To our knowledge, no systematic empirical research exists addressing the question of inhomogeneous wave propagation in a rotating piezoelectric body. Our work here is to present the analysis and result for this problem in the framework of inhomogeneous wave theory. The paper is organized in the following manner. selleck chemicals llc In the next section, the basic equations for motion in a rotating piezoelectric solid and their wave dispersion equations to harmonic waves are given. Next, using the inhomogeneous wave theory, we recast the dispersion equations in a general complex form which separable real solutions to define the phase velocity and attenuation are admitted. Thus, we can discuss the wave phase velocities, attenuations with three independent parameters: propagation angle, attenuation angle, and rotation speed.

Finally, in Sections 3 and 4, numerical results are presented and conclusions are inferred, respectively.2. Basic Governing EquationsWe consider a linear homogeneous piezoelectric body shown in Figure 1, and M is the material point rotating with the speed vector ��( = ��1e1 + ��2e2 + ��3e3). It should be mentioned that throughout this paper, all equations are expressed in the inertial frame ox1x2x39, in which there are base vector e1, e2, and e3 along three axes, respectively.Figure 1The rotating piezoelectric body.Thus, the momentum balance in a piezoelectric body can be written as��[?2u?t2+����(����u)+2����?u?t]=??��,(1)and equivalently, in component form:��[?2uj?t2+��jik��kmn��i��mun+2��jik��i��?uk?t]=��ij,i.

(2)In the above equation, �� is the mass density, t is the time variable, u is the displacement vector, �� is the Cauchy stress tensor, and ��jik is the permutation tensor. The subscripts range from 1 to 3. On account of rotation, the term �� �� (�� �� u) denotes the centripetal acceleration, and due to the time-varying motion, 2�� �� (?u/?t) corresponds to the Coriolis acceleration [3]. Further, the electric field can be described by the electrostatic equationDi,i=0,(3)where Di is the electric displacement vector, and with material equations��ij=Cijkl��kl?ekijEk,Di=?ijEj+eikl��kl,(4)where ��ij are the strain tensor and Ek the electric field vector while Cijkl, ekij, and ?ij are the elasticity, piezoelectricity, and permittivity tensors of the material. The Einstein summation is implied in the above equations over the repeated subscripts.The electric field vector can be derived from an electric Carfilzomib potential, that is,Ek=?��,k,(5)where is the electric potential. The geometric relationship between the strain and the displacement tensors is defined as��kl=12(uk,l+ul,k).(6)Eliminating ��kl and Ek from (4), (5), and (6) yields��ij=Cijkluk,l+ekij��,k,Di=??ij��,j+eikluk,l.