A model is presented to explain the normal mode features of dust particles in a planar zigzag crystal chain for the first and second neighbors. The degrees of freedom of particles are the longitudinal and transverse displacements in plane coupled by the first and second neighbor harmonic forces in two dimensions. The constant electric force required for the electrodes to keep the zigzag structure is calculated. The coupling between transverse and longitudinal dust-lattice modes is derived. The latter is considered to be due to the energy of the electrostatic (Yukawa) potential. Moreover, coupled (acoustic and optical) and decoupled (longitudinal and transverse) branches of dust lattice modes for different lattice parameters and structures are studied. Propagation of the longitudinal and acoustic modes is found to be strictly dependent on the value of the distance between the two chains; below that value mode may not propagate Finally it is shown that the frequencies of the acoustic (optical) branches increase (decrease) with increasing distance between the two chains.
