Abstract—Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically. Keywords—Anisotropic, layered, dispersion, elastic waves, frequency equations. I. INTRODUCTION NGINEERING materials such as fiber reinforced composite, graphite and laminate, where high strength-to- weight and stiffness-to-weight ratios are required. These materials are crucial for structural applications, and have resulted in considerable research activities on their behavior. Consequently studies of the propagation of elastic waves in the layered media [1]-[4], which are anisotropic in nature, become very important and have long been of interest to researchers in the fields of geophysics, acoustics, and nondestructive evaluation Compared to the extensive literature on the elastic waves in infinite anisotropic media; relatively little attention has been given to elastic waves in anisotropic plates. Although a complete review of the extensive literature on this subject cannot be undertaken, several salient contributions should be mentioned in [5]-[9]. Propagation of waves in free isotropic plates were first reported by Lamb in 1917 in his famous work [10], and followed by several authors [3] and [11]-[15]. Propagation of free guided waves in anisotropic homogeneous Manuscript received February 15, 2008. This work is supported by the Council of Scientific and Industrial Research, Extramural Research Division, CSIR Complex New Delhi INDIA, 110012 under research grant No. 22(0374)/04/EMR-II. Dr. K. L. Verma Dr, Eng. is with the Government Post Graduate College Hamirpur (HP) 177005 INDIA (phone: +91-1972-224252 fax: +91-1972- 224252; e-mail: klverma@ bsnl.in, kl.verma@redffmail.com). plate has been studied in detail by authors [16]-[18]. These studies provide an interesting picture of the rich dispersion characteristic of these guided waves. Several others authors [8], [12], [15] and [19] have studied free Lamb waves. In this paper analysis for the propagation of elastic waves in plates of general anisotropic media is investigated on the basis of an exact theory. Dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered special cases have also been deduced and discussed separately. It is also demonstrated that the particle motions for SH modes decouple from rest of the motion, if the propagation occurs along an in-plane axis of symmetry. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented and the results obtained theoretically have also been verified numerically and illustrated graphically. II. FORMULATION Consider an infinite generally- anisotropic plate, having thickness d, whose normal is aligned with the 3 x axis of a reference Cartesian coordinate system 1 2 3 ( , , ) i x x x x . The mid-plane of the plate is chosen to coincide with the 1 2 x x plane. The equations of motion in the absence of body forces ij j i u , (1) where = ij ijkl kl C e (2) is the density, t is the time, u i is the displacement in the x i direction, ij and e ij are the stress and strain tensor respectively; and the fourth order tensor of the elasticity C ijkl satisfies the (Green) symmetry conditions: C ijkl = C klij = C ijlk = C jikl . (3) Strain-displacement relation e u u ij ij ji ( ) , , 2 (4) On the Wave Propagation in Layered Plates of General Anisotropic Media K. L. Verma E World Academy of Science, Engineering and Technology International Journal of Physical and Mathematical Sciences Vol:2, No:1, 2008 22 International Scholarly and Scientific Research & Innovation 2(1) 2008 ISNI:0000000091950263 Open Science Index, Physical and Mathematical Sciences Vol:2, No:1, 2008 publications.waset.org/6992/pdf