Abstract
Nonlinear transverse vibrations of composite rods pre-loaded with lagging arranged symmetrically on both sides of the axis of the composite rod under the action of a statically applied transverse load are investigat-ed. The cases of attaching the lagging only to the ends of the composite rod, as well as when the laggings are continuously attached to the composite rod along its entire length, are considered. The results of the study of nonlinear transverse vibrations of composite rods under the action of a statically applied transverse load are presented. When conducting studies of transverse vibrations of composite rods, solutions of differential equations of vibration of prestressed through beams and stiffening cores of high-rise buildings are obtained. The obtained differential equations of vibration of composite rods allow us to determine the dynamic char-acteristics of prestressed through beams under various linear and boundary conditions. A method for com-posing differential equations of free and forced oscillations of prestressed through beams and stiffening cores of high-rise buildings and solving differential equations under various linear and nonlinear boundary conditions is developed.
 Expressions are given for determining the longitudinal forces and torques at the ends of the rod at any lo-cation of the lagging from the axis and at any different stiffness of the lagging
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