Szukana fraza: [Abstract = "Tapered beams are more efficient compared to uniform beams as they provide a better distribution of mass and strength and also meet special functional requirements in many engineering applications. In this paper, the linear and non\-linear fundamental frequency parameter values of the tapered Timoshenko beams are evaluated by using the coupled displacement field \(CDF\) method and closed form expressions are derived in terms of frequency ratio as a function of slenderness ratio, taper ratio and maximum amplitude ratio for hinged\-hinged and clamped\-clamped beam boundary conditions."]

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