Vibration suppression of a 90-m-tall steel

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could lead to an extremely high rate of fatigue damage accumulation and, consequently, an extremely short service life of the stack. The across-wind response analysis results show that the vortex-induced oscillation can be effectively suppressed by adding an additional damping to the stack. The damping of unlined, welded steel stacks reported in the literature normally lies within a range of 0.2 to 1.0 % of the critical damping, and this could lead to excessively high oscillation amplitudes as mentioned earlier. However, if the damping is raised to 2, 3, 4 and 5%, the maximum oscillation amplitude will be reduced to, approximately, 0.14, 0.11, 0.09 and 0.08 m, respectively. It was considered that the damping of 2 % would be sufficient to ensure the safety and serviceability of the stack. This could be achieved by installing a properly designed Tuned Mass Damper (TMD) at the top of the stack. 90.0 m 10.0 m 20.0 m 30.0 m 30.0 m 2.20 m 3.20 m 4.10 m 5.20 m (a) (b) (c) Figure 1 (a) A 90-m-tall steel stack in Rayong, (b) its basic dimensions, and (c)the first and second sway vibration mode shapes 2. DESIGN OF PENDULUM TUNED MASS DAMPER 1 st Mode 2 nd Mode A simple pendulum-type TMD was chosen as a device to introduce the required additional damping to the stack. It consists of a steel ring, three suspended wire ropes, and three viscous dampers as shown in Figure 2. The design of this TMD was aiming at an additional damping of about 4 to 5 % of the critical value. In the initial design, the well-known optimal design formulas for the case where the main structure is subjected to stationary random loading were adopted [2]. The ring mass of 1500 kg was found to be sufficient, and the corresponding optimal damping ratio of TMD was estimated to be around 11 to 12 %. The optimal frequency tuning was achieved by setting the length of pendulum arm to 0.38 m. With this optimal design, an additional damping in excess of 5 % could be expected. However, the maximum relative movement between the ring and the stack was estimated to be as high as 0.32 m. Such a large relative movement could lead to several problems in the design of viscous dampers and could shorten the service life of suspended ropes. It was therefore considered that the maximum relative movement must be limited to 0.10 m. To satify this constraint, the initial design was adjusted by raising the TMD damping ratio to a level much higher than the optimal level and, at the same time, raising the ring mass to compensate the reduction in damper effectiveness. Note that the cost of TMD is not so sensitive to this adjustment because the additional material cost of the steel ring is relatively low and the cost of viscous dampers remain practically unchange for increasing levels of design damping coefficient. After a few rounds of design adjustment, the final design was obtained: the ring mass was set to 3600 kg, and the TMD damping ratio was set to 40 %. With this final design, an additional damping of about 5 to 6 % to the
stack can be expected, and the maximum relative movement is limited to 0.10 m as required. An additional benefit from this adjustment is the improved robustness of TMD; the performance of this high-damping TMD is less sensitive to the error in frequency tuning compared to the case of the initial design. This robustness is one of the key factors for the success in the application of this TMD—this point will be discussed in the following sections. (a) (b) (c) (d) Figure 2 Pendulum TMD and its components: (a) steel ring, (b) viscous damper, (c) suspended wire rope, (d) drawings showing the assembly 3. PERFORMANCE TESTS A Stack Pendulum mass Stack Suspended cable Pendulum mass Damper Section A - A To ensure damper effectiveness, performance tests were carried out in six stages. The objective of tests in the first three stages was to separately identify the dynamic properties of the pendulum TMD and the stack. The fourth-stage test was made to check the dynamic properties of the combined stack- TMD system. Tests in the last two stages were carried out to examine the control effectiveness of TMD under normal service conditions. In the first stage, the pendulum system without viscous dampers was installed on the top segment of the stack in the fabrication yard as shown in Figure 3. The segment was firmly locked to the floor, so that it acted like a motionless supporting frame for the pendulum. Two uniaxial acceleration sensors were placed on the ring to measure its motions in two horizontal orthogonal directions. The acceleration signals were recorded by a portable data acquisition unit. By this way, the natural frequency and damping ratio of the pendulum could be easily identified from its free vibration records. The obtained free vibration records indicate that vibration frequency is strongly dependent on vibration amplitude (Figure 4 a and b). This amplitude dependent characteristic could not be explained by the geometric nonlinearity of the pendulum, which causes almost negligibly small variation in vibration frequency within the measured amplitude range. It was observed, however, that when the vibration amplitude was small, the two ends of suspended ropes were practically clamped to the
Page 1: The Eighth East Asia-Pacific Confer
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Vibration suppression of a 90-m-tall steel

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