Features of Vibrations of Structural Inhomogeneous Solid Media

摘要

Homogeneous or quasi-homogeneous classic models of deformation are generally used at a mathematical de-scription of deformation composite materials (CM). These theories, however, are limited within initial conditions and do not cover the most important properties of CM: heterogeneity of inertia and elasticity of components, their interaction when deforming, etc. Among the models that complement the classical theories, it is possible to allocate the so-called theory of mixture where CM is considered as two (or more) interacting homogeneous continuum. Therefore, the model increase of motion freedom degrees of the particles of such heterogeneous medium allows each component of CM to show their inertial properties. This leads to the identification of such exclusive features as "bifurcation of fre-quencies", i.e., to description of motion on each form of normal modes at two different frequencies. In the research this phenomenon was investigated by the analysis of biquadratic equation obtained at solving the proper value problem of heterogeneous medium, and was verified by testing the normal mode of frequencies of blades made of CM. In the particular case there was received a simple calculation formula for determination of bar technical frequencies from CM on the basis of the characteristic equation of natural vibrations. In this case the numerical results for the lower forms of the vibration normal mode coincide with the experimental data for homogeneous medium. The characteristic equation contains the introduced physical parameters of the two-component theory; therefore, it describes the other forms of vibration. However, in this case the freedom of structural fluctuations of CM each component is limited to their coupling and interaction, providing continuity and shared the compound materials.