Vibration and stability of elastically supported beams carrying an attached mass under axial and tangential loads

An Additional Contribution on the Transverse Vibration of a Uniform Circular Thick Beam With Non-Classical Boundary Conditions

“…In addition, the functional relation of the recent note [1] o!ers an excellent opportunity for veri"cation by comparison with the equation derived by Saito and Otomi [3]. This paper was concerned with the problem of the vibration and stability of an elastically supported Timoshenko beam carrying an attached mass under axial and tangential loads, and the vibration characteristics of such beams and the in#uence of translational and rotational spring supports on the critical load were clari"ed.…”

Non-Linear Transverse Vibrations of a Simply Supported Beam Carrying Concentrated Masses

“…There are (n+1) equations in equation (3). Note that the viscous damping coefficient m n ; and external excitation with amplitude F n mþ1 and frequency O n are added to the equations.…”

Dynamic stability of a beam on multiple supports subject to pulsating conservative axial loads

“…Substituting (28) into (27) and equating the coefficients of the sin COT/2 and cos cox/2 terms, a set of linear homogeneous algebraic equations in terms of c and d can be obtained. The condition for non-trivial solutions is:…”