One-dimensional equations for coupled extensional, radial, and axial-shear motions of circular piezoelectric ceramic rods with axial poling

Maugin G.A.: Continuum Mechanics of Electromagnetic Solids. Elsevier, Amsterdam (1988)

Eringen A.C., Maugin G.A.: Electrodynamics of Continua. Springer, New York (1990)

Cady W.C.: Piezoelectricity. McGraw-Hill, New York (1946)

Mason W.P.: Piezoelectric Crystals and their Application to Ultrasonics. Van Nostrand, New York (1950)

Yang J.S.: Analysis of Piezoelectric Devices. World Scientific, Singapore (2006)

Maurini C., dell’Isola F., del Vescovo D.: Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mech. Syst. Signal Process. 18, 1243–1271 (2004)

Maurini C., Pouget J., dell’Isola F.: On a model of layered piezoelectric beams including transverse stress effect. Int. J. Solids Struct. 4, 4473–4502 (2004)

Rosen, C.A.: Analysis and design of ceramic transformers and filter elements. Ph.D. dissertation, Syracuse University (1956)

Yang J.S.: Piezoelectric transformer structural modeling—a review. IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 54, 1154–1170 (2007)

Meitzler, A.H., Tiersten, H.F., Warner A.W., Berlincourt, D., Couqin, G.A., Welsh, F.S. III: IEEE Standard on Piezoelectricity. IEEE, New York (1988)

Love A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover, New York (1944)

Graff K.F.: Wave Motion in Elastic Solids. Ohio University Press, Columbus (1975)

Mindlin, R.D., Herrmann, G.: A one-dimensional theory of compressional waves, in an elastic rod. In: Proceedings of the First U.S. National Congress of Applied Mechanics, ASME, New York, pp. 187–191 (1952)

Mindlin RD., McNiven HD.: Axially symmetric waves in elastic rods. J. Appl. Mech. 27, 145–151 (1960)

Dokmeci M.C.: A theory of high frequency vibrations of piezoelectric crystal bars. Int. J. Solids Struct. 10, 401–409 (1974)

Chou C.S., Yang J.W., Huang Y.C., Yang H.J.: Analysis on vibrating piezoelectric beam gyroscope. Int. J. Appl. Electromagn. Mater. 2, 227–241 (1991)

Yang J.S.: Equations for the extension and flexure of a piezoelectric beam with rectangular cross section and applications. Int. J. Appl. Electromagn. Mech. 9, 409–420 (1998)

Yang J.S.: An Introduction to the Theory of Piezoelectricity. Springer, New York (2005)

Tiersten H.F.: Linear Piezoelectric Plate Vibrations. Plenum, New York (1969)

Adelman N.T., Stavsky Y.: Radial vibrations of axially polarized piezoelectric ceramic cylinders. J. Acoust. Soc. Am. 57, 356–360 (1975)

Wilson L.O., Morrison J.A.: Wave propagation in piezoelectric rods of hexagonal crystal symmetry. Q. J. Mech. Appl. Math. 30, 387–395 (1977)

Dai J.D., Winkel V., Oliveira J.E.B., Jen C.K.: Analysis of cladded acoustic fibers of hexagonal crystal symmetry. IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 39, 730–736 (1992)

Dai JD., Winkel V., Oliveira J.E.B., Jen C.K.: Analysis of cladded acoustic fibers of hexagonal crystal symmetry. IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 39, 730–736 (1992)

Üçer M., Akçakaya E.: A new approach to the analysis of piezoelectric cladded acoustic fibers. IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 46, 1088–1093 (1999)

Wei J.P., Su X.Y.: Wave propagation in a piezoelectric rod of 6 mm symmetry. Int. J. Solids Struct. 42, 3644–3654 (2005)

McNiven H.D., Mengi Y.: Dispersion of waves in transversely isotropic rods. J. Acoust. Soc. Am. 49, 229–236 (1971)

Mengi Y., McNiven H.D.: Axially symmetric waves in transversely isotropic rods. J. Acoust. Soc. Am. 50, 248–257 (1971)