Vibrations of Linear Piezostructures

ISBN-13: 9781119393405 / Angielski / Twarda / 2021 / 256 str.

Andrew J. Kurdila;Pablo A. Tarazaga

Opis

Vibrations of Linear Piezostructures is a self-contained and introductory text providing a focused and concise account of the general theory of vibrations of linear piezostructures. While piezoelectric materials and sensors have been studied for decades, a person seeking a general introduction to the theory for modeling and analysis of this emerging class of sensors, actuators, and active systems currently must assimilate approaches from older outdated texts, journal or conference articles, edited volumes, highly specialized texts, or manuscripts that primarily treat other topics such as crystallography, tensor mathematics, continuum mechanics, or continuum electrodynamics. The book deals with the fundamental principals, starting with a review of mathematics, continuum mechanics and elasticity, and continuum electrodynamics as they are applied to electromechanical piezostructures. It continues by developing the work related to linear constitutive laws of piezoelectricity. Following this, it addresses modeling of linear piezostructures via Newton's approach and consequently via Variational Methods. And in the end it presents a general discussion of weak and strong forms of the equations of motion, Galerkin approximation methods for the weak form, Fouier or modal methods, and finite element methods.

Spis treści

1.1 The Piezoelectric Effect 131.1.1 Ferroelectric Piezoelectrics 141.1.2 One Dimensional Direct and Converse Piezoelectric Effect 171.2 Applications 191.2.1 Energy Applications 191.2.2 Sensors 201.2.3 Actuators or Motors 201.3 Outline of the Book 222 Mathematical Background 272.1 Vectors, Bases, and Frames 272.2 Tensors 292.3 Symmetry, Crystals, and Tensor Invariance 332.3.1 Geometry of Crystals 332.3.2 Symmetry of Tensors 412.4 Problems 433 Review of Continuum Mechanics 453.1 Stress 453.1.1 The Stress Tensor 463.1.2 Cauchy's Formula 473.1.3 The Equations of Equilibrium 483.2 Displacement and Strain 493.3 Strain Energy 553.4 Constitutive Laws for Linear Elastic Materials 563.4.1 Triclinic Materials 593.4.2 Monoclinic Materials 603.4.3 Orthotropic Materials 603.4.4 Transversely Isotropic Materials 603.5 The Initial-Boundary Value Problem of Linear Elasticity 613.6 Problems 634 Review of Continuum Electrodynamics 654.1 Charge and Current 654.2 The Electric and Magnetic Fields 664.2.1 The Definition of the Static Electric Field 664.2.2 The Definition of the Static Magnetic Field 674.3 Maxwell's Equations 694.3.1 Polarization and Electric Displacement 694.3.2 Magnetization and Magnetic Field Intensity 734.3.3 Maxwell's Equations in Gaussian Units 754.3.4 Scalar and Vector Potentials 764.4 Problems 775 Linear Piezoelectricity 815.1 Constitutive Laws of Linear Piezoelectricity 815.2 The Initial-Value Boundary Problem of Linear Piezoelectricity 845.2.1 Piezoelectricity and Maxwell's Equations 845.2.2 The Initial-Boundary Value Problem 855.3 Thermodynamics of Constitutive Laws 875.4 Symmetry of Constitutive Laws for Linear Piezoelectricity 915.4.1 Monoclinic C2 Crystals 925.4.2 Monoclinic Cs Crystals 935.4.3 Trigonal D3 Crystals 945.4.4 Hexagonal C6v Crystals 945.5 Problems 956 Newton's Method for Piezoelectric Systems 976.1 An Axial Actuator Model 976.2 An Axial, Linear Potential, Actuator Model 1026.3 A Linear Potential, Beam Actuator 1046.4 Composite Plate Bending 1086.5 Problems 1167 Variational Methods 1197.1 A Review of Variational Calculus 1197.2 Hamilton's Principle 1227.2.1 Uniaxial Rod 1237.2.2 Bernoulli-Euler Beam 1257.3 Hamilton's Principle for Piezoelectricity 1267.3.1 Uniaxial Rod 1307.3.2 Bernoulli-Euler Beam 1327.4 Bernoulli-Euler Beam with a Shunt Circuit 1337.5 Relationship to other Variational Principles 1407.6 Lagrangian Densities 1437.7 Problems 1518 Approximations 1538.1 Classical, Strong, and Weak Formulations 1538.2 Modeling Damping and Dissipation 1618.3 Galerkin Approximations 1638.3.1 Modal or Eigenfunction Approximations 1678.3.2 Finite Element Approximations 1798.4 Problems 200Supplementary Material 201S.1 A Review of Vibrations 201S.1.1 SDOF Systems 201S.1.2 Distributed Parameter Systems 205S.1.3 MDOF Equations of Motion 219S.2 Tensor Analysis 222S.3 Distributional and Weak Derivatives 224

O autorze

Andrew J. Kurdila earned his PhD in Engineering Science and Mechanics in 1989 from the Georgia Institute of Technology, USA. Currently, he is the W. Martin Johnson Professor of Mechanical Engineering at Virginia Tech. His areas of specialty include robotics and autonomous and dynamical systems.Pablo A. Tarazaga earned his PhD in 2009 from Virginia Tech, USA and is currently the Director of the Vibrations, Adaptive Structures and Testing Laboratory and the Director of the Virginia Tech Smart Infrastructure Laboratory at Virginia Tech. His research interests include structural mechanics and dynamics and control.