Sub-wavelength resonators as seismic Rayleigh waves shield

We explore the thesis that tall structures can be protected by means of seismic metamaterials. Seismic metamaterials can be built as some elements are created over soil layer with different shapes, dimensions, patterns and from different materials. Resonances in these elements are acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. Analytically we proved that if we put infinite chain of SDOF resonator over the soil layer as an elastic, homogeneous and isotropic material, vertical component of Rayleigh wave, longitudinal resonance of oscillators will couple with each other, they would create a Rayleigh bandgap frequency, and wave will experience attenuation before it reaches the structure. As it is impossible to use infinite chain of resonators over soil layer, we considered finite number of resonators throughout our simulations. Analytical work is interpreted using finite element simulations that demonstrates the observed attenuation is due to bandgaps when oscillators are arranged at sub-wavelength scale with respect to the incident Rayleigh wave. For wavelength less than 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when impedance of oscillators matches impedance of soil. Since longitudinal resonance of SDOF resonator are proportional to its length inversely, a formed array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground. Optimum number of vertical pillars and their interval spacing called effective area of resonators are investigated. For 10 pillars with effective area of 1 meter and resonance frequency of 4.9 Hz, bandgap frequency causes attenuation and a sinusoidal impulsive force illustrate wave steering down phenomena. Simulation results proved analytical findings of this work.

Seismic Retrofitting of a Historic Structure with Limited Construction Documentation

Many buildings constructed during the middle of the 20th century were constructed with criteria that fall short of current requirements. Although shortcomings are possible in all aspects of the design, the inadequacies in terms of seismic design present a more pressing issue to human life. This risk has been seen in various earthquakes that have struck Italy recently, and subsequently, the codes have been altered to account for this underestimated danger. Structures built after these changes remain at risk and must be retrofitted depending on their use. This report centers around the Giovanni Michelucci Institute of Mathematics at the University of Bologna and the work required to modify the building so that it can withstand 60% of the current design requirements. The goal of this particular report is to verify the previous reports written in Italian and present an accurate analysis along with intervention suggestions for this particular building. The work began with an investigation into the previous sources and work to find out how the structure had been interpreted. After understanding the building, corrections were made where required, and the failing elements were organized graphically to more easily show where the building needed the most work. Once the critical zones were mapped, remediation techniques were tested on the top floor, and the modeling techniques and effects of the interventions were presented to assist in further work on the structure.