Numerically Stable form of Green’s Function for a Free-Free Uniform Timoshenko Beam

Beam models are widely applied in civil engineering, transport, and industry because the beams basic structural elements. When dealing with high-order modes of beam context applying modal analysis method, numerical instability issue affects numeric simulation accuracy many boundary conditions. There two solutions literature to overcome this shortcoming, namely refinement asymptotic form for high order reshaping terms within equation eliminate source instability. In paper, is signalled when standard Green’s function, which includes hyperbolic functions, a free-free Timoshenko length-long beam. A new way proposed based on set eigenfunctions, including an exponential construct function. To end, it starts from general function characteristic obtained; then, condition, associated differential operator distilled. The stability verified application results compared those obtained by using