Abstract
We present the results of SPH simulations with multi-million particles models. The models were constructed with an exponential disk, Spitzer's isothermal sheet in the vertical direction and a NFW halo. In models having a bulge, a spherical Hernquist profile was used. The models were evolved for approximately 5 Gyr using Gadget 2. We present 1D and 2D Fourier analysis to quantify bar characteristics as length, strength, and pattern speeds. Fourier 2D analysis is also applied to show the effects of the swing amplification mechanism. Indeed, the density waves begin to be amplified as tightly wound leading spirals and unwound to open leading structures. Afterwards, the waves wound into trailing patterns, reach their maximum amplitude and finally, fade away as tightly wound trailing spirals. The timescale for each wave packet is of the order of some 10^{8} years.
