In order to apply shape memory alloy (SMA) damper for effective control of cable vibration under external excitations, motion equations and corresponding state equation of the system made up of SMA dampers and a cable are described based on Hamilton Principle, and the system's optimization problems based on the linear quadratic regulator (LQR) active control algorithm are investigated to obtain the optimum cable vibration control effects and control forces. According to the equivalency between SMA damper optimum passive control effects and LQR active control effects, the optimal design principle and methods of SMA damper for cable vibration control are proposed. Utilizing the above optimal methods, a SMA damper is designed to control vibration of a practical cable under white noise excitations, and its control effects are compared with the LQR active control effects by numerical simulation. Results show that the cable vibration responses under both LQR active control and SMA damper optimum control are obviously less than those without control, and SMA damper optimum control effects are approached to the LQR active control effects. This may indicate the effectiveness of the supposed SMA damper optimum design methods for cable vibration control.

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A series of macro- and microscopic models have been proposed to numerically investigate the expansion response in hardened cement paste (HCP) caused by external sulfate attack (ESA). In the models, a HCP cylindrical specimen and a representative volume element (RVE) are respectively chosen as macroscopic and microscopic objects. Numerical simulation on the expansion response in the HCP specimen immersed into Na2SO4 solution is performed. The results show that the macroscopic and microscopic expansion responses in HCP induced by crystallization pressure are different. At the macroscale, the stress state (the radial, hoop and axial stresses) of HCP in the surface layer of the specimen transforms from a triaxial tension to tension–compression–tension state, and further becomes tension–compression–compression. But, the HCP is always in a triaxial tension state in the interior of the specimen without ESA. At the microscale, the hoop tensile stress in RVE increases rapidly with immersion time and is responsible for the initiation of microcracks in the cement paste of RVE. By comparing the macroscopic and microscopic expansion responses, the microscopic stress is larger than the macroscopic stress in the sulfate corrosion zone of the specimen. It indicates that, the analysis on the ESA-induced damage of HCP needs to consider both the macroscopic and microscopic expansive stresses.