A Comparative Study on Frequency Sensitivity of a Transmission Tower

Hindawi Publishing Corporation Journal of Sensors Volume 2015, Article ID 610416, 14 pages http://dx.doi.org/10.1155/2015/610416 Research Article A Comparative Study on Frequency Sensitivity of a Transmission Tower Peng-yun Li,1 Bo Chen,2 Wen-ping Xie,1 and Xiang Xiao3 1 Guangdong Power Grid Corporation Co. Ltd., Guangzhou 510080, China Key Laboratory of Roadway Bridge and Structural Engineering, Wuhan University of Technology, Wuhan 430070, China 3 School of Transportation, Wuhan University of Technology, Wuhan 430070, China 2 Correspondence should be addressed to Bo Chen; Received 15 November 2014; Accepted 25 December 2014 Academic Editor: Fei Dai Copyright © 2015 Peng-yun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Sensitivity analysis can take structural parameters as variable and achieve the relationship only with one time analysis, which will dramatically reduce the analytical work especially for large scale structures. The comparative study on frequency sensitivity of a transmission tower is actively carried out in this study. The three-dimensional analytical model of a transmission tower is established by using the finite element (FE) method. The sensitivity coefficients to natural frequencies are deduced based on the equation of motion of the tower. In addition, the expression of the frequency sensitivity to Young’s modulus, density of material, the cross area of members, torsional stiffness, and bending moment inertia is proposed. A real transmission tower constructed in China is taken as an example to examine the feasibility and reliability of the proposed sensitivity computation approach. An intensive parametric study is conducted in detail in order to compare the sensitivity coefficients of different physical parameters. The work on an example structure indicated that the magnitudes of the sensitivity coefficients of Young’s modulus, the density, and the cross area are much larger than those of the torsional stiffness and the bending moment inertia. 1. Introduction To be a typical spatial steel structure, the transmission tower is widely used as electrical power infrastructures throughout the world. The transmission tower is a high-rise structure with small damping and is prone to strong dynamic excitations, such as earthquakes and wind loadings [1–3]. It is frequently reported across the world that the excessive vibration of a transmission tower under dynamic excitations may induce the structural damage and even failure [4–6]. Therefore, it is necessary to evaluate the structural performance of the transmission tower subjected to external dynamic excitations. Many theoretical and experimental investigations have been carried out during the past two decades for examining the performance of the transmission tower [7, 8]. With regard to the approaches and techniques used for performance evaluation, the transmission tower system is conventionally designed and constructed using appropriate design standards without considering the dynamic optimization effects. Therefore, the common approach does not provide deep insights into the structural transient behaviour under strong dynamic excitations, even though the consideration of dynamic effects may be important. Thus, the vibration-based structural health monitoring (SHM) approaches have been widely utilized in the performance evaluation of civil engineering structures across the world [9–11]. The SHM process needs to develop or improve a mathematical model of a physical system using measurement data to describe the input, output, and noise relationship [12, 13]. Various methods have been developed to improve the quality of the finite element model of a structure using measurement data [14]. Doebling et al. (1998) [15] gave a comprehensive review on SHM. With regard to the different SHM algorithm used, the effects of various physical parameters on the structural responses can be examined in detail to determine the crucial parameters for structural dynamic design and assessment. For a transmission tower with determined parameters, it is troublesome to attain the relationship between dynamic characteristics and changed parameters by numerous recalculations which will be almost impossible for large 2 Journal of Sensors scale structures, while sensitivity analysis as an alternative approach can take structural parameters as variable and achieve the relationship only with one time analysis, which will dramatically reduce the analytical work especially for large scale structures [16]. The sensitivity analysis is a reasonable and powerful tool for investigating the effects of physical parameters on static and dynamic responses. The sensitivity analysis concerns the relationship between parameters available to the structural responses under dynamic excitations. The dependence of response measures, such as displacement, velocity, acceleration, stress, strain, natural frequency, mode shape, and frequency response, is implicitly defined through the governing equations of structural mechanics [17]. Dynamic sensitivity analysis is used to compute the rate of dynamic property change with respect to changes of structural physical parameters. Current studies on the dynamic assessment of the transmission tower focus on the response computation and mitigation. Up to now, the sensitivity analysis of the transmission tower for dynamic assessment has been investigated rarely. To this end, the comparative study on frequency sensitivity of a transmission tower is actively carried out in this study. The three-dimensional model of a transmission tower is established by using the FE method. The differential sensitivity analysis approach is presented based on the differential sensitivity coefficient, the absolute sensitivity coefficient, and the relative sensitivity coefficient, respectively. The sensitivity coefficients to natural frequencies are deduced based on the equation of motion of the tower. In addition, the expression of the frequency sensitivity to the Young’s modulus, density of material, the cross area of members, torsional stiffness, and bending moment inertia is proposed. A real transmission tower is taken as the example to investigate the effects of the structural parameters on the natural frequency through the detailed parametric study. An intensive parametric study is conducted to compare the sensitivity coefficients of different physical parameters. A real transmission tower constructed in China is taken as an example to examine the feasibility and reliability of the proposed sensitivity computation approach. The observations made indicate that the magnitudes of the sensitivity coefficients of the Young’s modulus, the density and the cross area are much larger than those of the torsional stiffness and the bending moment inertia. Th (...truncated)