Abstract
Applying the operator method, general solutions for dynamic governing equations involving anisotropic piezoelectric materials are derived. Based on the general solutions, a rigid solid with a sinusoidal surface moving along the surface of anisotropic piezoelectric materials is concerned. Dual series equations are obtained and solved analytically. Then, the electro-elastic fields are determined in series forms. A full contact problem leads to more simple forms. Numerical analysis is performed for the anisotropic piezoelectric material \({0^{\circ }}\) Graphite-epoxy, in which an illustrative example concerning the vertical mechanical displacement on the surface is displayed to validate the present approach. Results demonstrate that the contact behavior is considerably affected by both the velocity and material properties.
Similar content being viewed by others
References
Yu N., Polycarpou A.A.: Combining and contacting of two rough surfaces with asymmetric distribution of asperity heights. J. Tribol. Trans. ASME 126, 225–232 (2004)
Jackson R.L., Green I.: On the modeling of elastic contact between rough surfaces. Tribol. Trans. 54, 300–314 (2011)
Greenwood J.A., Williamson J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. A 295, 300–319 (1966)
Medina S., Nowell D., Dini D.: Analytical and numerical models for tangential stiffness of rough elastic contacts. Tribol. Lett. 49, 103–115 (2013)
Vakis A.I., Polycarpou A.A.: An advanced rough surface continuum-based contact and sliding model in the presence of molecularly thin lubricant. Tribol. Lett. 49, 227–238 (2013)
Song Z., Komvopoulos K.: Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities. Int. J. Solids Struct. 51, 1197–1207 (2014)
Vakis A.I.: Asperity interaction and substrate deformation in statistical summation models of contact between rough surfaces. J. Appl. Mech. Trans. ASME 81, 041012–2 (2014)
Longuet-Higgins M.S.: The statistical analysis of a random, moving surface. Philos. Trans. R. Soc. Lond. Ser. A 249, 321–387 (1957)
Kotwal C.A., Bhushan B.: Contact analysis of non-Gaussian surfaces for minimum static and kinetic friction and wear, Tribol. Transaction 39, 890–898 (1996)
McCool J.I.: Non-Gaussian effects in microcontact. Int. J. Mach. Tools Manuf. 32, 115–123 (1992)
Yu N., Polycarpou A.A.: Contact of rough surfaces with asymmetric distribution of asperity heights. J. Tribol. Trans. ASME 124, 367–376 (2002)
Liou J.L., Lin F.J.: A microcontact non-Gaussian surface roughness model accounting for elastic recovery. J. Appl. Mech. Trans. ASME 75, 031015 (2008)
Yuan Y.H., Du H.J., Chow K.S., Zhang M.S., Yu S.K., Liu B.: Performance analysis of an integrated piezoelectric ZnO sensor for detection of head–disk contact. Microsyst. Technol. 19, 1449–1455 (2013)
Loboda V., Sheveleva A., Lapusta Y.: An electrically conducting interface crack with a contact zone in a piezoelectric bimaterial. Int. J. Solids Struct. 51, 63–73 (2014)
Yang F.Q.: Boussinesq contact of transversely isotropic piezoelectric materials. Int. J. Appl. Electrom. 43, 347–352 (2013)
Wu Y.F., Yu H.Y., Chen W.Q.: Indentation responses of piezoelectric layered half-space. Smart Mater. Struct. 22, 015007 (2013)
Hüeber S., Matei A., Wohlmuth B.: A contact problem for electro-elastic materials. ZAMM. Z. Angew. Math. Mech. 93, 789–800 (2013)
Beom H.G.: A unified representation of plane solutions for anisotropic piezoelectric elasticity. Int. J. Eng. Sci. 72, 22–35 (2013)
Chung M.Y.: Green’s function for an anisotropic piezoelectric half-space bonded to a thin piezoelectric layer. Arch. Mech. 66, 3–17 (2014)
Zhou Y.T., Lee K.Y.: Frictional contact of anisotropic piezoelectric materials indented by flat and semi-parabolic stamps. Arch. Appl. Mech. 83, 673–695 (2013)
Wang B.L., Mai Y.W., Sun Y.G.: Surface cracking of a piezoelectric strip bonded to an elastic substrate (Mode I crack problem). Arch. Appl. Mech. 73, 434–447 (2003)
Sneddon I.N.: Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Company, Amsterdam (1966)
Carbone G., Mangialardi L.: Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface. J. Mech. Phys. Solids 52, 1267–1287 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, YT., Kim, TW. A general solution approach to dynamic contact between a sinusoidal rigid solid and piezoelectric materials with anisotropy. Acta Mech 226, 3865–3879 (2015). https://doi.org/10.1007/s00707-015-1398-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-015-1398-z