Analyzing the Nonlinear Dynamics of the Three Degree of Freedom Frame Structure Based on the NewMark-β Method and the Effect of Stiffness on the Displacement of the Structure

The analytical method of the simplified model of a structure has provided a basis for the analysis under the effect of earthquake (dynamic) load, which has an important importance in the seismic analysis of the structure. In this article, three degree of freedom steel frame structure is simulated and analyzed in MATLAB based on the NewMark-β method, taking into account the effect of harmonic loads. The vibration response of the steel frame structure has been analyzed considering the stiffness. The results show that the NewMark-β method is a new idea for earthquake response. The construction of the steel frame according to the range of changes of its elastic modulus through dynamic analysis makes the seismic analysis of the frame structures more practical, as well as the analysis of the SS model, which provides a basis for the size of the stiffness coefficient. By applying force on the top and bottom floors, different structural responses are observed according to the stiffness of the structure. The structure of the SS frame and the effect of the force on it when the force is applied to its floors, according to the height of the floors and the position of applying the force with the change of time, the binding stiffness of the amount of displacement will also change and the stability of the structure will be greatly reduced.The analytical method of the simplified model of a structure has provided a basis for the analysis under the effect of earthquake (dynamic) load, which has an important importance in the seismic analysis of the structure. In this article, three degree of freedom steel frame structure is simulated and analyzed in MATLAB based on the NewMark-β method, taking into account the effect of harmonic loads. The vibration response of the steel frame structure has been analyzed considering the stiffness. The results show that the NewMark-β method is a new idea for earthquake response. The construction of the steel frame according to the range of changes of its elastic modulus through dynamic analysis makes the seismic analysis of the frame structures more practical, as well as the analysis of the SS model, which provides a basis for the size of the stiffness coefficient. By applying force on the top and bottom floors, different structural responses are observed according to the stiffness of the structure. The structure of the SS frame and the effect of the force on it when the force is applied to its floors, according to the height of the floors and the position of applying the force with the change of time, the binding stiffness of the amount of displacement will also change and the stability of the structure will be greatly reduced.

Analyzing the Nonlinear Dynamics of the Three Degree of Freedom Frame Structure Based on the NewMark-β Method and the Effect of Stiffness on the Displacement of the Structure Keywords:

NewMark-β method , Reinforced Concrete , Steel Structure , Hardness Reduction , Dynamic Load , Seismic