Free vibrations of bevelled cone thin-walled constructions of variable thickness

Abstract

One of the possible approaches to dynamic calculation of arbitrary profile supported by conic shell restrained on bevelled end is presented in the paper. Resolving system of ordinary differential equations is obtained in the frame of technical theory of shells with the help of Lagrange variation principle. Boundary value problem on definition of natural frequencies and oscillations forms of thin-walled construction of swept-back box beam of wing with shell variable thickness is solved by the finite-difference method of increased accuracy. The results of calculation of oscillation frequencies in dependence of shell geometrical parameters are tabulated; the forms of longitudinal oscillations are presented graphically. Unlike the well-known works the variable thickness of a construction in length is under consideration. The change of thin elastic construction thickness influences greatly on characteristic values of frequencies and forms of free oscillations which should be account while designing the construction elements of public and transport mechanical engineering, building constructions.