COVID-19 Update: We are currently shipping orders daily. However, due to transit disruptions in some geographies, deliveries may be delayed. To provide all customers with timely access to content, we are offering 50% off Science and Technology Print & eBook bundle options. Terms & conditions.
Vibration of Functionally Graded Beams and Plates - 1st Edition - ISBN: 9780128042281, 9780128042700

Vibration of Functionally Graded Beams and Plates

1st Edition

Authors: Snehashish Chakraverty Karan Kumar Pradhan
Paperback ISBN: 9780128042281
eBook ISBN: 9780128042700
Imprint: Academic Press
Published Date: 26th January 2016
Page Count: 248
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


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


No. of pages:
© Academic Press 2016
26th January 2016
Academic Press
Paperback ISBN:
eBook ISBN:

About the Authors

Snehashish Chakraverty

Prof. S. Chakraverty has 30 years of experience as a researcher and teacher. Presently he is working in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, as Senior (Higher Administrative Grade) Professor. Prior to this, he was with CSIR—Central Building Research Institute, Roorkee, India. After completing Graduation from St. Columba’s College (Ranchi University), his career started from the then University of Roorkee (currently Indian Institute of Technology Roorkee) and completed M. Sc. (Mathematics) and M. Phil. (Computer Applications) from there securing the first positions in the university. Dr. Chakraverty received his Ph.D. from IIT Roorkee in 1992. Thereafter, he completed his postdoctoral research at the Institute of Sound and Vibration Research (ISVR), University of Southampton, England and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill universities, Canada, during 1997–1999 and a visiting professor of the University of Johannesburg, South Africa, during 2011–2014. So far, he has authored/co-authored 21 books, published 374 research papers in journals and conferences; another book is in press and he is now writing two books. He is in the editorial boards of various international journals, book series and conferences. Prof. Chakraverty is the Chief Editor of International Journal of Fuzzy Computation and Modelling (IJFCM), Inderscience Publishers, Switzerland (, Associate Editor of the “Computational Methods in Structural Engineering” section of Frontiers in Built Environment and an editorial board member of Springer Nature Applied Sciences, IGI Research Insights Books, Springer Book Series of Modeling and Optimization in Science and Technologies, Coupled Systems Mechanics (Techno Press), Curved and Layered Structures (De Gruyter), Journal of Composites Science (MDPI), Engineering Research Express (IOP) and Applications and Applied Mathematics: An International Journal. He is also the reviewer of around 50 national and international journals of repute, and he was the president of the Section of Mathematical Sciences (including Statistics) of Indian Science Congress (2015-2016) and was the vice president of Orissa Mathematical Society (2011-2013). Prof. Chakraverty is a recipient of prestigious awards such as Indian National Science Academy (INSA) nomination under International Collaboration/Bilateral Exchange Program (with the Czech Republic), Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist Award (1997), BOYSCAST Fellow (DST), UCOST Young Scientist Award (2007, 2008), Golden Jubilee Director’s Award (CBRI; 2001), INSA International Bilateral Exchange Award ([2010-11 (selected but could not undertake), 2015 (selected)], and Roorkee University gold medals (1987, 1988) for first positions in M.Sc. and M. Phil. (Comp. Appl.). He has so far guided 18 Ph.D. students and is guiding 9 students currently. Prof. Chakraverty has undertaken around 16 research projects as principle investigator funded by international and national agencies, with a total worth of about Rs.1.5 crores. A good number of international and national conferences, workshops, and training programs have also been organized by him. His present research area includes differential equations (ordinary, partial, and fractional), numerical analysis and computational methods, structural dynamics (FGM, Nano) and fluid dynamics, mathematical and uncertainty Modeling, soft computing and machine intelligence (artificial neural network, fuzzy, interval and affine computations).

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

Ratings and Reviews