Providing free vibrations and stability of a multi-span beam under temperature changes by selecting the support system

This study presents a newly developed method for reasonable selection of boundary conditions and number of pinned intermediate supports for a straight multi-span beam. This method might help to obtain the required values of the first frequency of free vibrations and the critical load from the action of axial force, resulting from the changing the beam temperature. The method is based on known concepts of beam vibration and stability theories and uses support coefficients as a criterion for selecting the appropriate support system for a multi-span beam. These coefficients are obtained by solving the corresponding differential equations of the dynamic behavior of the beam and are determined only by the support conditions. Comparative calculations of the straight pipeline using the developed and finite element methods for beam and shell models were carried out, which showed good convergence. Normalization of the values of the support coefficients allowed to combine both conditions, for the first natural vibration frequency and the first critical force, and express it as a single criterion for the selection of the support system. The selection of the support system is shown as three general methods of fixing multi-beam beams with a constant span length. This approach can be applied to any straight beams and support conditions for which support coefficient values are known. To this end, a general algorithm for selecting a support system with known support coefficients and requirements for their normalization is given. The results obtained can be used in the calculation and design of any multi-span beam structures to control the values of their free vibration frequencies and stability by selecting an appropriate support system during the engineering design process.