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We analytically derive the effective layer elastic energy of smectic-A andsmectic-C liquid crystals by adiabatic elimination of the orientational degreeof freedom from the generalized Chen-Lubensky model. In the smectic-A phase,the effective layer bending elastic modulus is calculated as a function of thewavelength of the layer undulation mode. It turns out that an unlocking of thelayer normal and the director reduces the layer bending rigidity forwavelengths smaller than the director penetration length. In the achiralsmectic-C phase, an anisotropic bending elasticity appears due to the couplingbetween the layer displacement and director. The effective layer bendingrigidity is calculated as a function of the angle $\vartheta$ between the layerundulation wave-vector and the director field. We compute the free energyminimizer $\vartheta=\theta$. It turns out that $\theta$ varies from $0\deg$ to$90\deg$ depending on the tilt angle, undulation wave-length and other elasticconstants. We also discover a new important characteristic length and thediscontinuous change of $\theta$. Using the elastic constants of Chen-Lubenskymodel, we determine the parameters of the more macroscopic model [Y. Hatwalneand T. C. Lubensky, Phys. Rev. E {\bf 52}, 6240 (1995)]. We then discuss thehydrodynamics, and demonstrate the alignment of director and the propagation ofthe anisotropic layer displacement wave in the presence of an oscillatory walland a vibrating cylindrical source respectively.

Effective elastic theory of smectic-A and smectic-C liquid crystals