Engineering Physics Annotation << Back LINEARIZATION OF THE STATE EQUATION FOR COMPOSITE ROD IN ESTIMATION OF NATURAL FREQUENCIES OF LONGITUDINAL VIBRATIONS I.A. TARASYUK, A.S. KRAVCHUK The paper is devoted to the investigation of longitudinal vibrations of composite rods made of nonlinearly elastic and hereditarily viscoelastic materials. For the fi rst time, the instantaneous deformation functions of the material components are modelled by means of the three-linear Prandtl’s diagrams with different instantaneous proportionality limits and tangential Young’s moduli in compression and tension. To solve the problem, it is applied a homogenization method based on estimation of the effective deformation characteristics using the Voigt’s and the Reuss’ hypotheses. The effective instantaneous secant and tangential Young’s moduli, proportionality limits, as well as the creep and relaxation kernels of the material are obtained in the explicit form. In the simplest cases, it is obtained the analytical estimation of the infl uence of the components deformation characteristics on the natural frequencies of longitudinally and transversely layered, as well as structurally heterogeneous rods. It became possible after linearization of the effective Prandtl’s diagram based on the criterion of the equality of the specifi c potential energy of the rod deformation. Key words: longitudinal vibrations, composite material, homogenization, nonlinear elasticity, nonlinear hereditary viscoelasticity, rheology. Contacts: E-mail: ivan.a.tarasyuk@gmail.com, E-mail: ask_belarus@inbox.ru Pp. 63-69.