Exact analysis of structures with periodicity using U-transformation / H.C. Chan, C.W. Cai, Y.K. Cheung.

Format:

Book

Author/Creator:

Chan, H. C. (Hon Chuen)

Contributor:

Cai, C. W.

Cheung, Y. K.

Language:

English

Subjects (All):

Structural analysis (Engineering).

Mechanics, Analytic.

Transformation groups.

Physical Description:

1 online resource (348 p.)

Other Title:

Structures with periodicity using U-transformation

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, 1998.

Language Note:

English

Summary:

This book introduces an analytical method, the U-transformation method, for the exact analysis of structures with the periodic property. The physical meaning of U-transformation is fully explained and the application of this technique to derive exact analytical solutions for a wide variety of structures with the periodic property is thoroughly illustrated. The book also provides useful exact and explicit formulas for many practical engineering problems. Many of these solutions are new results that have just appeared in international journals. The practical engineering structures considered in

Contents:

PREFACE; CONTENTS; Chapter 1 UNCOUPLING OF THE DYNAMIC EQUATION FOR CYCLIC PERIODIC STRUCTURES AND U-TRANSFORMATION; 1.1 Dynamic Equation; 1.2 Mode Subspaces of Cyclic Periodic Structures; 1.3 U-Transformation; Chapter 2 ANALYTICAL SOLUTIONS FOR CYCLIC PERIODIC STRUCTURES; 2.1 Regular Polygon Frames; 2.1.1 Static Problem; 2.1.2 Natural Vibration; 2.1.3 Forced Vibration; 2.2 Prism Shells with Regular Polygon Cross Section; 2.2.1 Natural Vibration; 2.2.2 Buckling Load; Chapter 3 LINEAR PERIODIC STRUCTURES - DISCRETE SYSTEMS

3.1 Periodic Mass-Spring System with Single Degree of Freedom Substructure3.1.1 Periodic Mass-Spring System with Fixed Extreme Ends; 3.1.2 Periodic Mass-Spring System with Free Extreme Ends; 3.1.3 Periodic Mass-Spring System with One End Fixed and the Other Free; 3.2 Periodic Mass-Spring System with Two Degrees of Freedom Substructures; 3.3 Transverse Vibration of Plane Trusses; 3.3.1 Governing Equations; 3.3.2 Static Problem; 3.3.3 Natural Vibration; 3.3.4 Dynamic Response; Chapter 4 LINEAR PERIODIC STRUCTURES - CONTINUOUS SYSTEMS; 4.1 Continuous Beams - Static Displacements

4.1.1 Continuous Beam with Extreme Ends Simply Supported4.1.2 Continuous Beam with Extreme Ends Clamped; 4.1.3 Continuous Beam with One Extreme End Simply Supported and the Other Clamped; 4.2 Continuous Beams - Dynamic Analysis; 4.2.1 Natural Vibration; 4.2.2 Dynamic Response; 4.3 Continuous Beams with Periodic Elastic Supports; 4.3.1 Static Problem; 4.3.2. Natural frequency; 4.4 Continuous Deep Beams; 4.4.1. Uniformly Distributed Load; 4.4.2 Concentrated Load; 4.5 Continuous Plates; 4.5.1 Uniformly Distributed Load; 4.5.2 Concentrated Load; 4.6 Stiffened Plates

4.6.1 Static Solution of Stiffened Plates4.6.2 Stability Analysis of Stiffened Plates; 4.6.3 Natural Vibration of Stiffened Plates; Chapter 5 STRUCTURES WITH PERIODICITY IN TWO DIRECTIONS; 5.1 Governing Equation and Double U-Transformation; 5.2 Rectangular Orthogonal Networks - Lumped Mass System; 5.2.1 Dynamic Equation; 5.2.2. Natural Vibration; 5.2.3 Forced Vibration; 5.3 Rectangular Orthogonal Networks - Continuous System; 5.3.1 Governing Equation; 5.3.2 Natural Vibration; 5.3.3 Dynamic Response; 5.4 Rectangular Diagonal Networks - Lumped Mass System

5.5 Rectangular Diagonal Networks - Continuous System5.6 Rectangular Grids; 5.6.1 Static Problems; 5.6.2 Natural Vibration - Lumped Mass System; 5.6.3 Natural Vibration - Distributed Mass System; 5.7 Double Layer Grids; 5.7.1 Static Problems; 5.7.2 Natural Vibration; Chapter 6 EXACT SOLUTION OF THE FINITE ELEMENT EQUATION; 6.1 Beam Element; 6.1.1 Static Problem; 6.1.2 Buckling Load; 6.1.3. Natural Frequency; 6.1.4 Dynamic Response; 6.2 Plate Element; 6.2.1 Static Displacements; 6.2.2 Buckling Load; 6.2.3 Natural Frequency; 6.2.4 Dynamic Response; Chapter 7 NEARLY PERIODIC STRUCTURES

7.1 One Dimensional System

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 327-329) and index.

ISBN:

9789812815835

981281583X