Changing environmental conditions, especially temperature, have been observed to be a complicated factor affecting vibration properties, such as frequencies, mode shapes, and damping, of civil structures. This paper reviews technical literature concerning variations in vibration properties of civil structures under changing temperature conditions. Most of these studies focus on variations in frequencies of bridge structures, with some studies on variations in mode shapes and damping and other types of structures. Statistical approaches to correlation between temperature and frequencies are also reviewed. A quantitative analysis shows that variations in material modulus under different temperatures are the major cause of the variations in vibration properties. A comparative study on different structures made of different materials is carried out in laboratory. Two real structures, the 1377 m main span Tsing Ma Suspension Bridge and the 610 m tall Guangzhou New Television Tower, are examined. Both laboratory experiments and field testing, regardless of different construction materials used and structural types, verify the quantitative analysis. Variations in frequencies of reinforced concrete (RC) structures are much more significant than those of steel structures.

Structural damage often occurs only at several locations that exhibit stiffness reduction at sparse elements out of the large total number of elements in the entire structure. The conventional vibration-based damage detection methods employ a so-called l 2 regularization approach in model updating. This generally leads to the damaged elements distributed to numerous elements, which does not represent the actual case. A new l 1 regularization approach is developed to detect structural damage using the first few frequency data. The technique is based on the sparse recovery theory that a sparse vector can be successfully recovered using a small number of measurement data. One advantage of using frequency data is that the first few frequencies can be measured more accurately and conveniently than mode shapes and other modal properties. A cantilever beam is utilized to demonstrate the effectiveness of the proposed method. Only the first six modal frequencies are required to detect two damaged elements among 90 finite beam elements, which cannot be achieved using the conventional damage detection approach. The effects of measurement number, damage severity, number of damage, and noise level on damage detection results are also studied through a numerical example. The advantage of the new regularization approach over the conventional one is finally interpreted.

The eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level, which is time-consuming or even prohibitive for large-scale structures. Several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure. However, these approaches are not usually accurate, as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded. In this paper, a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures. With this new approach, the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form, which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results. The eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration. Upon convergence, the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly. The computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super-tall structure.

a b s t r a c tA substructure-based finite element model updating technique is proposed in this paper. A few eigenmodes of the independent substructures and their associated derivative matrices are assembled into a reduced eigenequation to recover the eigensolutions and eigensensitivities of the global structure. Consequently, only the concerned substructures and the reduced eigenequation are re-analyzed in the optimization process, thus reducing the computational load of the traditional model updating methods which perform on the global structure. Applications of the proposed substructure-based model updating to a frame structure and a practical bridge demonstrate that the present method is computationally effective and efficient.