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We promote an efficient method named harmony response analysis (HRA) as a comparison with transient response analysis and supercell plane wave expansion (supercell PWE) to study the behavior of Lamb wave in silicon-based one-dimensional composite plates. To implement HRA for dealing with Lamb waves in phononic-crystal plates, the viscous-spring artificial boundaries are employed to eliminate the boundary reflection in maximum. With the calculation of displacement field, the propagations of elastic waves under different frequency loads (inside/outside the completed band gap) are investigated in details. The method is then applied in plates both with and without substrate. We further study the plates with quasiperiodicity (generalized Fibonacci systems and double-period system) and investigate the change in band gaps induced by the quasiperiodicity.