combining advanced spectral energy methods with real-world engineering examples.
This book provides researchers, engineers, and postgraduate students in civil, mechanical, and aerospace engineering with a clear and practical framework for tackling complex dynamic structural problems, combining advanced spectral energy methods with real-world engineering examples.
- Introduces spectral density, multi-field energy theory, enhancing the precision of structural catastrophe analysis and enabling more informed engineering decisions
- Presents novel methodologies for addressing complex dynamic and multi-hazard scenarios, equipping readers to solve real-world engineering challenges
- Demonstrates practical implementation through analytical examples and case studies, bridging theory and practice to strengthen structural resilience and performance
- Provides a unified, theoretical framework for structural health monitoring and disaster evolution analysis, supporting proactive decision-making and long-term safety planning
- Delivers state-of-the-art insights tailored to civil, mechanical, and structural engineering, empowering professionals to innovate and raise industry standards
Researchers and graduate students in civil engineering, structural dynamics, and disaster prevention
1. Introduction
1.1 Background
1.2 State-in-art of energy analysis methods
1.3 Frame and contents of this book
2. Spectral density multi-field energy theory
2.1 Basic theoretical knowledge
2.1.1 Time-domain expressions of dynamic responses
2.1.2 Frequency-domain expression of dynamic responses
2.1.3 Theoretical knowledge of random vibration
2.2 Spectral density multi-field energy theory
2.2.1 Theoretical derivation
2.2.2 Advantages of spectral density multi-field energy theory
2.3 Application of spectral density multi-field energy theory in damage identification of a long-span cable-stayed bridge
2.3.1 Numerical model
2.3.2 Traditional mode shape curvature index
2.3.3 Distributed strain spectral density multi-field energy index
2.4 Application of spectral density multi-field energy theory in energy transfer of vibration isolation trenches
2.4.1 Energy transfer characteristics of vibration isolation trenches
2.4.2 Mathematical model of vibration isolation trenches
2.4.3 Energy transfer analysis of vibration isolation trenches
2.5 Summary
3. Spectral density multi-field energy damage identification method for large-span spatial structures
3.1 Damage identification method based on spectral density multi-field energy curvature
3.1.1 The concept of spectral density multi-field energy curvature
3.1.2 Curvature of same plane energy distribution
3.1.3 Curvature of different plane energy distribution
3.1.4 Damage parameter
3.1.5 The specific process of damage identification based on spectral density multi-field energy curvature
3.2 Application of damage identification based on spectral density multi-field energy curvature
3.2.1 Grid structure model
3.2.2 Analysis of damage identification results
3.3 Principal component analysis damage identification method based on spectral density multi-field energy
3.3.1 The concept of principal component analysis
3.3.2 Mathematical model and geometric interpretation of principal component analysis
3.3.3 Sample principal component
3.3.4 The specific process of principal component analysis damage identification method based on spectral density multi-field energy
3.4 Application of principal component analysis damage identification based on spectral density multi-field energy
3.5 Summary
4. Spectral density multi-field energy catastrophe analysis method
4.1 Fundamentals of Catastrophe Analysis
4.1.1 Time-frequency characteristics and catastrophe of structure
4.1.2 Advantages of spectral density multi-field energy in catastrophe analysis
4.2 Spectral density multi-field energy catastrophe analysis method
4.2.1 Theoretical derivation
4.2.2 The establishment of spectral density multi-field energy catastrophe analysis method
4.3 Application of spectral density multi-field energy catastrophe analysis method
4.3.1 Large-span spatial structure model
4.3.2 Catastrophe analysis results
4.4 Summary
5. Macro strain spectral density multi-field energy method
5.1 Macro strain and macro strain mode
5.1.1 Macro strain
5.1.2 Macro strain mode
5.1.3 Test and calculation of macro strain
5.2 Derivation of macro strain spectral density multi-field energy method
5.2.1 Spectral density multi-field energy representation of macro strain mode
5.2.2 Macro strain spectral density multi-field energy
5.2.3 Characteristics of macro strain spectral density multi-field energy method
5.3 Application of damage identification based on macro strain spectral density multi-field energy method
5.3.1 Numerical model of urban viaduct
5.3.2 Damage identification index
5.3.3 Damage identification under earthquake excitation
5.3.4 Damage identification under white noise excitation
5.3.5 Damage identification under impact excitation
5.3.6 Damage identification under multi-field excitation
5.4 Summary
6. Spectral density multi-field energy flow method
6.1 Energy flow in engineering structures
6.1.1 Energy transmission
6.1.2 Energy transfer process between components
6.1.3 Energy transfer process between subsystems
6.1.4 Energy flow structure
6.2 Spectral density multi-field energy flow analysis
6.2.1 Balanced equation for energy transfer
6.2.2 External excitation input power
6.2.3 Spectral density multi-field energy parameters
6.3 Disaster chain analysis based on spectral density multi-field energy flow
6.3.1 Damage analysis of the structural system
6.3.2 Failure analysis of non-structural systems
6.3.3 Disaster Chain Analysis Based on Energy Parameters
6.3.4 Disaster deduction method based on disaster chain
6.4 Disaster deduction and analysis of high-rise buildings
6.4.1 Project overview
6.4.2 Calculation of spectral density multi-field energy
6.4.3 Disaster chain analysis
6.4.4 Disaster deduction
6.5 Summary
7. Concluding Remarks
1.1 Background
1.2 State-in-art of energy analysis methods
1.3 Frame and contents of this book
2. Spectral density multi-field energy theory
2.1 Basic theoretical knowledge
2.1.1 Time-domain expressions of dynamic responses
2.1.2 Frequency-domain expression of dynamic responses
2.1.3 Theoretical knowledge of random vibration
2.2 Spectral density multi-field energy theory
2.2.1 Theoretical derivation
2.2.2 Advantages of spectral density multi-field energy theory
2.3 Application of spectral density multi-field energy theory in damage identification of a long-span cable-stayed bridge
2.3.1 Numerical model
2.3.2 Traditional mode shape curvature index
2.3.3 Distributed strain spectral density multi-field energy index
2.4 Application of spectral density multi-field energy theory in energy transfer of vibration isolation trenches
2.4.1 Energy transfer characteristics of vibration isolation trenches
2.4.2 Mathematical model of vibration isolation trenches
2.4.3 Energy transfer analysis of vibration isolation trenches
2.5 Summary
3. Spectral density multi-field energy damage identification method for large-span spatial structures
3.1 Damage identification method based on spectral density multi-field energy curvature
3.1.1 The concept of spectral density multi-field energy curvature
3.1.2 Curvature of same plane energy distribution
3.1.3 Curvature of different plane energy distribution
3.1.4 Damage parameter
3.1.5 The specific process of damage identification based on spectral density multi-field energy curvature
3.2 Application of damage identification based on spectral density multi-field energy curvature
3.2.1 Grid structure model
3.2.2 Analysis of damage identification results
3.3 Principal component analysis damage identification method based on spectral density multi-field energy
3.3.1 The concept of principal component analysis
3.3.2 Mathematical model and geometric interpretation of principal component analysis
3.3.3 Sample principal component
3.3.4 The specific process of principal component analysis damage identification method based on spectral density multi-field energy
3.4 Application of principal component analysis damage identification based on spectral density multi-field energy
3.5 Summary
4. Spectral density multi-field energy catastrophe analysis method
4.1 Fundamentals of Catastrophe Analysis
4.1.1 Time-frequency characteristics and catastrophe of structure
4.1.2 Advantages of spectral density multi-field energy in catastrophe analysis
4.2 Spectral density multi-field energy catastrophe analysis method
4.2.1 Theoretical derivation
4.2.2 The establishment of spectral density multi-field energy catastrophe analysis method
4.3 Application of spectral density multi-field energy catastrophe analysis method
4.3.1 Large-span spatial structure model
4.3.2 Catastrophe analysis results
4.4 Summary
5. Macro strain spectral density multi-field energy method
5.1 Macro strain and macro strain mode
5.1.1 Macro strain
5.1.2 Macro strain mode
5.1.3 Test and calculation of macro strain
5.2 Derivation of macro strain spectral density multi-field energy method
5.2.1 Spectral density multi-field energy representation of macro strain mode
5.2.2 Macro strain spectral density multi-field energy
5.2.3 Characteristics of macro strain spectral density multi-field energy method
5.3 Application of damage identification based on macro strain spectral density multi-field energy method
5.3.1 Numerical model of urban viaduct
5.3.2 Damage identification index
5.3.3 Damage identification under earthquake excitation
5.3.4 Damage identification under white noise excitation
5.3.5 Damage identification under impact excitation
5.3.6 Damage identification under multi-field excitation
5.4 Summary
6. Spectral density multi-field energy flow method
6.1 Energy flow in engineering structures
6.1.1 Energy transmission
6.1.2 Energy transfer process between components
6.1.3 Energy transfer process between subsystems
6.1.4 Energy flow structure
6.2 Spectral density multi-field energy flow analysis
6.2.1 Balanced equation for energy transfer
6.2.2 External excitation input power
6.2.3 Spectral density multi-field energy parameters
6.3 Disaster chain analysis based on spectral density multi-field energy flow
6.3.1 Damage analysis of the structural system
6.3.2 Failure analysis of non-structural systems
6.3.3 Disaster Chain Analysis Based on Energy Parameters
6.3.4 Disaster deduction method based on disaster chain
6.4 Disaster deduction and analysis of high-rise buildings
6.4.1 Project overview
6.4.2 Calculation of spectral density multi-field energy
6.4.3 Disaster chain analysis
6.4.4 Disaster deduction
6.5 Summary
7. Concluding Remarks
- Edition: 1
- Latest edition
- Published: August 1, 2026
- Language: English
ZX
Zhao-Dong Xu
Professor Zhao-Dong Xu is a National Distinguished Professor at Southeast University, China. His research focuses on structural vibration control and safety monitoring, structural dynamics, multi-hazard intelligent disaster prevention, and intelligent materials and structures. He has published extensively in prestigious international journals, including those of ASCE, ASME, Journal of Sound and Vibration (JSV), and Engineering Structures. Professor Xu also leads the International Joint Laboratory of Intelligent Disaster Prevention.
Affiliations and expertise
Civil Engineering School, Southeast University, Nanjing, China