Vibrations of Shells and Plates, Third Edition: (Mechanical Engineering)

With increasingly sophisticated structures involved in modern engineering, knowledge of the complex vibration behavior of plates, shells, curved membranes, rings, and other complex structures is essential for today’s engineering students, since the behavior is fundamentally different than that of simple structures such as rods and beams. Now in its third edition, Vibrations of Shells and Plates continues to lay an analytical and computational foundation for the study of vibration in these structures. Vibrations of Shells and Plates, Third Edition is updated with substantial new material reflecting advances made over the past decade since publication of the second edition. The author demonstrates how the vibration behavior of shells and plates differs from that of beams through theoretical development and examples. He also explains complicating effects on vibration such as the influence of rotation, shear, rotatory inertia, moment loading, residual stresses, and composite layers. New material includes the parabolic cylindrical shell, natural frequencies and modes, power series method, and explicit strain energy equations for many standard cases. Intended for graduate and post-graduate study in vibration, acoustics, noise control, and stress analysis, this textbook provides a strong foundation in vibration theory, offers analytical solutions that illustrate actual behavior of structures, and prepares students to perform finite element and finite difference analysis.

Table of Contents:
Preface to the Third Edition Preface to the Second Edition Preface to the First Edition Historical Development of Vibration Analysis of Continuous Structural Elements References Deep Shell Equations Shell Coordinates and Infinitesimal Distances in Shell Layers Stress-Strain Relationships Strain-Displacement Relationships Love Simplifications Membrane Forces and Bending Moments Energy Expressions Love’s Equations by Way of Hamilton’s Principle Boundary Conditions Hamilton’s Principle Other Deep Shell Theories Shells of Nonuniform Thickness References Radii of Curvature References Equations of Motion for Commonly Occurring Geometries Shells of Revolution Circular Conical Shell Circular Cylindrical Shell Spherical Shell Other Geometries References Nonshell Structures Arch Beam and Rod Circular Ring Plate Torsional Vibration of Circular Cylindrical Shell and Reduction to a Torsion Bar References Natural Frequencies and Modes General Approach Transversely Vibrating Beams Circular Ring Rectangular Plates That are Simply Supported Along Two Opposing Edges Circular Cylindrical Shell Simply Supported Circular Plates Vibrating Transversely Examples: Plate Clamped at Boundary Orthogonality Property of Natural Modes Superposition Modes Orthogonal Modes from Nonorthogonal Superposition Modes Distortion of Experimental Modes Because of Damping Separating Time Formally Uncoupling of Equations of Motion In-Plane Vibrations of Rectangular Plates In-Plane Vibration of Circular Plates Deep Circular Cylindrical Panel Simply Supported at All Edges Natural Mode Solutions by Power Series On Regularities Concerning Nodelines References Simplified Shell Equations Membrane Approximations Axisymmetric Eigenvalues of a Spherical Shell Bending Approximation Circular Cylindrical Shell Zero In-Plane Deflection Approximation Example: Curved Fan Blade Donnell-Mushtari-Vlasov Equations Natural Frequencies and Modes Circular Cylindrical Shell Circular Duct Clamped at Both Ends Vibrations of a Freestanding Smokestack Special Cases of the Simply Supported Closed Shell and Curved Panel Barrel-Shaped Shell Spherical Cap Inextensional Approximation: Ring Toroidal Shell The Barrel-Shaped Shell Using Modified Love Equations Doubly Curved Rectangular Plate References Approximate Solution Techniques Approximate Solutions by Way of the Variational Integral Use of Beam Functions Galerkin’s Method Applied to Shell Equations Rayleigh-Ritz Method Southwell’s Principle Dunkerley’s Principle Strain Energy Expressions References Forced Vibrations of Shells by Modal Expansion Model Participation Factor Initial Conditions Solution of the Modal Participation Factor Equation Reduced Systems Steady-State Harmonic Response Step and Impulse Response Influence of Load Distribution Point Loads Line Loads Point Impact Impulsive Forces and Point Forces Described by Dirac Delta Functions Definitions and Integration Property of the Dirac Delta Function Selection of Mode Phase Angles for Shells of Revolution Steady-State Circular Cylindrical Shell Response to Harmonic Point Load with All Mode Components Considered Initial Velocity Excitation of a Simply Supported Cylindrical Shell Static Deflections Rectangular Plate Response to Initial Displacement Caused by Static Sag The Concept of Modal Mass, Stiffness Damping, and Forcing Steady State Response of Shells to Periodic Forcing Plate Response to a Periodic Square Wave Forcing Beating Response to Steady State Harmonic Forcing References Dynamic Influence (Green’s) Function Formulation of the Influence Function Solution to General Forcing Using the Dynamic Influence Function Reduced Systems Dynamic Influence Function for the Simply Supported Shell Dynamic Influence Function for the Closed Circular Ring Traveling Point Load on a Simply Supported Cylindrical Shell Point Load Traveling Around a Closed Circular Cylindrical Shell in Circumferential Direction Steady-State Harmonic Green’s Function Rectangular Plate Examples Floating Ring Impacted by a Point Mass References Moment Loading Formulation of Shell Equations That Include Moment Loading Modal Expansion Solution Rotating Point Moment on a Plate Rotating Point Moment on a Shell Rectangular Plate Excited by a Line Moment Response of a Ring on an Elastic Foundation to a Harmonic Point Moment Moment Green’s Function References Vibration of Shells and Membranes Under the Influence of Initial Stresses Strain-Displacement Relationships Equations of Motion Pure Membranes Example: The Circular Membrane Spinning Saw Blade Donnell-Mushtari-Vlasov Equations Extended to Include Initial Stresses References Shell Equations with Shear Deformation and Rotary Inertia Equations of Motion Beams with Shear Deflection and Rotary Inertia Plates with Transverse Shear Deflection and Rotary Inertia Circular Cylindrical Shells with Transverse Shear Deflection and Rotary Inertia References Combinations of Structures Receptance Method Mass Attached to Cylindrical Panel Spring Attached to Shallow Cylindrical Panel Harmonic Response of a System in Terms of Its Component Receptances Dynamic Absorber Harmonic Force Applied Through a Spring Steady-State Response to Harmonic Displacement Excitation Complex Receptances Stiffening of Shells Two Systems Joined by Two or More Displacement Suspension of an Instrument Package in a Shell Subtracting Structural Subsystems Three and More Systems Connected Examples of Three Systems Connected to Each Other References Hysteresis Damping Equivalent Viscous Damping Coefficient Hysteresis Damping Direct Utilization of Hysteresis Model in Analysis Hysteretically Damped Plate Excited by Shaker Steady State Response to Periodic Forcing References Shells Made of Composite Material Nature of Composites Lamina-Constitutive Relationship Laminated Composite Equation of Motion Orthotropic Plate Circular Cylindrical Shell Orthotropic Nets or Textiles Under Tension Hanging Net or Curtain Shells Made of Homogeneous and Isotropic Lamina Simply Supported Sandwich Plates and Beams Composed of Three Homogeneous and Isotropic Lamina References Rotating Structures String Parallel to Axis of Rotation Beam Parallel to Axis of Rotation Rotating Ring Rotating Ring Using Inextensional Approximation Cylindrical Shell Rotating with Constant Spin About Its Axis General Rotations of Elastic Systems Shells of Revolution with Constant Spin About Their Axes of Rotation Spinning Disk References Thermal Effects Stress Resultants Equations of Motion Plate Arch, Ring, Beam, and Rod Limitations Elastic Foundations Equations of Motion for Shells on Elastic Foundations Natural Frequencies and Modes Plates on Elastic Foundations Ring on Elastic Foundation Donnell-Mushtari-Vlasov Equations with Transverse Elastic Foundation Forces Transmitted Into the Base of the Elastic Foundation Vertical Force Transmission Through the Elastic Foundation of a Ring on a Rigid Wheel Response of a Shell on an Elastic Foundation to Base Excitation Plate Examples of Base Excitation and Force Transmission Natural Frequencies and Modes of a Ring on an Elastic Foundation in Ground Contact at a Point Response of a Ring on an Elastic Foundation to a Harmonic Point Displacement References Similitude General Similitude Derivation of Exact Similitude Relationships for Natural Frequencies of Thin Shells Plates Shallow Spherical Panels of Arbitrary Contours (Influence of Curvature) Forced Response Approximate Scaling of Shells Controlled by Membrane Stiffness Approximate Scaling of Shells Controlled by Bending Stiffness References Interactions with Liquids and Gases Fundamental Form in Three-Dimensional Curvilinear Coordinates Stress-Strain-Displacement Relationships Energy Expressions Equations of Motion of Vibroelasticity with Shear Example: Cylindrical Coordinates Example: Cartesian Coordinates One-Dimensional Wave Equations for Solids Three-Dimensional Wave Equations for Solids Three-Dimensional Wave Equations for Inviscid Compressible Liquids and Gases (Acoustics) Interface Boundary Conditions Example: Acoustic Radiation Incompressible Liquids Example: Liquid on a Plate Orthogonality of Natural Modes for Three-Dimensional Solids, Liquids, and Gases References Discretizing Approaches Finite Differences Finite Elements Free and Forced Vibration Solutions References Index