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E-raamat: Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates [Taylor & Francis e-raamat]

(Michigan State University, East Lansing, USA), (National University of Singapore, Singapore)
  • Formaat: 308 pages, 160 Tables, black and white; 115 Illustrations, black and white
  • Ilmumisaeg: 13-Aug-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429101984
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Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and PlatesSuurem pilt
  • Formaat: 308 pages, 160 Tables, black and white; 115 Illustrations, black and white
  • Ilmumisaeg: 13-Aug-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429101984
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates offers an introduction to structural vibration and highlights the importance of the natural frequencies in design. It focuses on free vibrations for analysis and design of structures and machine and presents the exact vibration solutions for strings, membranes, beams, and plates. This book emphasizes the exact solutions for free transverse vibration of strings, membranes, beams, and plates. It explains the intrinsic, fundamental, and unexpected features of the solutions in terms of known functions as well as solutions determined from exact characteristic equations. The book provides:A single-volume resource for exact solutions of vibration problems in strings, membranes, beams, and plates A reference for checking vibration frequency values and mode shapes of structural problemsGoverning equations and boundary conditions for vibration of structural elements Analogies of vibration problems Structural Vibration: Exact Solutionsfor Strings, Membranes, Beams, and Plates provides practicing engineers, academics, and researchers with a reference for data on a specific structural member as well as a benchmark standard for numerical or approximate analytical methods-- Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates offers an introduction to structural vibration and highlights the importance of the natural frequencies in design. It focuses on free vibrations for analysis and design of structures and machine and presents the exact vibration solutions for strings, membranes, beams, and plates. This book emphasizes the exact solutions for free transverse vibration of strings, membranes, beams, and plates. It explains the intrinsic, fundamental, and unexpected features of the solutions in terms of known functions as well as solutions determined from exact characteristic equations. The book provides:A single-volume resource for exact solutions of vibration problems in strings, membranes, beams, and plates A reference for checking vibration frequency values and mode shapes of structural problemsGoverning equations and boundary conditions for vibration of structural elements Analogies of vibration problems Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates provides practicing engineers, academics, and researchers with a reference for data on a specific structural member as well as a benchmark standard for numerical or approximate analytical methods.
Preface xi
About the Authors xiii
Chapter 1 Introduction to Structural Vibration 1(8)
1.1 What is Vibration?
1(1)
1.2 Brief Historical Review on Vibration of Strings, Membranes, Beams, and Plates
2(2)
1.3 Importance of Vibration Analysis in Structural Design
4(2)
1.4 Scope of Book
6(1)
References
6(3)
Chapter 2 Vibration of Strings 9(24)
2.1 Introduction
9(1)
2.2 Assumptions and Governing Equations for Strings
9(1)
2.3 Boundary Conditions
10(1)
2.4 Constant Property String
11(1)
2.5 Two-Segment Constant Property String
12(6)
2.5.1 Different Densities
13(3)
2.5.2 A Mass Attached on the Span
16(2)
2.5.3 A Supporting Spring on the Span
18(1)
2.6 Transformation for Nonuniform Tension and Density
18(2)
2.7 Constant Tension and Variable Density
20(5)
2.7.1 Power Law Density Distribution
20(2)
2.7.2 Exponential Density Distribution
22(3)
2.8 Variable Tension and Constant Density
25(5)
2.8.1 Vertical String Fixed at Both Ends
26(2)
2.8.2 Vertical String with Sliding Spring on Top and a Free Mass at the Bottom
28(2)
2.9 Free-Hanging Nonuniform String
30(1)
2.10 Other Combinations
31(1)
References
31(2)
Chapter 3 Vibration of Membranes 33(38)
3.1 Introduction
33(1)
3.2 Assumptions and Governing Equations
33(1)
3.3 Constant Uniform Normal Stress and Constant Density
34(8)
3.3.1 Rectangular Membrane
34(1)
3.3.2 Three Triangular Membranes
35(3)
3.3.3 Circular and Annular Membranes
38(2)
3.3.4 Circular Sector Membrane and Annular Sector Membrane
40(2)
3.4 Two-Piece Constant-Property Membranes
42(5)
3.4.1 Two-Piece Rectangular Membrane
42(2)
3.4.2 Two-Piece Circular Membrane
44(3)
3.5 Nonhomogeneous Membranes
47(13)
3.5.1 Rectangular Membrane with Linear Density Distribution
49(2)
3.5.2 Rectangular Membrane with Exponential Density Distribution
51(1)
3.5.3 Nonhomogeneous Circular or Annular Membrane
52(8)
3.5.3.1 Power Law Density Distribution
52(6)
3.5.3.2 A Special Annular Membrane
58(2)
3.6 Hanging Membranes
60(6)
3.6.1 Membrane with a Free, Weighted Bottom Edge
61(2)
3.6.2 Vertical Membrane with All Sides Fixed
63(3)
3.7 Discussion
66(2)
References
68(3)
Chapter 4 Vibration of Beams 71(68)
4.1 Introduction
71(1)
4.2 Assumptions and Governing Equations
71(2)
4.3 Single-Span Constant-Property Beam
73(12)
4.3.1 General Solutions
73(2)
4.3.2 Classical Boundary Conditions with Axial Force
75(7)
4.3.3 Elastically Supported Ends
82(1)
4.3.4 Cantilever Beam with a Mass at One End
83(1)
4.3.5 Free Beam with Two Masses at the Ends
84(1)
4.4 Two-Segment Uniform Beam
85(24)
4.4.1 Beam with an Internal Elastic Support
86(3)
4.4.2 Beam with an Internal Attached Mass
89(4)
4.4.3 Beam with an Internal Rotational Spring
93(2)
4.4.4 Stepped Beam
95(4)
4.4.5 Beam with a Partial Elastic Foundation
99(10)
4.5 Nonuniform Beam
109(27)
4.5.1 Bessel-Type Solutions
110(12)
4.5.1.1 The Beam with Linear Taper
113(1)
4.5.1.2 Two-Segment Symmetric Beams with Linear Taper
114(2)
4.5.1.3 Linearly Tapered Cantilever with an End Mass
116(6)
4.5.1.4 Other Bessel-Type Solutions
122(1)
4.5.2 Power-Type Solutions
122(8)
4.5.2.1 Results for m = 6, n = 2
128(1)
4.5.2.2 Results for m = 8, n = 4
128(2)
4.5.3 Isospectral Beams and the m = 4, n = 4 Case
130(3)
4.5.4 Exponential-Type Solutions
133(3)
4.6 Discussion
136(1)
References
137(2)
Chapter 5 Vibration of Isotropic Plates 139(76)
5.1 Introduction
139(1)
5.2 Governing Equations and Boundary Conditions for Vibrating Thin Plates
139(2)
5.3 Exact Vibration Solutions for Thin Plates
141(31)
5.3.1 Rectangular Plates with Four Edges Simply Supported
141(1)
5.3.2 Rectangular Plates with Two Parallel Sides Simply Supported
142(9)
5.3.3 Rectangular Plates with Clamped but Vertical Sliding Edges
151(4)
5.3.4 Triangular Plates with Simply Supported Edges
155(2)
5.3.5 Circular Plates
157(3)
5.3.6 Annular Plates
160(1)
5.3.7 Annular Sector Plates
161(11)
5.4 Governing Equations and Boundary Conditions for Vibrating Thick Plates
172(12)
5.5 Exact Vibration Solutions for Thick Plates
184(25)
5.5.1 Polygonal Plates with Simply Supported Edges
184(1)
5.5.2 Rectangular Plates
185(12)
5.5.3 Circular Plates
197(3)
5.5.4 Annular Plates
200(1)
5.5.5 Sectorial Plates
201(8)
5.6 Vibration of Thick Rectangular Plates Based on 3-D Elasticity Theory
209(2)
References
211(4)
Chapter 6 Vibration of Plates with Complicating Effects 215(40)
6.1 Introduction
215(1)
6.2 Plates with In-Plane Forces
215(9)
6.2.1 Rectangular Plates with In-Plane Forces
215(6)
6.2.1.1 Analogy with Beam Vibration
217(1)
6.2.1.2 Plates with Free Vertical Edge
218(3)
6.2.2 Circular Plates with In-Plane Forces
221(3)
6.3 Plates with Internal Spring Support
224(8)
6.3.1 Rectangular Plates with Line Spring Support
225(2)
6.3.1.1 Case 1: All Sides Simply Supported
226(1)
6.3.1.2 Case 2: Both Horizontal Sides Simply Supported and Both Vertical Sides Clamped
227(1)
6.3.2 Circular Plates with Concentric Spring Support
227(5)
6.3.2.1 Case 1: Plate Is Simply Supported at the Edge
229(1)
6.3.2.2 Case 2: Plate Is Clamped at the Edge
229(2)
6.3.2.3 Case 3: Free Plate with Support
231(1)
6.4 Plates with Internal Rotational Hinge
232(4)
6.4.1 Rectangular Plates with Internal Rotational Hinge
232(1)
6.4.1.1 Case 1: All Sides Simply Supported
233(1)
6.4.1.2 Case 2: Two Parallel Sides Simply Supported, with a Midline Internal Rotational Spring Parallel to the Other Two Clamped Sides
233(1)
6.4.2 Circular Plates with Concentric Internal Rotational Hinge
233(3)
6.4.2.1 Case 1: Plate Is Simply Supported at the Edge
235(1)
6.4.2.2 Case 2: Plate Is Clamped at the Edge
235(1)
6.4.2.3 Case 3: Plate Is Free at the Edge
236(1)
6.5 Plates with Partial Elastic Foundation
236(5)
6.5.1 Plates with Full Foundation
237(1)
6.5.2 Rectangular Plates with Partial Foundation
238(1)
6.5.3 Circular Plates with Partial Foundation
238(3)
6.5.3.1 Case 1: Plate Is Simply Supported at the Edge
240(1)
6.5.3.2 Case 2: Plate Is Clamped at the Edge
240(1)
6.5.3.3 Case 3: Plate Is Free at the Edge
240(1)
6.6 Stepped Plates
241(8)
6.6.1 Stepped Rectangular Plates
241(4)
6.6.1.1 Case l: Plate Is Simply Supported on All Sides
244(1)
6.6.1.2 Case 2: Plate Is Simply Supported on Opposite Sides and Clamped on Opposite Sides
244(1)
6.6.2 Stepped Circular Plates
245(4)
6.6.2.1 Case 1: Circular Plate with Simply Supported Edge
247(1)
6.6.2.2 Case 2: Circular Plate with Clamped Edge
247(1)
6.6.2.3 Case 3: Circular Plate with Free Edge
247(2)
6.7 Variable-Thickness Plates
249(3)
6.7.1 Case l: Constant Density with Parabolic Thickness
251(1)
6.7.2 Case 2: Parabolic Sandwich Plate
252(1)
6.8 Discussion
252(1)
References
253(2)
Chapter 7 Vibration of Nonisotropic Plates 255(36)
7.1 Introduction
255(1)
7.2 Orthotropic Plates
255(25)
7.2.1 Governing Vibration Equation
255(3)
7.2.2 Principal Rigidities for Special Orthotropic Plates
258(4)
7.2.2.1 Corrugated Plates
258(1)
7.2.2.2 Plate Reinforced by Equidistant Ribs/Stiffeners
259(1)
7.2.2.3 Steel-Reinforced Concrete Slabs
260(1)
7.2.2.4 Multicell Slab with Transverse Diaphragm
261(1)
7.2.2.5 Voided Slabs
261(1)
7.2.3 Simply Supported Rectangular Orthotropic Plates
262(1)
7.2.4 Rectangular Orthotropic Plates with Two Parallel Sides Simply Supported
262(3)
7.2.4.1 Two Parallel Edges (i.e., y = 0 and y = b) Simply Supported, with Simply Supported Edge x = 0 and Free Edge x = a (designated as SSSF plates)
264(1)
7.2.4.2 Two Parallel Edges (i.e., y = 0, and y = b) Simply Supported, with Clamped Edge x = 0 and Free Edge x = a (designated as SCSF plates)
264(1)
7.2.4.3 Two Parallel Edges (i.e., y = 0 and y = b) Simply Supported, with Clamped Edges x = 0 and x = a (designated as SCSC plates)
265(1)
7.2.4.4 Two Parallel Edges (i.e., y = 0 and y = b) Simply Supported, with Clamped Edge x = 0 and Simply Supported Edge x = a (designated as SCSS plates)
265(1)
7.2.4.5 Two Parallel Edges (i.e., y = 0 and y = b) Simply Supported, with Free Edges x = 0 and x = a (designated as SFSF plates)
265(1)
7.2.5 Rectangular Orthotropic Thick Plates
265(14)
7.2.6 Circular Polar Orthotropic Plates
279(1)
7.3 Sandwich Plates
280(1)
7.4 Laminated Plates
281(5)
7.5 Functionally Graded Plates
286(3)
7.6 Concluding Remarks
289(1)
References
290(1)
Index 291
C.Y. Wang, Michigan State University

C.M. Wang, National University of Singapore
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