Control of extended beam dynamic behavior by means of supports at temperature changes

The dynamic behavior of beam structures at transient loads is largely determined by the spectrum of their natural frequencies of bending vibrations, in which the first natural frequency is usually the most dangerous. Changing the beam temperature results in a longitudinal force that shifts the spectrum of natural frequencies of bending vibrations into a dangerous resonant area and can even lead to a loss of beam stability when it reaches a critical value. An effective way to control the dynamic behavior of the beam is the reasonable choice of the support system, however, such a design approach is practically not considered in the known literature.This paper proposes a method of reasonable selection of a support scheme for rectilinear multi-span beams in order to provide the given values of the first eigen frequency of bending vibrations and the first critical load due to the action of axial force caused by changing the temperature of the beam. The technique is based on the known positions of beam vibration theory, Euler stability theory and uses support coefficients, which are pre-normalized to achieve comparable values, as a criterion for selecting the support scheme. The selected support scheme provides the specified value of the first eigen frequency, the value of the first critical temperature, or both at the same time.According to the developed methodology, comparative calculations of the pipeline by the finite element method for beam and shell models were carried out, which showed good convergence of results for all controlled parameters. The proposed approach can be used in designing structures of extended beams for control of their own frequency of the spectrum of vibrations and critical force (or temperature) by means of a reasonable selection of appropriate support systems.