Gang S. Chen is a professor at Marshall University. His industry experience includes working at Gates Corp., IBM, Sony, and DSI. He is also a Fellow of ASME and SAE. Jianfeng Xu is a professor and associate dean of the School of Mechanical Engineering at Huazhong University of Science and Technology. His industry experience includes working at Applied Materials and DSI. Wei Hua is a principal consultant at ABSWorld. His previous experience includes working at DSI.

• Preface vii1 Introduction 11.1 Definition of Microsystem, Vibrations and Dynamics 11.2 Engineering and Scientific Significance of Microsystem Dynamics 21.3 Organization of the Book 42 Vibrations and Dynamics 72.1 Introduction 72.2 Vibration of Linear System Under Deterministic Excitations 72.2.1 Vibration of Linear Discrete and Continuous Systems 72.2.2 Vibration of Linear Discrete Systems: Single-degree-of-freedom System 82.2.3 Vibrations of Linear Discrete Systems: Multiple-degree-of-freedom System 122.2.3.1 Eigenvalues and Eigenvectors 132.2.3.2 Forced Vibration Solution of an MDOF System 152.2.4 Vibrations of Continuous Systems 162.2.4.1 Transverse Vibrations of String and Wave Equation 162.2.4.2 Longitudinal Vibration of Rods and Torsional Vibration of Shafts 202.2.4.3 Transverse Vibration of Beams 212.3 Random Vibrations Under Deterministic Excitations 242.3.1 Probability Density, Autocorrelation, and Power Spectral Density Function 252.3.2 Response of an SDOF System to an Arbitrary Function Input 272.3.3 Power Spectral Density Function 292.3.4 Joint Probability Density Function and Cross-correlation Function 302.3.5 Response of Linear Dynamic System to a Random Input 322.4 Nonlinear Vibrations 352.4.1 Perturbation Method, Duffing Equation 352.4.2 Amplitude Frequency-dependent and Jump Phenomenon 392.4.3 Van der Pol's equation 392.4.4 Method of Variation of Parameter 402.4.5 Phase Plot, Limit Cycles, Self-excited Oscillations, and Chaos 412.4.6 Stability of Equilibrium 432.4.7 Parametrically Excited System and Mathieu's Equation 462.4.8 Transient and Nonstationary Vibrations 482.4.9 Multi-degree-of-freedom Systems 482.5 Advanced Dynamics 492.5.1 Kinematics of Rigid Body 492.5.2 Linear and Angular Momentums of Rigid Body 582.5.3 Euler Equations of Rigid Body 592.5.4 Lagrange Equations 603 Surface Forces and Interface Interactions 653.1 Introduction 653.2 Contact Between Two Solid Surfaces 653.2.1 Description of Surfaces 653.2.2 Contact Mechanics of Two Solid Surfaces 673.3 Forces Between Two Solid Surfaces 723.3.1 Adhesion 723.3.1.1 Solid-Solid Adhesion 723.3.1.2 Liquid-mediated Adhesion 763.3.2 Friction 793.3.3 Nanoscale Contact and Friction 844 Nanoscale Dynamics of Air-bearing Slider in Computer Hard Disk Drives 994.1 Introduction 994.1.1 Modern Hard Disk Drive 994.1.2 Head-disk Interface 994.1.3 Microsystem-based Active Slider Technology 1014.2 Dynamics of ABS in Sub-5-nm Clearance Regime 1044.2.1 Nonlinear Dynamics of Slider in Sub-5-nm Clearance Regime 1044.2.2 Multiple Interface Forces and System Modeling 1064.2.2.1 Air-bearing Slider Contact Model 1084.2.2.2 Intermolecular Force 1104.2.2.3 Electrostatic Force 1114.2.2.4 Meniscus Forces 1144.2.3 Nonlinear Dynamics Due to Nonlinear Air-bearing Stiffness and Vibro-impact 1154.3 Microsystem-based Active Slider Dynamics 1194.3.1 Microsystem-based Active Thermal Flying-height Control Slider 1194.3.2 Nanoscale Dynamics Sensing, Identification and Diagnosis 1344.3.3 Active Control of Microsystem-based-slider Vibrations 1474.3.4 Characterization of Dynamic Performance of Lubricant in Head-Disk Interface Using Molecular Dynamics 1615 Microdynamics of Lithium-ion Batteries 1775.1 Multiscale Systems in Lithium-ion Batteries 1775.1.1 Modern Lithium-ion Batteries 1775.1.2 Multiscale Characterizations of LIBs 1775.2 Microstructure and Microstructural Dynamics of LIBs 1805.2.1 Microstructure and Multiphysics System 1805.2.2 Modeling of Dynamics of LIBs 1865.2.2.1 Equivalent Circuit Models 1875.2.2.2 Electrochemical Model 1895.2.3 Microstructural Dynamics of Particles in LIBs 1915.3 Acoustic Emission Diagnosis of Microscale Damages of LIBs 1965.3.1 Detection of Damages in LIBs Using AE Testing 1965.3.2 Evaluation of Microcracking in LIBs 1975.3.3 Diagnosis and Identification of Microscale Damages of LIBs 2026 Dynamics of Actuator in Microsystems 2136.1 Introduction 2136.2 MEMS Actuators 2136.2.1 Structures of MEMS Actuators 2136.2.2 Electrostatically and Thermally Actuated Devices 2136.3 Modeling MEMS Structure and Solution 2196.4 Effects of Surface Forces and Surface Roughness on MEMS Actuators 2266.5 System Control of MEMS Actuators and Nonlinear Analysis 2336.6 Research and Development of Emerging MEMS 242References 253Index 259

Gang S. Chen is a professor at Marshall University. His industry experience includes working at Gates Corp., IBM, Sony, and DSI. He is also a Fellow of ASME and SAE. Jianfeng Xu is a professor and associate dean of the School of Mechanical Engineering at Huazhong University of Science and Technology. His industry experience includes working at Applied Materials and DSI. Wei Hua is a principal consultant at ABSWorld. His previous experience includes working at DSI.

• Preface vii1 Introduction 11.1 Definition of Microsystem, Vibrations and Dynamics 11.2 Engineering and Scientific Significance of Microsystem Dynamics 21.3 Organization of the Book 42 Vibrations and Dynamics 72.1 Introduction 72.2 Vibration of Linear System Under Deterministic Excitations 72.2.1 Vibration of Linear Discrete and Continuous Systems 72.2.2 Vibration of Linear Discrete Systems: Single-degree-of-freedom System 82.2.3 Vibrations of Linear Discrete Systems: Multiple-degree-of-freedom System 122.2.3.1 Eigenvalues and Eigenvectors 132.2.3.2 Forced Vibration Solution of an MDOF System 152.2.4 Vibrations of Continuous Systems 162.2.4.1 Transverse Vibrations of String and Wave Equation 162.2.4.2 Longitudinal Vibration of Rods and Torsional Vibration of Shafts 202.2.4.3 Transverse Vibration of Beams 212.3 Random Vibrations Under Deterministic Excitations 242.3.1 Probability Density, Autocorrelation, and Power Spectral Density Function 252.3.2 Response of an SDOF System to an Arbitrary Function Input 272.3.3 Power Spectral Density Function 292.3.4 Joint Probability Density Function and Cross-correlation Function 302.3.5 Response of Linear Dynamic System to a Random Input 322.4 Nonlinear Vibrations 352.4.1 Perturbation Method, Duffing Equation 352.4.2 Amplitude Frequency-dependent and Jump Phenomenon 392.4.3 Van der Pol's equation 392.4.4 Method of Variation of Parameter 402.4.5 Phase Plot, Limit Cycles, Self-excited Oscillations, and Chaos 412.4.6 Stability of Equilibrium 432.4.7 Parametrically Excited System and Mathieu's Equation 462.4.8 Transient and Nonstationary Vibrations 482.4.9 Multi-degree-of-freedom Systems 482.5 Advanced Dynamics 492.5.1 Kinematics of Rigid Body 492.5.2 Linear and Angular Momentums of Rigid Body 582.5.3 Euler Equations of Rigid Body 592.5.4 Lagrange Equations 603 Surface Forces and Interface Interactions 653.1 Introduction 653.2 Contact Between Two Solid Surfaces 653.2.1 Description of Surfaces 653.2.2 Contact Mechanics of Two Solid Surfaces 673.3 Forces Between Two Solid Surfaces 723.3.1 Adhesion 723.3.1.1 Solid-Solid Adhesion 723.3.1.2 Liquid-mediated Adhesion 763.3.2 Friction 793.3.3 Nanoscale Contact and Friction 844 Nanoscale Dynamics of Air-bearing Slider in Computer Hard Disk Drives 994.1 Introduction 994.1.1 Modern Hard Disk Drive 994.1.2 Head-disk Interface 994.1.3 Microsystem-based Active Slider Technology 1014.2 Dynamics of ABS in Sub-5-nm Clearance Regime 1044.2.1 Nonlinear Dynamics of Slider in Sub-5-nm Clearance Regime 1044.2.2 Multiple Interface Forces and System Modeling 1064.2.2.1 Air-bearing Slider Contact Model 1084.2.2.2 Intermolecular Force 1104.2.2.3 Electrostatic Force 1114.2.2.4 Meniscus Forces 1144.2.3 Nonlinear Dynamics Due to Nonlinear Air-bearing Stiffness and Vibro-impact 1154.3 Microsystem-based Active Slider Dynamics 1194.3.1 Microsystem-based Active Thermal Flying-height Control Slider 1194.3.2 Nanoscale Dynamics Sensing, Identification and Diagnosis 1344.3.3 Active Control of Microsystem-based-slider Vibrations 1474.3.4 Characterization of Dynamic Performance of Lubricant in Head-Disk Interface Using Molecular Dynamics 1615 Microdynamics of Lithium-ion Batteries 1775.1 Multiscale Systems in Lithium-ion Batteries 1775.1.1 Modern Lithium-ion Batteries 1775.1.2 Multiscale Characterizations of LIBs 1775.2 Microstructure and Microstructural Dynamics of LIBs 1805.2.1 Microstructure and Multiphysics System 1805.2.2 Modeling of Dynamics of LIBs 1865.2.2.1 Equivalent Circuit Models 1875.2.2.2 Electrochemical Model 1895.2.3 Microstructural Dynamics of Particles in LIBs 1915.3 Acoustic Emission Diagnosis of Microscale Damages of LIBs 1965.3.1 Detection of Damages in LIBs Using AE Testing 1965.3.2 Evaluation of Microcracking in LIBs 1975.3.3 Diagnosis and Identification of Microscale Damages of LIBs 2026 Dynamics of Actuator in Microsystems 2136.1 Introduction 2136.2 MEMS Actuators 2136.2.1 Structures of MEMS Actuators 2136.2.2 Electrostatically and Thermally Actuated Devices 2136.3 Modeling MEMS Structure and Solution 2196.4 Effects of Surface Forces and Surface Roughness on MEMS Actuators 2266.5 System Control of MEMS Actuators and Nonlinear Analysis 2336.6 Research and Development of Emerging MEMS 242References 253Index 259

Gang S. Chen is a professor at Marshall University. His industry experience includes working at Gates Corp., IBM, Sony, and DSI. He is also a Fellow of ASME and SAE. Jianfeng Xu is a professor and associate dean of the School of Mechanical Engineering at Huazhong University of Science and Technology. His industry experience includes working at Applied Materials and DSI. Wei Hua is a principal consultant at ABSWorld. His previous experience includes working at DSI.

• Preface vii1 Introduction 11.1 Definition of Microsystem, Vibrations and Dynamics 11.2 Engineering and Scientific Significance of Microsystem Dynamics 21.3 Organization of the Book 42 Vibrations and Dynamics 72.1 Introduction 72.2 Vibration of Linear System Under Deterministic Excitations 72.2.1 Vibration of Linear Discrete and Continuous Systems 72.2.2 Vibration of Linear Discrete Systems: Single-degree-of-freedom System 82.2.3 Vibrations of Linear Discrete Systems: Multiple-degree-of-freedom System 122.2.3.1 Eigenvalues and Eigenvectors 132.2.3.2 Forced Vibration Solution of an MDOF System 152.2.4 Vibrations of Continuous Systems 162.2.4.1 Transverse Vibrations of String and Wave Equation 162.2.4.2 Longitudinal Vibration of Rods and Torsional Vibration of Shafts 202.2.4.3 Transverse Vibration of Beams 212.3 Random Vibrations Under Deterministic Excitations 242.3.1 Probability Density, Autocorrelation, and Power Spectral Density Function 252.3.2 Response of an SDOF System to an Arbitrary Function Input 272.3.3 Power Spectral Density Function 292.3.4 Joint Probability Density Function and Cross-correlation Function 302.3.5 Response of Linear Dynamic System to a Random Input 322.4 Nonlinear Vibrations 352.4.1 Perturbation Method, Duffing Equation 352.4.2 Amplitude Frequency-dependent and Jump Phenomenon 392.4.3 Van der Pol's equation 392.4.4 Method of Variation of Parameter 402.4.5 Phase Plot, Limit Cycles, Self-excited Oscillations, and Chaos 412.4.6 Stability of Equilibrium 432.4.7 Parametrically Excited System and Mathieu's Equation 462.4.8 Transient and Nonstationary Vibrations 482.4.9 Multi-degree-of-freedom Systems 482.5 Advanced Dynamics 492.5.1 Kinematics of Rigid Body 492.5.2 Linear and Angular Momentums of Rigid Body 582.5.3 Euler Equations of Rigid Body 592.5.4 Lagrange Equations 603 Surface Forces and Interface Interactions 653.1 Introduction 653.2 Contact Between Two Solid Surfaces 653.2.1 Description of Surfaces 653.2.2 Contact Mechanics of Two Solid Surfaces 673.3 Forces Between Two Solid Surfaces 723.3.1 Adhesion 723.3.1.1 Solid-Solid Adhesion 723.3.1.2 Liquid-mediated Adhesion 763.3.2 Friction 793.3.3 Nanoscale Contact and Friction 844 Nanoscale Dynamics of Air-bearing Slider in Computer Hard Disk Drives 994.1 Introduction 994.1.1 Modern Hard Disk Drive 994.1.2 Head-disk Interface 994.1.3 Microsystem-based Active Slider Technology 1014.2 Dynamics of ABS in Sub-5-nm Clearance Regime 1044.2.1 Nonlinear Dynamics of Slider in Sub-5-nm Clearance Regime 1044.2.2 Multiple Interface Forces and System Modeling 1064.2.2.1 Air-bearing Slider Contact Model 1084.2.2.2 Intermolecular Force 1104.2.2.3 Electrostatic Force 1114.2.2.4 Meniscus Forces 1144.2.3 Nonlinear Dynamics Due to Nonlinear Air-bearing Stiffness and Vibro-impact 1154.3 Microsystem-based Active Slider Dynamics 1194.3.1 Microsystem-based Active Thermal Flying-height Control Slider 1194.3.2 Nanoscale Dynamics Sensing, Identification and Diagnosis 1344.3.3 Active Control of Microsystem-based-slider Vibrations 1474.3.4 Characterization of Dynamic Performance of Lubricant in Head-Disk Interface Using Molecular Dynamics 1615 Microdynamics of Lithium-ion Batteries 1775.1 Multiscale Systems in Lithium-ion Batteries 1775.1.1 Modern Lithium-ion Batteries 1775.1.2 Multiscale Characterizations of LIBs 1775.2 Microstructure and Microstructural Dynamics of LIBs 1805.2.1 Microstructure and Multiphysics System 1805.2.2 Modeling of Dynamics of LIBs 1865.2.2.1 Equivalent Circuit Models 1875.2.2.2 Electrochemical Model 1895.2.3 Microstructural Dynamics of Particles in LIBs 1915.3 Acoustic Emission Diagnosis of Microscale Damages of LIBs 1965.3.1 Detection of Damages in LIBs Using AE Testing 1965.3.2 Evaluation of Microcracking in LIBs 1975.3.3 Diagnosis and Identification of Microscale Damages of LIBs 2026 Dynamics of Actuator in Microsystems 2136.1 Introduction 2136.2 MEMS Actuators 2136.2.1 Structures of MEMS Actuators 2136.2.2 Electrostatically and Thermally Actuated Devices 2136.3 Modeling MEMS Structure and Solution 2196.4 Effects of Surface Forces and Surface Roughness on MEMS Actuators 2266.5 System Control of MEMS Actuators and Nonlinear Analysis 2336.6 Research and Development of Emerging MEMS 242References 253Index 259