Dynamic buckling of guyed stacks, masts and columns with constant inertia and algebraic polynomials generated by use of operator \(T_ n\) attached to Bessel functions (Q1068585)

A new method of analysis of the dynamic critical load of columns, guyed stacks and masts with constant inertia, under the combined action of horizontal loads, axial load and uniformly distributed loads along the vertical axis is presented. The integro-differential formulation of the problem leads to fourth- and fifth-order partial differential equations. In addition to the solution of the equation of motion in expansion series, the new method of solution proposed to solve the fifth-order partial differential equation has led to the differential equation of the plate on elastic foundations in the old Winkler hypothesis. Moreover, the operator \(T_ n\), attached to the Bessel functions \(J_ v\), has been used to generate a new set of algebraic polynomials.