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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.
