Enhanced descriptions from Syndetics:

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 provided by Syndetics

• 1 Historical Development of Vibration Analysis of Continuous Structural Elements (p. 1)
• References (p. 4)
• 2 Deep Shell Equations (p. 7)
• 2.1 Shell Coordinates and Infinitesimal Distances in Shell Layers (p. 8)
• 2.2 Stress-Strain Relationships (p. 13)
• 2.3 Strain-Displacement Relationships (p. 15)
• 2.4 Love Simplifications (p. 22)
• 2.5 Membrane Forces and Bending Moments (p. 24)
• 2.6 Energy Expressions (p. 28)
• 2.7 Love's Equations by Way of Hamilton's Principle (p. 30)
• 2.8 Boundary Conditions (p. 35)
• 2.9 Hamilton's Principle (p. 39)
• 2.10 Other Deep Shell Theories (p. 43)
• 2.11 Shells of Nonuniform Thickness References (p. 46)
• 2.12 Radii of Curvature (p. 47)
• References (p. 50)
• 3 Equations of Motion for Commonly Occurring Geometries (p. 51)
• 3.1 Shells of Revolution (p. 51)
• 3.2 Circular Conical Shell (p. 54)
• 3.3 Circular Cylindrical Shell (p. 56)
• 3.4 Spherical Shell (p. 57)
• 3.5 Other Geometries (p. 59)
• References (p. 63)
• 4 Nonshell Structures (p. 64)
• 4.1 Arch (p. 64)
• 4.2 Beam and Rod (p. 67)
• 4.3 Circular Ring (p. 68)
• 4.4 Plate (p. 69)
• 4.5 Torsional Vibration of Circular Cylindrical Shell and Reduction to a Torsion Bar (p. 72)
• References (p. 74)
• 5 Natural Frequencies and Modes (p. 75)
• 5.1 General Approach (p. 75)
• 5.2 Transversely Vibrating Beams (p. 77)
• 5.3 Circular Ring (p. 82)
• 5.4 Rectangular Plates that are Simply supported Along Two Opposing Edges (p. 86)
• 5.5 Circular Cylindrical Shell Simply Supported (p. 93)
• 5.6 Circular Plates Vibrating Transversely (p. 102)
• 5.7 Example: Plate Clamped at Boundary (p. 103)
• 5.8 Orthogonality Property of Natural Modes (p. 106)
• 5.9 Superposition Modes (p. 109)
• 5.10 Orthogonal Modes from Nonorthogonal Superposition Modes (p. 113)
• 5.11 Distortion of Experimental Modes Because of Damping (p. 117)
• 5.12 Separating Time Formally (p. 120)
• 5.13 Uncoupling of Equations of Motion (p. 122)
• 5.14 In-Plane Vibrations of Rectangular Plates (p. 124)
• 5.15 In-Plane Vibration of Circular Plates (p. 128)
• 5.16 Deep Circular Cylindrical Panel Simply Supported at All Edges (p. 131)
• 5.17 Natural Mode Solutions by Power Series (p. 133)
• 5.18 On Regularities Concerning Nodelines (p. 142)
• References (p. 143)
• 6 Simplified Shell Equations (p. 145)
• 6.1 Membrane Approximation (p. 145)
• 6.2 Axisymmetric Eigenvalues of a Spherical Shell (p. 146)
• 6.3 Bending Approximation (p. 151)
• 6.4 Circular Cylindrical Shell (p. 152)
• 6.5 Zero In-Plane Deflection Approximation (p. 153)
• 6.6 Example: Curved Fan Blade (p. 154)
• 6.7 Donnell-Mushtari-Vlasov Equations (p. 154)
• 6.8 Natural Frequencies and Modes (p. 157)
• 6.9 Circular Cylindrical Shell (p. 157)
• 6.10 Circular Duct Clamped at Both Ends (p. 159)
• 6.11 Vibrations of a Freestanding Smokestack (p. 161)
• 6.12 Special Cases of the Simply Supported Closed Shell and Curved Panel (p. 162)
• 6.13 Barrel-Shaped Shell (p. 163)
• 6.14 Spherical Cap (p. 165)
• 6.15 Inextensional Approximation: Ring (p. 167)
• 6.16 Toroidal Shell (p. 168)
• 6.17 The Barrel-Shaped Shell Using Modified Love Equations (p. 170)
• 6.18 Doubly Curved Rectangular Plate (p. 174)
• References (p. 176)
• 7 Approximate Solution Techniques (p. 178)
• 7.1 Approximate Solutions by Way of the Variational Integral (p. 179)
• 7.2 Use of Beam Functions (p. 181)
• 7.3 Galerkin's Method Applied to Shell Equations (p. 184)
• 7.4 Rayleigh-Ritz Method (p. 191)
• 7.5 Southwell's Principle (p. 196)
• 7.6 Dunkerley's Principle (p. 199)
• 7.7 Strain Energy Expressions (p. 201)
• References (p. 206)
• 8 Forced Vibrations of Shells by Modal Expansion (p. 207)
• 8.1 Model Participation Factor (p. 207)
• 8.2 Initial Conditions (p. 210)
• 8.3 Solution of the Modal Participation Factor Equation (p. 211)
• 8.4 Reduced Systems (p. 214)
• 8.5 Steady-State Harmonic Response (p. 215)
• 8.6 Step and Impulse Response (p. 216)
• 8.7 Influence of Load Distribution (p. 217)
• 8.8 Point Loads (p. 220)
• 8.9 Line Loads (p. 225)
• 8.10 Point Impact (p. 227)
• 8.11 Impulsive Forces and Point Forces Described by Dirac Delta Functions (p. 230)
• 8.12 Definitions and Integration Property of the Dirac Delta Function (p. 232)
• 8.13 Selection of Mode Phase Angles for Shells of Revolution (p. 233)
• 8.14 Steady-State Circular Cylindrical Shell Response to Harmonic Point Load with All Mode Components Considered (p. 236)
• 8.15 Initial Velocity Excitation of a Simply Supported Cylindrical Shell (p. 240)
• 8.16 Static Deflections (p. 243)
• 8.17 Rectangular Plate Response to Initial Displacement Caused by Static Sag (p. 243)
• 8.18 The Concept of Modal Mass, Stiffness Damping and Forcing (p. 246)
• 8.19 Steady State Response of Shells to Periodic Forcing (p. 248)
• 8.20 Plate Response to a Periodic Square Wave Forcing (p. 251)
• 8.21 Beating Response to Steady state Harmonic Forcing (p. 253)
• References (p. 255)
• 9 Dynamic Influence (Green's) Function (p. 256)
• 9.1 Formulation of the Influence Function (p. 257)
• 9.2 Solution to General Forcing Using the Dynamic Influence Function (p. 259)
• 9.3 Reduced Systems (p. 260)
• 9.4 Dynamic Influence Function for the Simply Supported Shell (p. 261)
• 9.5 Dynamic Influence Function for the Closed Circular Ring (p. 263)
• 9.6 Traveling Point Load on Simply Supported Cylindrical Shell (p. 264)
• 9.7 Point Load Traveling Around a Closed Circular Cylindrical Shell in Circumferential Direction (p. 267)
• 9.8 Steady-State Harmonic Green's Function (p. 271)
• 9.9 Rectangular Plate Examples (p. 272)
• 9.10 Floating Ring Impacted by a Point Mass (p. 277)
• References (p. 279)
• 10 Moment Loading (p. 281)
• 10.1 Formulation of Shell Equations That Include Moment Loading (p. 282)
• 10.2 Modal Expansion Solution (p. 284)
• 10.3 Rotating Point Moment on a Plate (p. 285)
• 10.4 Rotating Point Moment on a Shell (p. 287)
• 10.5 Rectangular Plate Excited by a Line Moment (p. 289)
• 10.6 Response of a Ring on an Elastic Foundation to a Harmonic Point Moment (p. 291)
• 10.7 Moment Green's Function (p. 295)
• References (p. 300)
• 11 Vibration of Shells and Membranes Under the Influence of Initial Stresses (p. 301)
• 11.1 Strain-Displacement Relationships (p. 302)
• 11.2 Equations of Motion (p. 305)
• 11.3 Pure Membranes (p. 309)
• 11.4 Example: The Circular Membrane (p. 311)
• 11.5 Spinning Saw Blade (p. 315)
• 11.6 Donnell-Mushtari-Vlasov Equations Extended to Include Initial Stresses (p. 318)
• References (p. 320)
• 12 Shell Equations with Shear Deformation and Rotatory Inertia (p. 322)
• 12.1 Equations of Motion (p. 322)
• 12.2 Beams with Shear Deflection and Rotatory Inertia (p. 325)
• 12.3 Plates with Transverse Shear Deflection and Rotatory Inertia (p. 329)
• 12.4 Circular Cylindrical Shells with Transverse Shear Deflection and Rotatory Inertia (p. 333)
• References (p. 336)
• 13 Combinations of Structures (p. 337)
• 13.1 Receptance Method (p. 338)
• 13.2 Mass Attached to Cylindrical Panel (p. 339)
• 13.3 Spring Attached to Shallow Cylindrical Panel (p. 342)
• 13.4 Harmonic Response of a System in Terms of Its Component Receptances (p. 344)
• 13.5 Dynamic Absorber (p. 347)
• 13.6 Harmonic Force Applied Though a Spring (p. 350)
• 13.7 Steady-State Response to Harmonic Displacement Excitation (p. 353)
• 13.8 Complex Receptances (p. 354)
• 13.9 Stiffening of Shells (p. 356)
• 13.10 Two Systems Joined by Two or More Displacement (p. 360)
• 13.11 Suspension of an Instrument Package in a Shell (p. 362)
• 13.12 Subtracting Structural Subsystems (p. 365)
• 13.13 Three and More Systems Connected (p. 370)
• 13.14 Examples of Three Systems Connected to Each Other (p. 374)
• References (p. 378)
• 14 Hysteresis Damping (p. 380)
• 14.1 Equivalent Viscous Damping Coefficient (p. 381)
• 14.2 Hysteresis Damping (p. 381)
• 14.3 Direct Utilization of Hysteresis Model in Analysis (p. 384)
• 14.4 Hysteretically Damped Plate Excited by Shaker (p. 386)
• 14.5 Steady State Response to Periodic Forcing (p. 388)
• References (p. 390)
• 15 Shells Made of Composite Material (p. 391)
• 15.1 Nature of Composites (p. 391)
• 15.2 Lamina-Constitutive Relationship (p. 392)
• 15.3 Laminated Composite (p. 397)
• 15.4 Equation of Motion (p. 399)
• 15.5 Orthotropic Plate (p. 400)
• 15.6 Circular Cylindrical Shell (p. 402)
• 15.7 Orthotropic Nets or Textiles Under Tension (p. 406)
• 15.8 Hanging Net or Curtain (p. 408)
• 15.9 Shells Made of Homogeneous and Isotropic Lamina (p. 410)
• 15.10 Simply Supported Sandwich Plates and Beams Composed of Three Homogeneous and Isotropic Lamina (p. 412)
• References (p. 414)
• 16 Rotating Structures (p. 415)
• 16.1 String Parallel to Axis of Rotation (p. 415)
• 16.2 Beam Parallel to Axis of Rotation (p. 422)
• 16.3 Rotating Ring (p. 425)
• 16.4 Rotating Ring Using Inextensional Approximation (p. 428)
• 16.5 Cylindrical Shell Rotating with Constant Spin About Its Axis (p. 431)
• 16.6 General Rotations of Elastic Systems (p. 432)
• 16.7 Shells of Revolution with Constant Spin About their Axes of Revolution (p. 433)
• 16.8 Spinning Disk (p. 436)
• References (p. 436)
• 17 Thermal Effects (p. 438)
• 17.1 Stress Resultants (p. 438)
• 17.2 Equations of Motion (p. 440)
• 17.3 Plate (p. 443)
• 17.4 Arch, Ring, Beam, and Rod (p. 443)
• 17.5 Limitations (p. 444)
• References (p. 445)
• 18 Elastic Foundations (p. 446)
• 18.1 Equations of Motion for Shells on Elastic Foundations (p. 447)
• 18.2 Natural Frequencies and Modes (p. 447)
• 18.3 Plates on Elastic Foundations (p. 448)
• 18.4 Ring on Elastic Foundation (p. 449)
• 18.5 Donnell-Mushtari-Vlasov Equations with Transverse Elastic Foundation (p. 451)
• 18.6 Forces Transmitted into the Base of the Elastic Foundation (p. 451)
• 18.7 Vertical Force Transmission Through the Elastic Foundation of a Ring on a Rigid Wheel (p. 453)
• 18.8 Response of a Shell on an Elastic Foundation to Base Excitation (p. 458)
• 18.9 Plate Examples of Base Excitation and Force Transmission (p. 460)
• 18.10 Natural Frequencies and Modes of a Ring on an Elastic Foundation in Ground Contact at a Point (p. 462)
• 18.11 Response of a Ring on an Elastic Foundation to a Harmonic Point Displacement (p. 464)
• References (p. 468)
• 19 Similitude (p. 469)
• 19.1 General Similitude (p. 469)
• 19.2 Derivation of Exact Similitude Relationships for Natural Frequencies of Thin Shells (p. 471)
• 19.3 Plates (p. 472)
• 19.4 Shallow Spherical Panels of Arbitrary Contours (Influence of Curvature) (p. 474)
• 19.5 Forced Response (p. 476)
• 19.6 Approximate Scaling of Shells Controlled by Membrane Stiffness (p. 477)
• 19.7 Approximate Scaling of Shells Controlled by Bending Stiffness (p. 478)
• References (p. 479)
• 20 Interactions with Liquids and Gases (p. 480)
• 20.1 Fundamental Form in Three-Dimensional Curvilinear Coordinates (p. 480)
• 20.2 Stress-Strain-Displacement Relationships (p. 482)
• 20.3 Energy Expressions (p. 486)
• 20.4 Equations of Motion of Vibroelasticity with Shear (p. 487)
• 20.5 Example: Cylindrical Coordinates (p. 492)
• 20.6 Example: Cartesian Coordinates (p. 493)
• 20.7 One-Dimensional Wave Equations for Solids (p. 495)
• 20.8 Three-Dimensional Wave Equations for Solids (p. 496)
• 20.9 Three-Dimensional Wave Equations for Inviscid Compressible Liquids and Gases (Acoustics) (p. 498)
• 20.10 Interface Boundary Conditions (p. 502)
• 20.11 Example: Acoustic Radiation (p. 502)
• 20.12 Incompressible Liquids (p. 505)
• 20.13 Example: Liquid on Plate (p. 506)
• 20.14 Orthogonality of Natural Modes for Three-Dimensional Solids, Liquids, and Gases (p. 511)
• References (p. 513)
• 21 Discretizing Approaches (p. 515)
• 21.1 Finite Differences (p. 515)
• 21.2 Finite Elements (p. 520)
• 21.3 Free and Forced Vibration Solutions (p. 533)
• References (p. 538)
• Index (p. 539)

Author notes provided by Syndetics