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It has been generally accepted that steel moment-resisting frames behave in a ductile manner under seismic excitations. However, during the 1994 Northridge earthquake in California, weld fractures at the beam-to-column connections occurred in many steel buildings. Such brittle failures obviously precluded the traditional ductile-behaviour assumption and had a significant effect on the responses of steel moment-resisting frames. In this paper, the performance of a friction damping system for retrofitting steel moment-resisting frames was investigated under long-distance earthquakes. For this purpose, the 1985 Mexico City (SCT), the 1995 Bangkok, or the 1977 Romania ground motions, all scaled to a peak ground acceleration of 0.17g, were considered in this study. Responses of the building under the 1940 El Centro N-S component were also included for comparison. The results of the study show that a friction damping system can reduce the seismic responses significantly. The devices can also prevent the total collapse and joint failures of the building equipped with friction dampers, while the one without dampers would collapse, even under a peak ground acceleration of only 0.17g.

When using data recorded by dense instrument arrays to fit the coherency model of spatial variation of seismic ground motions, the selected frequency range may affect the fitting parameters, which also affects the synthesized time history of the ground motion field. In this study, the acceleration of the 5th and the 45th Earthquake of the SMART-1 array was selected. The Abrahamson and Loh models were used to perform the parameter fitting of the coherency for frequency ranges of 0–8, 0–16 and 0–24Hz, and the obtained results were different. The smaller the frequency range, the lower the fitted lagged coherency. The influence of frequency range on fitting parameters of Loh model is much greater than that of Abrahamson model. Based on the relative relationship of ground motion energy distribution in each frequency band represented by the power spectra, from the perspective of power spectrum energy, the energy ratio concept was introduced, i.e. the ratio of the power spectra for a specific frequency range to the total power spectra. Based on the energy ratio, a method for determining the effective frequency range of the coherency model was developed. Through the comparison and analysis of the horizontal-component acceleration of the SMART-1 array, it was found that when the frequency range was 0–5Hz, the energy ratio exceeded 95%, when the frequency range was 0–8Hz, the energy in the frequency band reached approximately 99% of the total energy. Therefore, it is recommended that when the parameters of the coherency model are fitted, the frequency corresponding to an energy ratio of 95% can be used as the effective frequency. Within this range, the contamination of high-frequency components on the fitting results is minimized.

The problems of elastic wave propagation in the micropolar porous materials have been attempted under the interaction of micro-rotation tensor and porous distribution in this material. We obtain the existence of three coupled longitudinal and two coupled shear waves propagating with different phase speeds. Numerically, the phase speed and attenuation of five basic waves are computed. We consider the incident plane waves at the boundary of micropolar porous materials, then the dispersive nature of the incident waves is studied and the existence of critical angle for the incident shear wave is found. The amplitude and energy ratios of various reflected waves for the incident coupled longitudinal and shear waves are obtained analytically and numerically. Further, the influence of different material parameters is studied using dispersion relation and the relevant numerical values.

The problem of incident plane waves at the interface of micropolar thermoelastic half-space with voids and micropolar elastic half-space with voids has been attempted. The amplitude and energy ratios of various reflected and refracted waves for the incident $P$- and $S$-waves are obtained with the help of appropriate boundary conditions at the interface. The effect of linear thermal expansion and microinertia on the amplitude and energy ratios due to the incident $P$- and $S$-waves are discussed. Numerically and analytically, these amplitude and energy ratios are computed to show the effect of linear thermal expansion and microinertia. It is observed that the effect of linear thermal expansion is less for incident $S$-wave and the effect of microinertia is less for incident $P$-wave.

This chapter has two objectives: (1) to present the micro-mechanics model of Piezoelectric Fiber-Reinforced Composites (PFRCs) and illustrate some of its advantages and (2) to analytically study the impacts of normal/shear initial stresses and rotation on energies carried by different reflected/transmitted waves at the interface of two dissimilar PFRCs. Numerical studies are performed on PFRCs comprised of PZT-5A-epoxy combination and CdSe-epoxy combination, which are modeled employing Strength of Materials (SM) technique with Rule of Mixtures (RM). Some electro-mechanical advantages of PFRC over monolithic piezoelectric materials are demonstrated. Due to incidence of a quasi-longitudinal (qP) wave, three reflected/transmitted waves, viz. quasi-longitudinal (qP), quasi-transverse (qSV), and electro-acoustic (EA) waves are generated in the PFRCs. The propagation directions of all reflected/transmitted waves are graphically demonstrated. The closed-form expressions of amplitude ratios of all reflected/transmitted waves are derived utilizing appropriate electro-mechanical boundary conditions. As the amplitude ratios cannot be used exclusively to validate the numerical results, the expressions of energy ratios of all reflected/transmitted waves and interaction energy are derived, which exhibit the influence of existing parameters, and the law of conservation of energy is established. This work presents a novel effort to develop a connection between deriving the PFRC’s micro-mechanical model and analyzing the wave reflection/transmission phenomenon in it.