In this paper, the dynamic behavior of two identical adjacent structures connected with viscous dampers is investigated under base acceleration. The base acceleration is modeled as harmonic excitation as well as stationary white-noise random process. Each adjacent structure is modeled as a two-degree-of-freedom system. The governing differential equations of motion of the coupled system are derived and solved for relative displacement and absolute acceleration responses. A parametric study is conducted to study the influence of important system parameters on the response behavior of damper connected structures. The important parameters considered are excitation frequency, mass ratio, and stiffness ratio of the structure. It is observed that the viscous damper is quite effective in controlling the dynamic response of identical connected structures. For a given coupled structure and excitation, it is found that there exists an optimum value of damping coefficient of damper for which the peak responses under harmonic excitation and the mean square response quantities under stationary white-noise excitation attain the minimum value. The close-form expressions for optimum parameter and corresponding response are derived for an undamped system. Finally, it is observed that the damping ratio of the connected structures does not have noticeable effects on the optimum damper damping. This implies that the proposed close-form expressions of undamped structures can be used for the damped connected structures as well.
Dynamic response of two adjacent single degree-of-freedom (SDOF) structures connected with friction damper under base excitation is investigated. The base excitation is modeled as a stationary white-noise random process. As the force-deformation behavior of friction damper is non linear, the dynamic response of connected structures is obtained using the equivalent linearization technique. It is observed that there exists an optimum value of the limiting frictional force of the damper for which the mean square displacement and the mean square absolute acceleration responses of the connected structures attains the minimum value. The close form expressions for the optimum value of damper frictional force and corresponding mean square responses of the coupled undamped structures are derived. These expressions can be used for initial optimal design of the friction damper for connected structures. A parametric study is also carried out to investigate the influence of system parameters such as frequency ratio and mass ratio on the response of the coupled structures. It has been observed that the frequency ratio has significant effect on the performance of the friction damper, whereas the effects of mass ratio are marginal. Finally, the verification of the derived close from expressions is made by correlating the response of connected structures under real earthquake excitations.
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