Approximation of a supports stiffness influence on support coefficient values for a spring-hinged beam by quadratic functions

The paper proposes the approximation for the dependence of the beam first frequency on the torsional stiffness of its supports using quadratic analytical functions. For this purpose, a numerical solution of a beam's free vibration equation for a large range of torsional stiffness of supports is made and support coefficients are calculated. The obtained values are divided into three subbands, each of which is approximated by a quadratic function. This approach reduced the approximation error and allowed to use a quadratic polynomial. This allows solving the direct problem of analytical approximation, as well as solving the inverse problem of finding the required stiffness of the supports to achieve the required coefficient of supports and, accordingly, the frequency of vibration of the beam. Normalizing the obtained support coefficients is proposed for a more convenient estimation of the effect of their values on the first frequency of beam vibration. (paper)