Forced vibrations of portal frames with viscoelastic intermediate links

In this study, forced vibrations of portal frames are investigated. Members of the frames have three degrees of freedom in each end and in total they have six degrees of freedom. While constituting the frames, infinitely small link elements are used in some connections of the members. The governing equations are derived within the scope of the Euler- Bernoulli beam theory by using energy based finite elements method. Optimum damping coefficients of viscoelastic link elements are investigated for different damping coefficients of members. The results of frames constituted by connecting the members continuously and by connecting the members with link elements in some desired joints (The frames with intermediate viscoelastic hinges) are compared and presented in graphics and tables. The obtained results are compared with the results of same models constituted on SAP 2000 packet program. It is seen that the results obtained from this study are harmonious with the results obtained by using SAP 2000. Also, numerical results show that if there is no material damping or there is very small material damping, the difference of the responses for the small changes of damping coefficient of intermediate viscoelastic hinges becomes great. However, if the material damping coefficient is high, then the effect of the damping of intermediate viscoelastic hinges on the responses decreases and for the big differences of the value of damping coefficient the results are very close to each other. Keywords: Viscoelastic intermediate hinge, Damping coefficient of material, Viscous damping, Rate independent damping (Hysteretic damping, Structural damping), Finite element method, Forced vibration of portal frames, Dynamic response factor, Modal damping, Modal stiffness, Modal mass, Link element having rotational two rotational degrees of freedom, Periodic load