In this book, uncertainty modeling of nanobeams, microbeam, and FG beams is presented using non-probabilistic approaches which include interval and fuzzy concepts.

Dr. Subrat Kumar Jena presently working as a Postdoctoral Fellow at the Department of Applied Mechanics in the Indian Institute of Technology Delhi, New Delhi, India. His academic journey includes an enriching tenure as an Honorary Postdoctoral Fellow at the Nonlinear Multifunctional Composites - Analysis & Design (NMCAD) Lab, Department of Aerospace Engineering, Indian Institute of Science (IISc), Bengaluru, India, under the mentorship of Prof. Dineshkumar Harursampath. Dr. Jena holds a PhD from the Department of Mathematics, National Institute of Technology Rourkela, Odisha, India, supervised by Prof. S. Chakraverty. His research expertise encompasses Computational Solid Mechanics, Multifunctional Materials, Applied Mathematics, Mathematical Modelling, and Uncertainty Quantification. Dr. Jena earned his M.Sc. in Mathematics and Scientific Computing from Motilal Nehru National Institute of Technology Allahabad (NIT Allahabad), Prayagraj, India. His research contributions are widely recognized, with 34 research papers in peer-reviewed international journals, 2 international conference papers, 9 book chapters, and 4 books (2 other books are ongoing) to his credit. Recently, Dr. Jena has been honoured with the "Mathematics 2022 Best PhD Thesis Award" by the Mathematics Journal, Basel, Switzerland, for his exceptional research work. This accolade came with a prize of CHF 500 and a certificate, marking a significant milestone in his academic journey. In addition, Dr. Jena has received an IOP Publishing Top-Cited Paper Award in 2021 and 2022 from India, published across the entire IOP Publishing journal portfolio in the past three years i.e., 2018-2020 and 2019-2021, respectively, for his paper that ranked among the top 1% of the most-cited papers in the materials subject category. In 2020-2021, one of his papers published in ZAMM - Journal of Applied Mathematics and Mechanic (Wiley) was among the most cited papers. Furthermore, three of his papers have been recognized as the best-cited papers published in the Curved and Layered Structures Journal (De Gruyter). His contributions to the field of shell buckling, particularly in the area of static or dynamic analysis of general structures, have been acknowledged, as he is included in the Shell Buckling website as "Shell Buckling People." He has also featured in Stanford University's Top 2% Most Influential Scientists List multiple times. Dr. Jena's eminence as a reviewer and guest editor for many prestigious international journals is underscored by his review of over 100 manuscripts.

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 a 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 University of Roorkee (now Indian Institute of Technology, Roorkee) and did M.Sc. (Mathematics) and M.Phil. (Computer Applications) from the said institute securing the first positions in the university. Dr. Chakraverty received his Ph.D. from IIT-Roorkee in 1993. Thereafter, he did his post-doctoral research at the 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, during 1997-1999 and visiting professor at the University of Johannesburg, Johannesburg, South Africa, during 2011-2014. He has authored/co-authored/edited 31 books, published 430 research papers (till date) in journals and conferences, and two books are ongoing. 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 Publisher, Switzerland (http://www.inderscience.com/ijfcm), associate editor of Computational Methods in Structural Engineering, Frontiers in Built Environment and Curved and Layered Structures (De Gruyter) and happens to be the 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), 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 - Orissa Mathematical Society (2011-2013). Prof. Chakraverty is a recipient of prestigious awards, viz. 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 (CBRI) Award (2001), INSA International Bilateral Exchange Award ([2010-2011] selected but could not undertake [2015] selected), Roorkee University Gold Medals (1987, 1988) for first positions in M.Sc. and M.Phil. (Computer Application). He is in the list of 2% world scientists (2020 and 2021) in Artificial Intelligence and Image Processing category based on an independent study done by Stanford University scientists. Prof. Chakraverty has received an IOP Publishing Top-Cited Paper Award in 2021 and 2022 from India, published across the entire IOP Publishing journal portfolio in the past three years i.e., 2018-2020 and 2019-2021, respectively, for his paper that ranked among the top 1% of the most-cited papers in the materials subject category. In 2020-2021, one of his papers published in ZAMM - Journal of Applied Mathematics and Mechanic (Wiley) was among the most cited papers. He has already guided 25 Ph.D. students and 12 are ongoing. Prof. Chakraverty has undertaken around 16 research projects as a principal investigator funded by international and national agencies totalling about Rs. 1.5 crores. He has hoisted around eight international students with different international/national fellowships to work in his group as PDF, Ph.D., visiting researchers for different periods. 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 modelling, soft computing and machine intelligence (artificial neural network, fuzzy, interval, and affine computations).

1. Introduction to Structural Uncertainties and Micro-, Nano-, and Functionally Graded Beams. 2. Preliminaries. 3. Vibration of Euler-Bernoulli Nanobeam with Uncertainty. 4. Stability Analysis of Euler-Bernoulli Nanobeam with Uncertainty. 5. Vibration of Nanobeam Based on One-Variable First-Order Shear Deformation Beam Theory in Uncertain Environment. 6. Stability Analysis of Timoshenko Nanobeam with Uncertainty. 7. Vibrations of Functionally Graded Beam with Uncertainty. 8. Vibration of Functionally Graded Beam with Complicating Effects in Uncertain Environment.