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Mathematical Techniques for Vibrations and Fluid Structure Interaction Theory and Applications

Overview:

This proposed edited volume presents a coherent mathematical and computational toolkit for vibration phenomena and coupled fluid–structure interaction (FSI), with a special focus on cylindrical shells and multi-layered functionally graded material (FGM) structures. The book bridges foundational modeling (PDE formulation, boundary/interface conditions, non dimensionalization, and energy methods) with practical solution approaches (separation of variables, integral transforms, perturbation and asymptotic techniques) and modern numerical methods (finite difference/finite element/spectral schemes, eigenvalue solvers, and time integration).

Beyond classical vibration theory, the volume addresses modeling ingredients frequently required in current research and engineering analysis: ring-support and stiffener effects, layered construction, temperature dependence, and parametric sensitivity for shell structures. It also provides a structured entry to FSI: coupling conditions, added-mass effects, stability considerations, and algorithmic strategies for partitioned and monolithic coupling. Worked examples and focused case studies demonstrate how analytical insight and computation reinforce each other for reliable prediction and design guidance.

The volume is intended for graduate students, researchers, and practitioners in applied mathematics, mechanical/aerospace/civil engineering, and computational mechanics who require a mathematically grounded pathway from governing equations to validated simulation and design-level conclusions.

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