Parametric Dependence of Spectral Properties of Elastic Vibrations in Composite Thin Films

Abstract

Solution for the long-wavelength region of the elastic vibration spectrum is obtained in an explicit form for a bi-layered plate based on recently proposed approach, which significantly simplifies both numeric and analytic studies of layered structures. We explore the behavior in the full range of elastic moduli, mass densities, and thicknesses of the layers on account of properly defined scaled parameters. The analysis reveals some non-trivial properties of the spectrum in composite free plates. In particular, it is shown that dependence of acoustic properties on material parameters of the added layer can be, rather unexpectedly, strongly non-monotonous. Thus, for a number of natural modes with the increase of a thickness ratio of a stiffer material the eigenfrequency may, e.g., decrease before it starts increasing, or have a sharp rise followed by a significant drop and only then resumes a steady growth. A quasi-oscillatory behavior is also possible. The property of avoided crossing between spectral branches allows to establish a continuous one-to-one correspondence between surface or interface modes and volume acoustic waves at shorter wavelengths, on one side, and fundamental or gapped modes at long wavelengths, on the other side. For composites with non-symmetric stacking the existence of a spectral property reminiscent of the A and S mode alternation of the Lamb solutions is demonstrated. We also discuss the implications of the above results to the electron-phonon heat exchange in composite nanostructures.