結構動力學

周思達、沃德·海倫、劉莉編*的《結構動力學 (英文版)》從工程結構的動力學設計與分析的需求入 手，闡述工程設計與分析中的結構動力學問題，結構 動力學的基本假設、任務、載荷類型、離散途徑和建 模方法；介紹典型連續結構系統的動力學建模方法和 特殊邊界與載荷條件下的解；重點介紹結構動力學的 時域分析方法，包括不同邊界和載荷條件下單自由度 系統的特徵分析方法和響應求解方法，以及多自由度 系統的響應數值求解方法與特徵值問題，從而引出多 自由度系統的實模態分析；面向結構的動力學設計， 介紹結構動力學的頻域方法，在複數域建立結構的傳 遞函數、頻率響應函數，從而闡釋結構的複頻域分析 方法與模態參數；總結並介紹結構動力學的反問題之 一——實驗模態分析。本書為全英文編寫，面向研究 型大學研究生培養的國際化和工程領域的全球化需求 ，藉助國外知名高校的經典參考書的成功經驗和人員 基礎，符合國際學術水平、國內實際需求，為相關教 學和工程研究提供良好的支持。 ^[1] 

1 Introduction to Structural Dynamics

1．1 Essential Characteristics and Basic Assumptions

1．1．1 Essential Characteristics

1．1．2 Basic Assumptions in Structural Dynamics of This Book

1．2 Missions of Structural Dynamics

1．2．1 Response Analysis

1．2．2 Inverse Problem of Type I： System Identification

1．2．3 Inverse Problem Type II： Load Identification

1．2．4 Vibration Control

1．3 Types of Dynamic Loads

1．3．1 Periodic Load

1．3．2 Impulsive Load

1．3．3 Random Load

1．4 Formulation of the Equations of Motion

1．4．1 Direct Equilibration Using d'Alembert's Principle

1．4．2 Variational Approach

1．5 Continuous and Discrete Structural Systems

References

2 Time-Domain Analysis of Continuous Systems

2．1 Free Transverse Vibration of Strings

2．2 Free Axial Vibration of Elastic Rods

2．3 Free Torsional Vibration of Cylinder Rods

2．4 Free Transverse Vibration of Euler-Bernoulli Beams

2．4．1 Simple Supported Beams

2．4．2 Cantilever Beams

2．4．3 Fixed-Fixed Beams

2．4．4 Free-Free Beams

2．5 Free Transverse Vibration of Rectangular Thin Plates

2．5．1 Kinematic Description

2．5．2 Equilibrium Equation

2．5．3 Boundary Conditions

2．5．4 Solutions of Rectangular Thin Plates with Simple-supported Edges

2．6 Some Properties of Natural Modes

2．6．1 Orthogonality of Mode Shapes

2．6．2 Modal Scaling

2．6．3 Expansion Theorem

2．6．4 Rayleigh Quotient

Problems

References

3 Time-Domain Analysis of SDOF Systems

3．1 From Continuous Systems to Generalized SDOF Systems

3．1．1 Historical Rayleigh's Method

3．1．2 An Improved Approach of Rayleigh's Method

3．2 Mathematical Modelling of Lumped-Parameter Systems

3．2．1 Direct Equilibration Modeling Using d'Alembert's Principle

3．2．2 Modeling Based on Principle of Virtual Displacements

3．3 Free Vibration of SDOF Systems

3．3．1 Free Vibration of Undamped SDOF Systems

3．3．2 Free Vibration of Viscous-Damped SDOF Systems

3．4 Dynamic Behavior of Undamped SDOF Systems under Harmonic Excitation

3．5 Viscous-Damped SDOF Systems to Harmonic Excitation

3．5．1 General Solution

3．5．2 Steady-State Response

3．5．3 Complex Expression of the Response

3．5．4 Resonance Response

3．5．5 Forced Vibration by Support Motion

3．5．6 Vibration Isolation

3．5．7 Motion Transducer

3．6 Expansion to Periodic Excitation via Fourier Series

3．6．1 Fourier Series for Arbitrary Periodic Functions

3．6．2 Steady-State Response under Arbitrary Periodic Excitations

3．7 Response to Impulsive Loading

3．7．1 Pulse Excitation

3．7．2 Shock Response Spectrum

3．7．3 Shock Isolation

3．8 Response of SDOF Systems in Case of the General Dynamic Excitation

3．8．1 Impulse Function

3．8．2 Impulse Response

3．8．3 Duhamel Integration

3．8．4 Arbitrary Support Motion

3．9 Damping

3．9．1 Damping Models in Structural Dynamics

3．9．2 Energy Losses and Equivalent Viscous Damping

3．9．3 Illustration of the Errors Due to the Equivalence

Problems

References

4 Time-Domain Analysis of MDOF Systems

4．1 Continuous Systems to MDOF Systems： Discretization Approaches

4．1．1 Direct Lumped-Parameter Methods

4．1．2 Generalized Displacements & Rayleigh-Ritz's Methods

4．1．3 Assumed Mode Method： a Realization of General Rayleigh-Ritz Methods

4．1．4 Choosing the Shape Functions

4．1．5 Finite Element Method

4．2 Modeling of Equations of Motion for MDOF Systems

4．2．1 Direct Equilibration Modeling Using d'Alembert's Principle

4．2．2 Modeling with Principle of Virtual Displacements

4．2．3 Modeling with Lagrange's Equations

4．3 Free Vibration of Undamped MDOF Systems

4．3．1 Eigenvalue Problem， Natural Frequencies and Mode Shapes

4．3．2 Orthogonality

4．3．3 Modal Scaling

4．3．4 Eigenvalue Separation Property

4．4 Rayleigh and Rayleigh-Ritz's Methods for MDOF Systems： Model Reduction

4．4．1 Rayleigh Quotient for MDOF Systems

4．4．2 Rayleigh's Method for MDOF Systems

4．4．3 Rayleigh-Ritz's Method for MDOF Systems

4．4．4 Assumed Mode Method for MDOF Systems

4．5 MDOF Systems with Rigid-Body Modes

4．5．1 Small Fictitious Stiffness

4．5．2 Eigenvalue Shifting

4．5．3 Constraining of Rigid-Body Modes

4．6 Damping in MDOF systems

4．7 Numerical Evaluation of Responses of MDOF Systems

4．7．1 Numerical Derivatives

4．7．2 Central Difference Method

4．7．3 Newmark-β Method

4．8 Dynamic Response of MDOF Systems： Mode Superposition Method

4．8．1 Transformation of Coordinates

4．8．2 Modal Damping

4．8．3 Initial Conditions in Modal Coordinates

4．8．4 Mode Superposition for Free Vibration of Undamped MDOF Systems

4．8．5 Mode Superposition of Free Vibration of Damped MDOF Systems

4．8．6 Mode Superposition of Forced Vibration of Undamped MDOF Systems

4．8．7 Mode Superposition of Forced Vibration of Damped MDOF Systems

4．8．8 Mode-Displacement Solution and Mode-Acceleration Solution

Problems

References

5 Frequency-Domain Analysis

5．1 Frequency-Domain Analysis of SDOF Systems

5．1．1 System Equations and Transfer Function

5．1．2 Poles， Natural Frequencies， Damping Ratio and Residues

5．1．3 Transfer Function Plots

5．1．4 Frequency Response Function and Impulse Response Function

5．1．5 Influence of Mass， Damping and Stiffness Changes -．

5．2 Frequency-Domain Analysis of MDOF Systems

5．2．1 System Equations and Transfer Function

5．2．2 Poles， Natural Frequencies and Damping Ratio

5．2．3 Modal Vectors and Residues

5．2．4 Modal Participation Factors

5．2．5 Frequency Response Function Matrix and Impulse Response Function Matrix

5．2．6 Undamped and Proportionally Damped Systems

5．2．7 Orthogonality

5．2．8 Modal Vector Scaling

5．2．9 Numerical and Experimental Approaches

References

6 Experimental Modal Analysis and Applications

6．1 Basic Modal Model Equations

6．1．1 Modal Model

6．1．2 State Space Model

6．1．3 Rational Fraction Polynomial Model

6．2 Modal Parameter Estimation

6．2．1 Basic Concept

6．2．2 SDOF Methods

6．2．3 MDOF Time-Domain Methods

6．2．4 MDOF Frequency-Domain Methods

6．2．5 Output-Only or Operational Modal Analysis

6．2．6 Conclusions

6．3 Modal Validation

6．3．1 Modal Scale Factor and Modal Assurance Criterion

6．3．2 Mode Participation

6．3．3 Reciprocity

6．3．4 Mode Complexity

6．3．5 Modal Phase Collinearity and Mean Phase Deviation

6．3．6 Modal Confidence Factor

6．3．7 Synthesis of Frequency Response Functions

6．3．8 Discussion

6．4 Applications of Modal Parameters

6．4．1 Forced Response Analysis

6．4．2 Sensitivity Analysis

6．4．3 Structural Dynamics Modification & Assembly

6．5 Combining Numerical and Experimental Models

6．5．1 Model Updating

6．5．2 Pre-Test Analysis

References ^[2]