INVESTIGATION OF THE PASSAGE OF VIBRATIONS THROUGH A FIXED SECTION OF AN ELONGATED PLATE CAUSED BY THE ACTION OF THE AXIAL FORCE AT THE END

Abstract

A method has been developed for the experimental study of forced elastic vibrations of a cantilevered thin-walled structural element in the form of a rod-strip, excited due to the passage of vibrations through the section of a finite length fixed along one of the surfaces caused by axial loading by a harmonic force applied to the end of the fixed section. The experimental dependence of the amplitude values of the vibration accelerations of the point at the end of the console on the frequency of the excited bending vibrations of the end of the rod is obtained, indicating the passage of vibrations through the fixing section of the finite length, which occurs due to the transformation of longitudinal vibrations in the loading zone into longitudinal-transverse-shear vibrations of the rod-strip in the fixing zone, followed by their transformation into predominantly bending vibrations of the cantilever part of the rod. For the theoretical study of the described phenomenon, a transformational model of deformation of the rod-strip is constructed, taking into account the deformability of the fastening section of finite length on the basis of the refined model of S. Timoshenko. The cantilever part of the rod is represented by the classical Kirchhoff-Love model, taking into account geometric nonlinearity in determining axial deformations. The kinematic conditions of coupling of the fixed and cantilever parts of the rod are formulated. On the basis of the Hamilton-Ostrogradsky variational equation, the equations of motion of the non-fixed and fixed parts of the rod, as well as the boundary conditions for them and the force condition of conjugation of the marked parts of the rod are obtained. Numerical experiments have been carried out for a rod-strip made of aluminum alloy D16AT, showing a noticeable passage of vibrations through the fixing section of the final length into the cantilever part of the rod with a decrease in the dynamic shear modulus of the material to a certain value.