Influence of the suspended pendulum on the dynamic behavior of structures

Abstract

Buildings subjected to dynamic loads respond to severe deformation. To minimize vibrational responses, adding a suspended pendulum tuned mass damper (SPTMD) is a common method to dissipate energy. SPTMDs are composed of mass blocks suspended by rods that can be easily swayed against the building movement and effectively reduce response. Additionally, it can be utilized to tune the building's low natural frequency. The main purpose of this research is to investigate the existence of the SPTMD's effects on the dynamic responses of a solid frame under various conditions. To this end, the finite element method (FEM) is employed to numerically simulate and analyze models due to seismic loading. Afterward, experimental tests due to sinusoidal loading are performed. For numerical investigation, at first, the finite element (FE) model of a solid support body (SSB) is created. In this model, fixed support at the bottom of the SSB as a boundary condition (BC) and downward gravity acceleration as a loading on the whole system are considered. The response surface optimization (RSO) method is used to determine the appropriate element size in order to achieve mesh independence analysis. RSO is an optimization technique for redoing analyses by changing the values of variable parameters. In the static analysis, element size is chosen as an input variable parameter and the number of elements, nodes, maximum displacement, and first modal frequency are chosen as output variables. The element size is defined between 5 and 50 mm and the Latin hypercube sampling design with 100 samples is considered to perform parametric analysis. The results show the appropriate element size is about 10 mm. Following that, static, modal, and dynamic numerical analysis are performed and using the mechanical model, analytical EOM and natural frequency relationships are extracted. The frequency responses are validated from the reference paper. Moreover, the free vibration displacement time history result from the numerical method is verified with the analytical method. In the second step, a FE model of a suspended pendulum (SP) as a SPTMD system is created. This mechanical system is suspended from a pivot point, which is comprised of a rod and a point mass. This point is a revolute joint type, which has a single rotational degree of freedom (DOF). This means that the system can be freely rotated around the pivot point. The equation of motion (EOM) and the natural frequency relationships for the free vibration of SP are extracted. The rotation time history response of the numerical (ANSYS Workbench FEM result) is verified with the analytical (Matlab) for the SP. Furthermore, the natural frequency responses for different mass ratios obtained from the FE model are validated using the analytical relationship. Finally, a combined system of SSB and SP with two degrees of freedom is considered. In this system, the first DOF belongs to SSB, which is a translational type and the second belongs to SP, which is a rotational type. The natural frequency responses of the combined system for different mass ratios are obtained to illustrate the SP effect on response reduction. As well as, the effect of the SP on the displacement time history reduction of the solid frame (SSB) is illustrated. Then, three different solid models are considered and the effect of the SP on the seismic response reduction of the models is presented. For the experimental tests, specimens are developed based on numerical studies. For this procedure, three steel structures with two suspended pendulums are created. The structure specimens are SSB, SSB1R, and SSB1&3R and the pendulum specimens are SPS and SPL. The difference in structure is in column direction and the difference in SP is in the length of the rod. In order to investigate the influence of the SP on the dynamic responses, sinusoidal displacement loading is applied to the shaking table, which has 1D DOF movement. The loading variables are amplitude (100 and 80 mm) and frequency (0.25 and 0.5 Hz). Totally, nine specimens are considered and four loads are applied to each of the specimens. During these experiments, displacement and acceleration of the top plate are measured. Moreover, the effects of structurally asymmetric conditions due to column rotation cause torsion on the structure are investigated. It is observed in the case with the pendulum and without the pendulum. These tests are performed in the Experimental Mechanical Laboratory of Civil Engineering Faculty, at Istanbul Technical University The results revealed that when the system has a severe stiffness weakness on one side, SP has a clear mitigation effect on the displacement response. Meanwhile, SP enforces SSB to vibrate in areas near the equilibrium position (not turning and vibration). The pendulum makes the structure's rotation less even in SSB1R stiffness is not symmetrical and twisting occurs. The suspended pendulum can eliminate the effect of column non-uniformity that causes asymmetric stiffness.