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I need a technically sound yet practical study of a wind-turbine main shaft that pinpoints its vibration and bending behaviour. The core of the job is to build an analytical model—closed-form where possible—then back it up with a finite-element simulation so the theory and the numerics agree. Scope • Develop the governing equations for bending and torsional vibration of the hollow steel shaft, including boundary conditions representative of a hub and gearbox connection. • Extract natural…