Analyzing the nonlinear dynamic model of structures is an interesting area in nonlinear science. During the past few decades, many authors consider the dynamic modeling with damping and without damping and try to analysisanalyse them analytically and numerically [1-8, 14, 20, 23,25] 25.]
The ideasidea of using metallic energy dissipatersdissipators in earthquake design havehas been considered a lot in the previous studyingstudies. Kelly et al [17][seventeen] developed the work on the Mechanismsmechanisms of energy absorption in special devices, for use in earthquake resistant structures. Skinner et all [24]al [twenty-four] considered the Hysteretichysteretic dampers for earthquake-resistant structures. Kelly et al. [16][sixteen] had a concentrateconcentrated review on current uses of energy absorbing devices. To dissipate the energy present in the vibration of a structure during an earthquake, the inelastic deformation of metals can be effective. Many researchers have worked; based on the use of low-yield metals with triangular and hourglass shapes. Among the best known devices are the patented added damping and stiffness device (A.D.A.S.) and variations such as the T.A.D.A.S. These devices exhibit stable hysteretic behavior; they are insensitive to thermal effects, and extremely reliable. A.D.A.S. devices have been used in the seismic retrofit of several structures in Mexico City [28][twenty-eight.]