This book presents a detailed and application-oriented approach to modeling and vibration analysis of multidirectional Functionally Graded (FG) nanostructures using advanced analytical, semi-analytical, and numerical methods. To design more efficient and durable nanostructures used in applications such as sensors, micro-pumps, drug delivery systems, or underwater pipelines, scientists are now turning to a special class of materials called FG Materials. These materials are not uniform; rather, their properties change gradually across the structure. This book deals with nanostructures where these property variations occur not just in one direction, but in multiple directions, which is a more realistic and effective design strategy. The authors investigate how these tiny structures vibrate when exposed to dynamic environments using accurate mathematical models. Such analysis is key for preventing failure, improving sensitivity, and optimizing designs in high-performance nano-devices. The book implements advanced analytical, semi-analytical, and numerical techniques, offering high accuracy and computational efficiency in vibration analysis. The authors incorporate various nonlocal theories to accurately capture small-scale effects essential for nanoscale structures and also present comparative case studies and parametric analyses to facilitate a deeper understanding of how material gradation affects vibration behavior. In addition, the book provides both analytical formulations and MATLAB-based implementations, enabling readers to apply concepts in real-world scenarios. The book is tailored for researchers and engineers involved in designing and analyzing next-generation nanoscale systems and bridges the theoretical development of nonlocal theories with practical implementation strategies to support the design and optimization of nanoscale devices and structures in various engineering fields.

Snehashish Chakraverty, Ph.D., is a Professor in the Department of Mathematics at the National Institute of Technology Rourkela, India.  He is a globally recognized academician and researcher with over 30 years of experience in the fields of mathematical modeling, structural mechanics, uncertainty quantification, and computational methods. Dr. Chakraverty has authored more than 35 books and 340 peer-reviewed journal articles published by reputed publishers. He has also served as the editor and editorial board member of numerous international journals and has received numerous national and international awards for his contributions to mathematical modeling and applied mechanics. His recent research spans soft computing, AI techniques in mechanics, and computational modeling of smart structures.

Akash Kumar Gartia is a Senior Research Fellow in the Department of Mathematics at the National Institute of Technology Rourkela, India. His research focuses on the mathematical modeling and vibration analysis of functionally graded nanostructures. He employs advanced computational techniques to investigate size-dependent behavior and dynamic responses of such advanced structures under various boundary and loading conditions. He has authored multiple peer-reviewed journal articles and book chapters and actively serves as a reviewer and guest editor for reputed international journals. His work contributes to the development of efficient, reliable models for next-generation nanostructures with practical relevance in engineering applications.