Stability of Elastically Restrained Timoshenko Cantilevers With Attached Masses Subjected to a Follower Force

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Abstract
In this investigation, the individual and primarily the coupling effects on the critical load are assessed for a variety of parameters, such as elastic spring supports, concentrated masses (positioning, translational, and rotational inertia) as well as transverse shear deformation and rotatory inertia of the column. The problem, in its most general form, is reduced to a system of two-coupled partial-differential equations subject to the appropriate boundary conditions. A solution methodology is developed and successfully demonstrated through numerous examples.

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