INVERSE PROBLEM FOR A TIMOSHENKO BEAM WITH AN ADDITIONAL VISCOELASTIC SUPPORT UNDER NONSTATIONARY DEFORMATION

The non-stationary loading of a mechanical system consisting beam hinged at the edges and an additional support installed in span is considered. deformation modeled on basis Timoshenko's hypotheses, taking into account influence rotatory inertia shear. described by partial differential equations, which solved analytically means expansion unknown functions relevant Fourier series further use Laplace integral transformation. It assumed that has linear-elastic linear-viscous components, displacements coincide point where connected to beam. reaction between replaced external concentrated force applied beam, varies time. law time variation this determined solving Volterra equation. inverse problem deformable solid mechanics solved, is, it deflection with known, whereas impulse load causing unknown. application connection are considered be known do not change process (when obtaining solution was supposed these could any points except for its ends). reduced two equations first kind regard unknowns disturbing plate support, analytical numerical method. Analytical relations calculation results specific parameters given. obtained work can used indirect measurement shock loads acting beams supports, only elastic but also characteristics taken account.