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Piezoelectric beams are the most common energy converters for mechanical-to-electrical energy. In this paper, an analytical method is introduced and developed for modeling piezoelectric vibrationbased energy harvester, which is a strain energy method, and it is simple enough and straightforward than similar methods, such as finite element and FRFs approaches. Closed-form expressions have been extracted for the open-circuit natural frequencies, open-circuit voltage, generated current, and maximum output power which are important parameters of the energy harvesting system, therefore measurements don't need the experimental setup to take. Piezoelectric layers are also investigated in both parallel and series connections which produce equal power at optimum resistive load but cause different voltage and current in the resistive load. The maximum output power occurs when the equivalent capacitive reactance of piezoelectric layers is equal to the resistive load; in addition, the optimum load resistance in series connection is 4 times larger than the parallel connection. Depending on the type of generator's usage and its application, an appropriate decision regarding the parallel or series connection could be made. The maximum normalized power density in the fundamental natural frequency, at the optimum thickness and the optimum load resistance, was 18.717 . mW g cm 2 3( ) RECEIVED

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TADAS dampers are a type of passive structural control system used in the seismic design or retrofitting of structures. These types of dampers are designed so that they would yield before the main components of the structure during earthquake. This dissipates a large portion of the earthquake's energy and reduces the energy dissipation demand in the main components of the structure. Considering its suitable performance, this damper has been the subject of numerous studies. However, there are still ambiguities regarding the effect of the number of these dampers on the retrofitting of reinforced concrete (RC) frames and their design procedure. In this study, a singlestory, single-bay RC frame with the scale of 1:3, equipped with the TADAS damper, was subjected to hysteresis loading until the drift of 4%. Then, for further assessment, 48 calibrated numerical models were constructed in ABAQUS and the effects of the number of TADAS dampers and column axial force upon the stiffness, strength, and ductility of the frame were accurately investigated. Also, a number of formulations were presented to calculate how the stiffness and lateral strength of the retrofitted frame are affected by an increase in the number of the TADAS plates. The results showed that if the shear capacity of the retrofitted frame is three times that of the initial frame, the structure would have the best response. In addition, if the axial force in the columns exceeds 0.2 P cr the energy dissipation and ductility factor of the frame drastically decrease.

Yielding dampers operate based on plastic deformations and energy dissipation. Given its low yield stress point and high ductility, low-yield steel is a suitable choice to build yielding dampers. In the present study, using the ABAQUS software, a number of pushover analyses have been carried out on a steel frame equipped with low-yield yielding dampers (LYDs). Therefore, using 40 pushover analyses, the effects of the number of the LYDs and the column’s axial force have been evaluated. All of the models were analyzed and their force-displacement curves were obtained. Using the obtained, different seismic aspects of the frame – i.e., ductility, strength, energy dissipation, stiffness – were assessed. Also, to calculate the values of effective stiffness and yield and ultimate strengths, a number of analytical relationships have been formulated. Finally, contour plots have been obtained which can be used to calculate the stiffness of the proposed LYD. Comparing results showed that the damper can, to an acceptable level, improve the seismic parameters of the structure. Also, if the stiffness and yield strength of all of the LYDs added to the frame are, respectively, 3.25 and 0.13 times those of the bare frame, the frame will have its best performance.