Wave processes in the locally nonhomogeneous solids

There is proposed a method of studying wave processes in locally nonhomogeneous solids with account for geometrically non-uniform surface. The method is based on the equation system of the locally nonhomogeneous elastic solid model obtained within the local gradient approach and the use of averaging operation to separate oscillatory and slowly variable over period of oscillation components of displacement and density fields.
At the example of a layer there is illustrated an application of the method to study the frequencies of natural oscillations for different fixing conditions at the layer surfaces. It was established that the dependence of frequencies of natural oscillations of the layer on the characteristic sizes the nearsurface and structural nonhomogeneities in the case of the free layer surfaces is much higher comparing to the fixed  surfaces case.

  1. Eringen A. C. Nonlocal Continuum Field Theories. Springer, New York (2002).
  2. Wang Q., Liew K. Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures. Physics Letters A 363 (3) (2007) 236–242.
  3. Burak Y. I., Nagirnyi T. S. Mathematical modeling of local gradient processes in inertial thermomechanical systems. Int. Appl. Mech. 28, 775 (1992).
  4. Nahirnyj T., Tchervinka K. Mathematical Modeling of Structural and Near-Surface Non-Homogeneities in Thermoelastic Thin Films. Int. J. Eng. Sci, 91, 49–62 (2015).
  5. Nahirnyj T., Tchervinka K. Thermodynamic models and methods of thermomechanics with regard to the nearsurface and structural non-homogeneities. Bases of nanomechanics I. Lviv, Spolom, 2012. 264 p.
  6. Nahirnyj T., Tchervinka K. Basics of mechanics of local non-homogeneous elastic bodies. Bases of nanomechanics II. Lviv, Rastr-7, 2014. 168 p.
  7. Mytropolskyj Yu. A. Averaging method in nonlinear mechanics. (1971).
  8. Hrebennikov E. A. Averaging method in applied problems. (1986).
  9. Nahirnyj T., Tchervinka K. Modeling of wave processes in solids with regard to the effects of nearsurface nonhomogeneity. Visn. Lviv un-ty. Ser. mech.-mat. Iss. 54, 117–124 (1999)
  10. Nahirnyj T., Tchervinka K. Modeling and study of the temperature effect on natural oscillations of the layer. Visn. Lviv un-ty. Ser. mech.-mat. Iss. 60, 102–106 (2002).