Graduate Thesis Or Dissertation
 

Exact frequencies and mode shapes of a rotating beam

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/js956k408

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  • The exact frequencies and mode shapes of flexural vibration of a rotating beam are found. The beam has a linear mass and stiffness distribution. With certain simplifying assumptions, the kinetic and potential energies of the rotating beam are found. Hamilton's principle is then used to determine the equation governing the blade deflection and the boundary conditions. The equation governing the blade deflection is a fourth order linear differential equation with polynomial coefficients. By assuming the deflection to be represented by a power series, the exact solution to the differential equation is obtained. The rotating beam boundary conditions are then used to find the exact frequencies and mode shapes. The exact frequencies for cantilever and hinged beams with different rotation rates, mass and stiffness distributions, root offset, and tip mass are found. The exact results are then compared to the results obtained by some approximate methods.
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  • File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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