The propagation properties of waves in Timoshenko beams resting on flexible supports and with periodically attached harmonic locally resonant oscillators are studied by the transfer matrix methodology. Through calculating the differential equations of the beam for the flexible vibration and the dynamic equations of the oscillators in series, the matrix of dynamic stiffness and the resulting transfer matrix are derived. Accordingly, the band gap in infinite system characterized by the propagation constant can be verified by comparing to the curve of transmission property, determined with the finite element method for the finite system. The mechanism of each band gap formation is further explored. Numerical results show that different from the single degree-of-freedom mass-spring model, one more locally resonant band gap is generated in the system of two oscillators in series. The introduction of flexible supports, allowing for variable internal coupling between the adjacent cells, produces an extra band gap with a minimum frequency of zero. It is also found that the starting frequencies of the locally resonant gaps are related to the spring stiffness and mass of the oscillator. Therefore, the positions and widths of the band gaps can be tuned by properly adjusting the four parameters of the oscillators and also the stiffness of the flexible supports.

Existing methodologies to calculate the minimum separation distance between adjacent buildings are based on the estimations of the peak relative horizontal displacement of adjacent structures that are characterized by unknown pounding probabilities. The present study proposes a probabilistic performance-based procedure for determining the critical separation distance (CSD) with a designed pounding probability for adjacent buildings under different structural properties and seismic hazard sites. In the proposed procedure, the pounding events are formulated as single-barrier, first-passage reliability problems using the performance-based seismic design theory. Using the random vibration theory, the nongeometric spectral characteristics of the relative displacement response of adjacent buildings are deduced, and the approximate analytical solutions of the seismic pounding fragility are obtained by employing analytical approximations. Based on the seismic pounding fragility of adjacent buildings, the calculation of the CSD is described as an inverse reliability problem, and the specific CSDs with a target probability of pounding during the design life of the given adjacent buildings are derived using a proposed piecewise fitting iterative search algorithm. The proposed procedure is applied to different linear elastic single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. The accuracy and efficiency of the proposed methodology for determining CSD are verified by referencing the importance of sampling using the elementary events (ISEE) method. Furthermore, different parametric analyses are conducted based on the proposed methodology and that consider the influences of different ratios of natural periods, the floor numbers of the adjacent buildings, and the different site hazard curves on the value of the CSD to verify that the procedure to determine the CSD of the adjacent buildings, as proposed in this paper, can obtain a uniform pounding probability for adjacent structures with different structural properties and seismic hazard sites.

Waste poly(ethylene terephthalate) (PET) drinking bottles and end-of-life scrap rubber tires are common municipal solid wastes discarded and produced every day, which are usually disposed of in landfills and stockpiles, occupying a great quantity of land and causing serious environmental issues. This study aims to first turn waste PET into two value-added derived additives under the chemical treatment of two amines, namely triethylenetetramine (TETA) and ethanolamine (EA), respectively, and then adopt them in association with crumb rubber (CR) to modify virgin bitumen for preparing various rubberized asphalt mixtures. Subsequently, the high- and low-temperature properties of the rubberized binder modified by PET additives (PET-TETA and PET-EA) were comparatively characterized through dynamic shear rheometer (DSR) and bending beam rheometer (BBR) tests, while the rutting resistance, fatigue resistance, and dynamic modulus of the further fabricated mixtures were evaluated and validated through mixture tests. The results obtained indicate that 2 wt.% PET-TETA and PET-EA contribute to increase the rutting failure temperature of asphalt rubber from 82.2 °C to 85.5 °C and 84.2 °C, respectively, retaining the high grade of PG 82; the low-temperature grade of asphalt rubber slightly decreased from PG-28 to PG-22 as the additive was added; the rut depth slightly changed from 3.10 mm to nearly 3.70 mm; and PET-TETA exhibits the potential to be capable of extending the fatigue life of asphalt rubber in contrast with PET-EA at different stress levels within 450 kPa. Based on the findings of this study, the developed recycling approach is considered to be applicable to not only alleviate the environmental concerns caused by the landfills and stockpiles of those wastes but also make them valuable for building more durable pavement.

The characteristic receptance method of analyzing the free wave propagation of a finite monocoupled periodic system with a single disorder is applied to study the vibration transmission through the periodic bearing, due to horizontal ground motion, into which the shear modulus or thickness disorder of a rubber layer has been introduced. The upper building and laminated rubber isolator are respectively modeled as two different types of periodic systems. The superstructure model is formulated according to the Euler-Bernoulli beam theory for the walls, while the floors are considered as lumped masses. The shear beam theory along with the lumped-mass model is used to describe the bearing with the rubber layers, reinforced by periodically placing vulcanized steel shims. The point impedance of the superstructure obtained from the indirect receptance and propagation constant is utilized in the development of the displacement transmissibility function of the bearing. The study of the seismic response and dynamic transmission characteristics of the bearings shows that a small shear modulus or large thickness in the disordered element generally enhances the isolated capability. The presented analysis indicates how disorders can be used most effectively for vibration isolation in existing laminated rubber bearings or the design of new laminated rubber bearings.