9789810249281

Presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution.

Preface

v

U Transformation and Uncoupling of Governing Equations for Systems with Cyclic Bi-periodicity

1

(26)

Dynamic Properties of Structures with Cyclic Periodicity

1

(10)

Governing Equation

1

(1)

U Matrix and Cyclic Matrix

2

(4)

U Transformation and Uncoupling of Simultaneous Equations with Cyclic Periodicity

6

(3)

Dynamic Properties of Cyclic Periodic Structures

9

(2)

Uncoupling of Simulataneous Equations with Cyclic Periodicity for Variables with Two Subscripts

11

(4)

Double U Transformation

11

(2)

Uncoupling of Simulataneous Equations with Cyclic Periodicity for Variables with Two Subscripts

13

(2)

Uncoupling of Simultaneous Equations with Cyclic Bi-periodicity

15

(12)

Cyclic Bi-periodic Equation

15

(1)

Uncoupling of Cyclic Bi-periodic Equations

16

(4)

Uncoupling of Simultaneous Equations with Cyclic Bi-periodicity for Variables with Two Subscripts

20

(7)

Bi-periodic Mass-Spring Systems

27

(54)

Cyclic Bi-periodic Mass-Spring System

27

(17)

Static Solution

28

(4)

Example

32

(2)

Natural Vibration

34

(2)

Example

36

(3)

Forced Vibration

39

(3)

Example

42

(2)

Linear Bi-periodic Mass-Spring Systems

44

(37)

Bi-periodic Mass-Spring System with Fixed Extreme Ends

44

(6)

Natural Vibration Example

50

(5)

Forced Vibration Example

55

(2)

Bi-periodic Mass-Spring System with Free Extreme Ends

57

(5)

Natural Vibration Example

62

(5)

Forced Vibration Example

67

(2)

Bi-periodic Mass-Spring System with One End Fixed and the Other Free

69

(6)

Natural Vibration Example

75

(6)

Bi-periodic Structures

81

(44)

Continuous Truss with Equidistant Supports

81

(34)

Governing Equation

81

(9)

Static Solution

90

(4)

Example

94

(5)

Natural Vibration

99

(3)

Example

102

(5)

Forced Vibration

107

(5)

Example

112

(3)

Continuous Beam with Equidistant Roller and Spring Supports

115

(10)

Governing Equation and Static Solution

116

(5)

Example

121

(4)

Structures with Bi-periodicity in Two Directions

125

(78)

Cable Networks with Periodic Supports

125

(31)

Static Solution

128

(6)

Example

134

(5)

Natural Vibration

139

(5)

Example

144

(5)

Forced Vibration

149

(4)

Example

153

(3)

Grillwork with Periodic Supports

156

(19)

Governing Equation

159

(6)

Static Solution

165

(4)

Example

169

(6)

Grillwork with Periodic Stiffened Beams

175

(28)

Governing Equation

178

(7)

Static Solution

185

(6)

Example

191

(12)

Nearly Periodic Systems with Nonlinear Disorders

203

(60)

Periodic System with Nonlinear Disorders --- Monocoupled System

203

(16)

Governing Equation

204

(6)

Localized Modes in the System with One Nonlinear Disorder

210

(2)

Localized Modes in the System with Two Nonlinear Disorders

212

(7)

Periodic System with One Nonlinear Disorder --- Two-degree-coupling System

219

(20)

Governing Equation

220

(4)

Perturbation Solution

224

(5)

Localized Modes

229

(10)

Damped Periodic Systems with One Nonlinear Disorder

239

(24)

Forced Vibration Equation

239

(6)

Perturbation Solution

245

(10)

Localized Property of the Forced Vibration Mode

255

(8)

References

263

(2)

Nomenclature

265

(2)

Index

267

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Amazon no longer offers textbook rentals. We do!

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

Exact Analysis of Bi-Periodic Structures

9810249284

Supplemental Materials

Summary

Table of Contents

Supplemental Materials

Rewards Program