Localized waves near the stress-free surface or the free edge of a solid with a thin nematic coating are investigated. The nematic media is described using an approximate linear low-frequency model. Being a non-traditional material this medium possesses a strong anisotropy of elastic and viscous properties and some additional freedom caused by the long polymer chain and molecules. As shown, the specific wave phenomena, observed earlier in the infinite nematic media, in the case of a coating with finite thickness lead to the appearance of the quasi-resonance zones where the phase speed and the attenuation of waves in heterogeneous composites are strongly perturbed.
FinkelmannHKockHJRehageH. Liquid crystalline elastomers – a new type of liquid of liquid crystalline material. Die Makromol Chem Rapid Commun1981; 2: 317–322.
2.
BrandHRGFinkelmannH. Physical properties of liquid crystalline elastomers. In: DemusD. (eds) Handbook of Liquid Crystals. New York: Wiley, 1998.
3.
FerryJD. Viscoelastic properties of polymers. New York: Wiley, 1980.
4.
de GennesP-GProstJ. Physics of liquid crystals. Oxford: Clarendon Press, 1993.
5.
DonaldAMWindleAH. Liquid crystals polymers. Cambridge: Cambridge University Press, 1992.
KupferJFinkelmannH. Liquid crystal elastomer: influence of the orientational distribution of the crosslinks on the phase behaviour and reorientation process. Die Makromol Chem Rapid Commun1994; 15: 1353–1367.
8.
de GennesPG. In: HelfrichWHeppkeG. (eds) Liquid crystals of one- and two-dimensional order. Berlin: Springer, 1980.
9.
BrandHRPleinerH. Electrohydrodynamics of nematic liquid crystalline elastomers. Physica1994; A208: 359–372.
TerentjevEMWarnerM. Linear hydrodynamics and viscoelasticity of nematic elastomers. Eur Phys J2001; 4: 343–353.
12.
HuangYYAhirSVTerentjevEM. Dispersion rheology of carbon nanotubes in a polymer matrix. Phys Rev2006; 73: 125422.
13.
TerentjevEMKamotskiiIVZakharovDDFradkinL. Propagation of acoustic waves in nematic elastomers. Phys Rev E2002; 66: 05270.
14.
FradkinLKamotskiiIVTerentjevEMZakharovDD. Low frequency acoustic waves in nematic elastomers. Proc R Soc London2003; 459: 2627–2642.
15.
SinghB. Reflection of homogeneous elastic waves from free surface of nematic elastomer half-space. J Phys D: Appl Phys200; 40: 584–592.
16.
SchmidtkeJStilleWStroblG. Static and dynamic light scattering of a nematic side-group polysiloxane. Macromolecules2000; 33: 2922–2928.
17.
SchoonsteinMStilleWStroblG. Effect of the network on the director fluctuations in a nematic side-group elastomer analyzed by static and dynamic light scattering. Eur Phys J E2001; 5: 511–517.
18.
GraffKF. Wave motion in elastic solids. Columbus, OH: Ohio State University Press, 1975.
19.
KnopoffAL. A matrix method for elastic wave problem. Bull Seismol Soc Am1964; 54: 431–438.
20.
KornGAKornTM. Mathematical handbook. New York: McGraw-Hill, 1968.
21.
ZakharovDDKaptsovAV. Influence of nematic coating to the propagation of fundamental modes in elastic plates. Acoust Phys2011; 57(1): 59–65.
22.
KonenkovYuK. A Rayleigh-type flexural wave. Sov Phys Acoust1960; 6: 122–123.
23.
ThurstonRNMcKennaJ. Flexural acoustic waves along the edge of a plate. IEEE Trans Son Ultrason1974; 21: 296–297.
24.
SinhaBK. Some remarks on propagation characteristics of ridge guide for acoustic waves at low frequencies. J Acoust Soc Am1974; 56: 16–18.
25.
KauffmannC. A new bending wave solution for the classical plate equation. J Acoust Soc Am1998; 104: 2220–2222.
ZakharovDD. Two-dimensional dynamic equations of a thin asymmetrically laminated generally anisotropic elastic plate. Dokl Phys1994; 336: 378–380.
34.
ZakharovDDBeckerW. 2D problems of thin asymmetric laminates. Z Angew Math Phys2000; 51: 49–66.
35.
ZakharovDD. High order approximate low frequency theory of elastic anisotropic lining and coating. J Acoust Soc Am2006; 119: 1961–1970.
36.
ZakharovDD. Effective high-order approximations of layered coatings and linings of anisotropic elastic, viscoelastic and nematic materials. J Appl Math Mech2010; 74: 403–418.
37.
AlshitsVIGierulskiWLyubimovVNRadowiczA. Resonance excitation of quasi-Rayleigh waves in plates on soft or hard substrates. Crystallogr Rep1997; 42: 20–27.
38.
ShuvalovALEveryAG. Some properties of surface acoustic waves in anisotropic-coated solids, studied by the impedance method. Wave Motion2002; 36: 257–273.
39.
KuznetsovaIEZaitsevBDKuznetsovaAS. Acoustic waves in structure piezoelectric plate–polymeric nanocomposite film. Ultrasonics2008; 48: 587–590.
40.
DuJXianKYongY-K. Love wave propagation in piezoelectric layered structure with dissipation. Ultrasonics2009; 49: 281–286.
