ABSTRACT
A discrete-layer model is presented and applied to the free vibration of layered anisotropic spheres with coupling among the elastic, electric, and magnetic fields. Through-thickness approximations in the radial direction are pre-integrated and combined with independent approximations in the azimuthal and circumferential directions to provide estimates of the natural frequencies for a variety of representative geometries. Results are in excellent agreement with existing analytical studies and additional results are presented for higher-order spheroidal modes. Predictions of the level of influence of magnetoelectric coupling are also given.
ABSTRACT
Brillouin-light-scattering measurements and finite-element modeling of vibrational spectra in the range of 5-40 GHz are presented for an array of monocrystalline GaN nanowires with hexagonal cross sections. Analysis of the spectra is substantially complicated by the presence of a distribution of nanowire diameters. The measurements and calculations reveal a variety of modes with simple flexural, higher-order flexural, approximately 'plane-strain', approximately longitudinal and torsional displacement patterns that are similar to the corresponding modes of isotropic cylinders. The largest peaks in the spectra with acoustic angular wavenumbers in the range of 4 to ~15 µm(-1) were determined to arise from modes with relatively large transverse displacements, consistent with inelastic light scattering arising predominantly from surface ripple. These dominant modes have finite frequencies in the limit of zero wavenumber, corresponding to transverse standing waves. At higher wavenumbers, the spectra provide evidence for increased scattering through elasto-optic coupling, especially with respect to the emergence of a peak from a mode analogous to the longitudinal guided modes of thin films.
Subject(s)
Gallium/chemistry , Models, Chemical , Nanostructures/chemistry , Nanostructures/ultrastructure , Computer Simulation , Microwaves , Particle Size , Scattering, Radiation , VibrationABSTRACT
Elastic constants and cross-sectional dimensions of imprinted nanolines of poly(methyl methacrylate) (PMMA) on silicon substrates are determined nondestructively from finite-element inversion analysis of dispersion curves of hypersonic acoustic modes of these nanolines measured with Brillouin light scattering. The results for the cross-sectional dimensions, under the simplifying assumption of vertical sides and a semicircular top, are found to be consistent with dimensions determined from critical-dimension small-angle x-ray scattering measurements. The elastic constants C(11) and C(44) are found to be, respectively, 11.6% and 3.1% lower than their corresponding values for bulk PMMA. This result is consistent with the dimensional dependence of the quasi-static Young's modulus determined from buckling measurements on PMMA films with lower molecular weights. This study provides the first evidence of size-dependent effects on hypersonic elastic properties of polymers.
ABSTRACT
A noncontacting electromagnetic-acousticresonance technique is presented for generating and detecting vibrational modes with prescribed symmetries in piezoelectric trigonal crystals with cylindrical geometry. This technique provides the experimental basis for determining all elastic constants from a single specimen, while overcoming difficulties in mode identification that can occur in traditional resonant-ultrasound spectroscopy. Narrow-band tone-burst excitation and piezoelectric coupling are employed with various geometrical configurations of electrodes near the surface of a quartz specimen. The geometries of the specimen and plates include all of the symmetry elements of the crystallographic point group, which enable selection of the irreducible representation of excited vibrational modes simply by switching electrical leads to the electrodes.
