Vibration of Functionally Graded Beams and Plates

Dr. Snehashish Chakraverty is a Senior Professor in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, with over 30 years of teaching and research experience. A gold medalist from the University of Roorkee (now IIT Roorkee), he earned his Ph.D. from IIT Roorkee and completed post-doctoral work at the University of Southampton (UK) and Concordia University (Canada). He has also served as a visiting professor in Canada and South Africa. Dr. Chakraverty has authored/edited 38 books and published over 495 research papers. His research spans differential equations (ordinary, partial, fractional), numerical and computational methods, structural and fluid dynamics, uncertainty modeling, and soft computing techniques. He has guided 27 Ph.D. scholars, with 10 currently under his supervision.He has led 16 funded research projects and hosted international researchers through prestigious fellowships. Recognized in the top 2% of scientists globally (Stanford-Elsevier list, 2020–2024), he has received numerous awards including the CSIR Young Scientist Award, BOYSCAST Fellowship, INSA Bilateral Exchange, and IOP Top Cited Paper Awards. He is Chief Editor of International Journal of Fuzzy Computation and Modelling and serves on several international editorial boards.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.

• 1. Introduction2. Origin and basics of functionally graded structural members2.1. History of FG materials2.2. Variation of material properties (power-law and exponential laws)3. Analytical and numerical methods3.1. History of various methods3.2. Analytical Methods3.3. Computational procedure of numerical method(s)4. Functionally graded beams4.1. Power-law variation4.2. Shear deformation beam theories4.3. Kinematic relations 4.4. Vibration of FG beams5. Functionally graded plates5.1. Power-law and exponential law variation5.2. Classical plate theory5.3. Kinematic relations6. Vibration of rectangular FG plates 6.1. Power-law variation6.2. Exponential law variation7. Vibration of circular and elliptic FG plates 8. Vibration of triangular FG plates 9. Functionally graded plates with complicating effects9.1. Thermal environments9.2. Elastic foundations9.3. Piezoelectricity10. Practical examples and experimental studies