Vibration of Functionally Graded Beams and Plates

Vibration of Functionally Graded Beams and Plates

1st Edition - January 26, 2016

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  • Authors: Snehashish Chakraverty, Karan Kumar Pradhan
  • eBook ISBN: 9780128042700
  • Paperback ISBN: 9780128042281

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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.

Key Features

  • Defines the basic preliminaries of vibration and FG materials
  • Introduces historical background and recent developments in functionally graded materials with references for further reading
  • Shows computational procedures with simulation results
  • Includes many easy to understand example problems
  • Presents various analytical and numerical procedures for each solution


Researchers in materials and mechanics of materials, and designers of thermal resistant technology for nuclear power generation, aerospace, automotive and structural engineering

Table of Contents

    • Chapter 1: Introduction
      • Abstract
      • 1.1 Structural Beams and Plates
      • 1.2 Background of Composites
      • 1.3 Vibration Preliminaries
    • Chapter 2: Origin and Basics of Functionally Graded Structural Members
      • Abstract
      • 2.1 History and Application of FG Composites
      • 2.2 Variation of Material Properties
      • 2.3 Beam and Plate Theories
      • 2.4 Governing Equations
    • Chapter 3: Analytical and Numerical Methods
      • Abstract
      • 3.1 History of Various Methods
      • 3.2 Analytical Methods
      • 3.3 Numerical Method(s)
    • Chapter 4: Functionally Graded Beams
      • Abstract
      • 4.1 Vibration of Uniform FG Beam
      • 4.2 Concluding Remarks
    • Chapter 5: Vibration Problems of Functionally Graded Rectangular Plates
      • Abstract
      • 5.1 Numerical Modeling
      • 5.2 Convergence and Comparison Studies
      • 5.3 Results and Discussions
      • 5.4 Concluding Remarks
    • Chapter 6: Vibration Problems of Functionally Graded Elliptic Plates
      • Abstract
      • 6.1 Numerical Modeling
      • 6.2 Convergence and Comparison Studies
      • 6.3 Results and Discussions
      • 6.4 Concluding Remarks
    • Chapter 7: Vibration Problems of Functionally Graded Triangular Plates
      • Abstract
      • 7.1 Types of FG Triangular Elements
      • 7.2 Numerical Modeling
      • 7.3 Convergence and Comparison Studies
      • 7.4 Results and Discussions
      • 7.5 Concluding Remarks
    • Chapter 8: Complicating Effects
      • Abstract
      • 8.1 Winkler and Pasternak Foundations
      • 8.2 Thermal Environments
      • 8.3 Piezoelectricity
      • 8.4 Concluding Remarks
    • Chapter 9: Practical Examples and Experimental Studies
      • Abstract
      • 9.1 Practical Applications
      • 9.2 Experimental Studies
    • References
    • Index

Product details

  • No. of pages: 248
  • Language: English
  • Copyright: © Academic Press 2016
  • Published: January 26, 2016
  • Imprint: Academic Press
  • eBook ISBN: 9780128042700
  • Paperback ISBN: 9780128042281

About the Authors

Snehashish Chakraverty

Dr. Snehashish Chakraverty has over thirty years of experience as a teacher and researcher. Currently, he is a Senior Professor in the Department of Mathematics (Applied Mathematics Group) at the National Institute of Technology Rourkela, Odisha, India. He has a Ph.D. from IIT Roorkee in Computer Science. Thereafter he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill Universities, Canada, and visiting professor at the University of Johannesburg, South Africa. He has authored/co-authored 14 books, published 315 research papers in journals and conferences, and has four more books in development. Dr. Chakraverty is on the Editorial Boards of various International Journals, Book Series and Conferences. Dr. Chakraverty is the Chief Editor of the International Journal of Fuzzy Computation and Modelling (IJFCM), Associate Editor of Computational Methods in Structural Engineering, Frontiers in Built Environment, and is the Guest Editor for several other journals. He was the President of the Section of Mathematical sciences (including Statistics) of the Indian Science Congress. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy and Interval Computations), Numerical Analysis, Mathematical Modeling, Uncertainty Modelling, Vibration and Inverse Vibration Problems.

Affiliations and Expertise

Full Professor, Department of Mathematics, Applied Mathematics Group, National Institute of Technology Rourkela, Rourkela, Odisha, India

Karan Kumar Pradhan

Karan Kumar Pradhan is the Assistant Professor (NPIU, TEQIP-III) in Department of Basic Science, Parala Maharaja Engineering College, Berhampur (Odisha). Formerly, he was the Senior Research Fellow, Department of Mathematics, National Institute of Technology, Rourkela, India and also the recipient of SERB National Post-Doctoral Fellowship. KK Pradhan’s research interests are numerical modeling, vibration problems, and structural members.

Affiliations and Expertise

Senior Research Fellow, Dept of Mathematics, National Institute of Technology, Rourkela, India

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