Free Vibration of Axially Loaded Shear Beams Carrying Elastically Restrained Lumped-Tip Masses via Asymptotic Timoshenko Beam Theory

摘要: AbstractClassical shear beam theory does not consider the rotation of cross sections. This paper studies free vibration axially loaded beams carrying lumped masses at elastically supported ends where rotational motion section is taken into account. By using asymptotic analysis Timoshenko theory, a unified analytical approach for dealing with free-vibration problems nonclassical subjected to axial compressive or tensile force according Engesser’s model presented. A simple characteristic equation derived translational and springs attached end masses. The resulting frequency compared classical one. condition causing collapse ones found. Natural frequencies are evaluated mode shapes given explicitly. influences spring coefficients, loads, inertia on natural ...