| Preface |
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xi | |
| About the Authors |
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xiii | |
| Chapter 1 Introduction to Structural Vibration |
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1 | (8) |
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1 | (1) |
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1.2 Brief Historical Review on Vibration of Strings, Membranes, Beams, and Plates |
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2 | (2) |
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1.3 Importance of Vibration Analysis in Structural Design |
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4 | (2) |
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6 | (1) |
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6 | (3) |
| Chapter 2 Vibration of Strings |
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9 | (24) |
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9 | (1) |
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2.2 Assumptions and Governing Equations for Strings |
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9 | (1) |
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10 | (1) |
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2.4 Constant Property String |
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11 | (1) |
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2.5 Two-Segment Constant Property String |
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12 | (6) |
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2.5.1 Different Densities |
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13 | (3) |
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2.5.2 A Mass Attached on the Span |
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16 | (2) |
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2.5.3 A Supporting Spring on the Span |
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18 | (1) |
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2.6 Transformation for Nonuniform Tension and Density |
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18 | (2) |
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2.7 Constant Tension and Variable Density |
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20 | (5) |
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2.7.1 Power Law Density Distribution |
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20 | (2) |
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2.7.2 Exponential Density Distribution |
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22 | (3) |
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2.8 Variable Tension and Constant Density |
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25 | (5) |
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2.8.1 Vertical String Fixed at Both Ends |
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26 | (2) |
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2.8.2 Vertical String with Sliding Spring on Top and a Free Mass at the Bottom |
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28 | (2) |
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2.9 Free-Hanging Nonuniform String |
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30 | (1) |
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31 | (1) |
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31 | (2) |
| Chapter 3 Vibration of Membranes |
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33 | (38) |
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33 | (1) |
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3.2 Assumptions and Governing Equations |
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33 | (1) |
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3.3 Constant Uniform Normal Stress and Constant Density |
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34 | (8) |
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3.3.1 Rectangular Membrane |
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34 | (1) |
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3.3.2 Three Triangular Membranes |
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35 | (3) |
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3.3.3 Circular and Annular Membranes |
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38 | (2) |
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3.3.4 Circular Sector Membrane and Annular Sector Membrane |
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40 | (2) |
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3.4 Two-Piece Constant-Property Membranes |
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42 | (5) |
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3.4.1 Two-Piece Rectangular Membrane |
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42 | (2) |
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3.4.2 Two-Piece Circular Membrane |
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44 | (3) |
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3.5 Nonhomogeneous Membranes |
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47 | (13) |
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3.5.1 Rectangular Membrane with Linear Density Distribution |
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49 | (2) |
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3.5.2 Rectangular Membrane with Exponential Density Distribution |
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51 | (1) |
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3.5.3 Nonhomogeneous Circular or Annular Membrane |
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52 | (8) |
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3.5.3.1 Power Law Density Distribution |
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52 | (6) |
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3.5.3.2 A Special Annular Membrane |
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58 | (2) |
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60 | (6) |
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3.6.1 Membrane with a Free, Weighted Bottom Edge |
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61 | (2) |
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3.6.2 Vertical Membrane with All Sides Fixed |
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63 | (3) |
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66 | (2) |
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68 | (3) |
| Chapter 4 Vibration of Beams |
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71 | (68) |
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71 | (1) |
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4.2 Assumptions and Governing Equations |
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71 | (2) |
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4.3 Single-Span Constant-Property Beam |
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73 | (12) |
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73 | (2) |
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4.3.2 Classical Boundary Conditions with Axial Force |
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75 | (7) |
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4.3.3 Elastically Supported Ends |
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82 | (1) |
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4.3.4 Cantilever Beam with a Mass at One End |
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83 | (1) |
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4.3.5 Free Beam with Two Masses at the Ends |
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84 | (1) |
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4.4 Two-Segment Uniform Beam |
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85 | (24) |
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4.4.1 Beam with an Internal Elastic Support |
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86 | (3) |
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4.4.2 Beam with an Internal Attached Mass |
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89 | (4) |
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4.4.3 Beam with an Internal Rotational Spring |
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93 | (2) |
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95 | (4) |
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4.4.5 Beam with a Partial Elastic Foundation |
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99 | (10) |
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109 | (27) |
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4.5.1 Bessel-Type Solutions |
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110 | (12) |
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4.5.1.1 The Beam with Linear Taper |
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113 | (1) |
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4.5.1.2 Two-Segment Symmetric Beams with Linear Taper |
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114 | (2) |
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4.5.1.3 Linearly Tapered Cantilever with an End Mass |
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116 | (6) |
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4.5.1.4 Other Bessel-Type Solutions |
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122 | (1) |
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4.5.2 Power-Type Solutions |
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122 | (8) |
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4.5.2.1 Results for m = 6, n = 2 |
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128 | (1) |
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4.5.2.2 Results for m = 8, n = 4 |
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128 | (2) |
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4.5.3 Isospectral Beams and the m = 4, n = 4 Case |
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130 | (3) |
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4.5.4 Exponential-Type Solutions |
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133 | (3) |
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136 | (1) |
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137 | (2) |
| Chapter 5 Vibration of Isotropic Plates |
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139 | (76) |
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139 | (1) |
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5.2 Governing Equations and Boundary Conditions for Vibrating Thin Plates |
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139 | (2) |
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5.3 Exact Vibration Solutions for Thin Plates |
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141 | (31) |
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5.3.1 Rectangular Plates with Four Edges Simply Supported |
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141 | (1) |
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5.3.2 Rectangular Plates with Two Parallel Sides Simply Supported |
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142 | (9) |
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5.3.3 Rectangular Plates with Clamped but Vertical Sliding Edges |
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151 | (4) |
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5.3.4 Triangular Plates with Simply Supported Edges |
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155 | (2) |
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157 | (3) |
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160 | (1) |
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5.3.7 Annular Sector Plates |
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161 | (11) |
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5.4 Governing Equations and Boundary Conditions for Vibrating Thick Plates |
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172 | (12) |
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5.5 Exact Vibration Solutions for Thick Plates |
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184 | (25) |
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5.5.1 Polygonal Plates with Simply Supported Edges |
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184 | (1) |
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185 | (12) |
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197 | (3) |
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200 | (1) |
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201 | (8) |
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5.6 Vibration of Thick Rectangular Plates Based on 3-D Elasticity Theory |
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209 | (2) |
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211 | (4) |
| Chapter 6 Vibration of Plates with Complicating Effects |
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215 | (40) |
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215 | (1) |
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6.2 Plates with In-Plane Forces |
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215 | (9) |
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6.2.1 Rectangular Plates with In-Plane Forces |
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215 | (6) |
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6.2.1.1 Analogy with Beam Vibration |
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217 | (1) |
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6.2.1.2 Plates with Free Vertical Edge |
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218 | (3) |
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6.2.2 Circular Plates with In-Plane Forces |
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221 | (3) |
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6.3 Plates with Internal Spring Support |
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224 | (8) |
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6.3.1 Rectangular Plates with Line Spring Support |
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225 | (2) |
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6.3.1.1 Case 1: All Sides Simply Supported |
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226 | (1) |
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6.3.1.2 Case 2: Both Horizontal Sides Simply Supported and Both Vertical Sides Clamped |
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227 | (1) |
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6.3.2 Circular Plates with Concentric Spring Support |
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227 | (5) |
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6.3.2.1 Case 1: Plate Is Simply Supported at the Edge |
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229 | (1) |
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6.3.2.2 Case 2: Plate Is Clamped at the Edge |
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229 | (2) |
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6.3.2.3 Case 3: Free Plate with Support |
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231 | (1) |
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6.4 Plates with Internal Rotational Hinge |
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232 | (4) |
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6.4.1 Rectangular Plates with Internal Rotational Hinge |
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232 | (1) |
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6.4.1.1 Case 1: All Sides Simply Supported |
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233 | (1) |
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6.4.1.2 Case 2: Two Parallel Sides Simply Supported, with a Midline Internal Rotational Spring Parallel to the Other Two Clamped Sides |
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233 | (1) |
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6.4.2 Circular Plates with Concentric Internal Rotational Hinge |
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233 | (3) |
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6.4.2.1 Case 1: Plate Is Simply Supported at the Edge |
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235 | (1) |
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6.4.2.2 Case 2: Plate Is Clamped at the Edge |
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235 | (1) |
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6.4.2.3 Case 3: Plate Is Free at the Edge |
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236 | (1) |
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6.5 Plates with Partial Elastic Foundation |
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236 | (5) |
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6.5.1 Plates with Full Foundation |
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237 | (1) |
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6.5.2 Rectangular Plates with Partial Foundation |
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238 | (1) |
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6.5.3 Circular Plates with Partial Foundation |
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238 | (3) |
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6.5.3.1 Case 1: Plate Is Simply Supported at the Edge |
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240 | (1) |
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6.5.3.2 Case 2: Plate Is Clamped at the Edge |
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240 | (1) |
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6.5.3.3 Case 3: Plate Is Free at the Edge |
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240 | (1) |
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241 | (8) |
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6.6.1 Stepped Rectangular Plates |
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241 | (4) |
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6.6.1.1 Case l: Plate Is Simply Supported on All Sides |
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244 | (1) |
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6.6.1.2 Case 2: Plate Is Simply Supported on Opposite Sides and Clamped on Opposite Sides |
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244 | (1) |
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6.6.2 Stepped Circular Plates |
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245 | (4) |
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6.6.2.1 Case 1: Circular Plate with Simply Supported Edge |
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247 | (1) |
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6.6.2.2 Case 2: Circular Plate with Clamped Edge |
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247 | (1) |
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6.6.2.3 Case 3: Circular Plate with Free Edge |
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247 | (2) |
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6.7 Variable-Thickness Plates |
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249 | (3) |
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6.7.1 Case l: Constant Density with Parabolic Thickness |
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251 | (1) |
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6.7.2 Case 2: Parabolic Sandwich Plate |
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252 | (1) |
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252 | (1) |
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253 | (2) |
| Chapter 7 Vibration of Nonisotropic Plates |
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255 | (36) |
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255 | (1) |
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255 | (25) |
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7.2.1 Governing Vibration Equation |
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255 | (3) |
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7.2.2 Principal Rigidities for Special Orthotropic Plates |
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258 | (4) |
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7.2.2.1 Corrugated Plates |
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258 | (1) |
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7.2.2.2 Plate Reinforced by Equidistant Ribs/Stiffeners |
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259 | (1) |
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7.2.2.3 Steel-Reinforced Concrete Slabs |
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260 | (1) |
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7.2.2.4 Multicell Slab with Transverse Diaphragm |
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261 | (1) |
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261 | (1) |
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7.2.3 Simply Supported Rectangular Orthotropic Plates |
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262 | (1) |
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7.2.4 Rectangular Orthotropic Plates with Two Parallel Sides Simply Supported |
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262 | (3) |
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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) |
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264 | (1) |
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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) |
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264 | (1) |
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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) |
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265 | (1) |
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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) |
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265 | (1) |
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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) |
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265 | (1) |
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7.2.5 Rectangular Orthotropic Thick Plates |
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265 | (14) |
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7.2.6 Circular Polar Orthotropic Plates |
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279 | (1) |
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280 | (1) |
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281 | (5) |
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7.5 Functionally Graded Plates |
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286 | (3) |
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289 | (1) |
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290 | (1) |
| Index |
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291 | |