Vibration of Functionally Graded Beams and Plates

Vibration of Functionally Graded Beams and Plates uses numerically efficient computational techniques to analyze vibration problems associated with FG beams and plates. Introductory material on FG materials and structural members, as well as a range of vibration and shear deformation theories are discussed, providing a valuable summary of these broader themes.

The latest research and analysis of vibration in FG materials is presented in an application-oriented manner, linking the research to its importance in fields such as aerospace, nuclear power, and automotive engineering.

The book also features research on the complicating effects of thermal environments, piezoelectricity, and elastic foundations. The innovative computational procedures and simulation results are shown in full throughout, providing a uniquely valuable resource for users of numerical modeling software.

This book is essential reading for any researcher or practitioner interested in FG materials, or the design of technology for the nuclear power, aerospace, and automotive industries.

Defines the basic preliminaries of vibration and FG materialsIntroduces historical background and recent developments in functionally graded materials with references for further readingShows computational procedures with simulation resultsIncludes many easy to understand example problemsPresents various analytical and numerical procedures for each solution

1.      Introduction
2.      Origin and basics of functionally graded structural members
2.1. History of FG materials
2.2. Variation of material properties (power-law and exponential laws)
3.      Analytical and numerical methods
3.1. History of various methods
3.2. Analytical Methods
3.3. Computational procedure of numerical method(s)
4.      Functionally graded beams
4.1. Power-law variation
4.2. Shear deformation beam theories
4.3. Kinematic relations 
4.4. Vibration of FG beams
5.       Functionally graded plates
5.1. Power-law and exponential law variation
5.2. Classical plate theory
5.3. Kinematic relations
6.       Vibration of rectangular FG plates 
6.1. Power-law variation
6.2. Exponential law variation
7.      Vibration of circular and elliptic FG plates 
8.      Vibration of triangular FG plates 
9.      Functionally graded plates with complicating effects
9.1. Thermal environments
9.2. Elastic foundations
9.3. Piezoelectricity
10.  Practical examples and experimental studies