Thermoelastic Damping in Micro- and Nano-Mechanical Systems

The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electro-mechanical systems (MEMS and NEMS). The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener's well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.Comment: 10 pages. Submitted to Phys. Rev.

Possible configurations for Weiss domains in uniaxial ferroelectric crystals

The variational principle proposed in another paper of ours [Internat. J. Engrg. Sci. 30 (1992), no. 12, 1715--1729; MR1185410 (93h:82078)] is here applied to derive the configuration of Weiss domains in uniaxial crystals. It is proved that the configuration which was proposed by L. Landau and E. Lifshits [Phys. J. Sowjet. 8 (1935), no. 2, 153--169] is not possible even in the presence of an electric field. Moreover, another possible configuration is proposed in the absence of an electric field

Structure of Weiss domains in elastic ferroelectric crystals

The structure of Weiss domains in ferroelectric crystals in each of which the polarization vector is constant, is investigated through a new variational principle. The general field equations are obtained and it is shown that in the presence of external electric field the total electric field is also constant in Weiss domains but is usually different from that of the polarization field. Moreover, it is proved that domain walls can only be planar surfaces. Finally the case corresponding to pure polarization fields is also treated and an illustrative problem is considered

Structure of weiss domains in elastic ferroelectric crystals

In this work a variational principle is proposed to study the existence and structure of Weiss domains in elastic ferroelectric crystals. Weiss domains are defined as certain subregions of the crystal in each of which the polarization vector is uniform and has a constant magnitude which is equal to the saturation polarization per unit mass for the crystal. The variational principle differs from previous ones in that the variations of the domain walls are also taken into account and it is a direct generalization of the one corresponding to the rigid crystals which we have proposed earlier. In deriving the general theory the dependence on the polarization gradients are also considered and the effect of this dependence when passing from one domain to another is represented by an appropriately chosen surface energy on domain walls. The domain structure is studied under homogeneous deformation. The effect of a small deformation field on the shape of domains is illustrated in the case of a rectangular uniaxial crystal which has initially no electric field inside. It is shown that the deformation creates a small electric field in the crystal and domain walls change slightly