The paper presents a method to detect, locate and evaluate damage severity of Euler-Bernoulli beams, based on how natural frequencies change due to damages. Previous researches that dealt with this issue focused only on quantitative changes, mainly considering a global stiffness reduction in the damaged area. The authors have contrived a correlation between the strain energy stored in a segment of the beam, which is proportional with the mode shape curvature of a considered vibration mode at that location, and the frequency change for this mode if damage appears on that segment. This reveals that for an element of the beam, the stiffness change of a certain mode for a given damage varies between zero and a maximum, depending solely on the location of that element. Moreover, one has to consider different stiffness changes for a damaged element placed on a certain location, depending on the vibration mode. This rule how frequencies of various modes change due to damage are used to create patterns, based on relative frequency shifts, which characterize damaged beams in respect to defect location and severity. The method was validated by numerous experiments, which proved its accuracy and reliability.

For the study and design of the elastomeric seismic devices is essential to know the mathematical relation between the horizontal displacement and the force leading it. In this paper we present mathematical models for three types of devices: (i) natural rubber bearings, (ii) lead rubber bearings and (iii) hybrid device combining the two first mentioned bearings. For all devices the specific domains of operation are determined and for each domain the relations connecting horizontal displacement and stiffness is contrived, highlighting the hysteretic behaviour in respect to ground excitation. Finally we present numerical results and a comparison between the three devices, defining the opportunity to involve them in specific applications, in function of the type and nature of the isolated structure.