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Building structures begin to deteriorate once they are built due to harsh environment such as earthquake. To inspect present buildings and bridges following major disastrous events, such as earthquakes and hurricanes is often time-consuming and of high expense. This is also the case in regular operating conditions. Indeed critical members and connections are hidden under cladding and other architectural surface covers. This study aims to propose a novel method for identification of damages occurred in beams based on deflection under static loading. In this paper damage location on a beam is determined using statistical hypothesis testing applied on the deflection of the beam. It is worth mentioning that the statistical hypothesis testing is an appropriate method for statistical inference which can be used to judge a claim concerning an event in regards to different scenarios and possibilities. The statistical claim which would be analyzed is that damage is present among elements of the beam. Deflection of beam as a derivation of stiffness will be utilized here. Hence the basic idea in this study; to locate damages, is behind of calculating the difference between measured and estimated deflection of nodes of each element in both intact and damaged structures. Elements damage can be specified by applying damage index which is defined as D(x). Element’s damages can be judged through the damage index sign in two nodes of every element: The element will be considered damaged if the index is positive for both nodes of middle element or it is positive in only one node of element leading edges of fulcrums. To illustrate the efficiency and robustness of proposed method three different examples are considered. First example is a simple beam with five different scenarios including single and multiple damages. Second example is also presented to show comparison of the proposed method with the study by Abdo [18] and finally third instant is considered for showing reliability of the method in different beam types. For all of the examples, the deflection of damaged beams is recorded via sensors under only one state of static loading and the statistical parameters of the undamaged beams are generated under several static loading. Then by calculation of damage index, we can decide about damage locations. All examples show good performance of the novel method in damage localization. The most important result obtained from these examples is that, the more fine mesh, the better and the more accurate performance of the method. Of course this assertion is more important in the elements leading edges of fulcrums. Further, the performance of this method is demonstrated through damage simulation where the measured data are contaminated with noise and hence to evaluate the stability of the proposed method against various noise levels, scenarios are considered with different such levels.

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In this study, the static deflection and natural frequency of an electrostatically excited patch-coated microcantilever beam are analyzed. The proposed model is considered as the main element of many microsensors and microswitches. Firstly, the nonlinear motion equation is extracted by means of Hamilton principle, assuming shortening effect. Secondly, differential equations, governing the static deflection and free vibration equation around the stability point, are solved using Galerkin method and the three mode shapes of a uniform microbeam are employed as the comparison function. By assuming that the volume of deposited layer is constant, the variation of natural frequency and static deflection are examined in three different cases. In any cases, it is presumed that the second layer is initially deposited on the entire length of microbeam. In the first case, one end of coated layer is considered fix at the clamped side of microcantilever, and then its length is decreased from other side, where its thickness is increased. In the second case, one end of coated layer is perceived fix at the free side of microcantilever, and then its length is decreased from other side, where its thickness is escalated. In the third case, the length of second layer is decreased from both of left and right ends, where its thickness is expanded. In addition, the effect due to the change of the second layer position is considered on mechanical behavior of the system.

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With development of micro-electromechanical phase shifter, the study of deformation and instability of micro-switches is very important. The static behavior and pull-in instability of the clamped-clamped micro-beam subjected to local electrostatic loads which is used in DMTL phase shifter is investigated. Taking into account of nonlinear effects caused by radius of curvature for the first time, the nonlinear differential equation of the system is obtained using Euler-Bernoulli beam theory and effects of small sizes by employing the principle of virtual work. By considering the local electrostatic static voltage applied on the micro-beam, the governing partial differential equation is further discretized with the aid of Galerkin’s method, and the effect of system parameters on static deflection and pull-in voltage of the micro-switches are investigated. It is found that curvature nonlinearity has a great effect on the mechanical behavior of the micro-switches. Increasing this parameter leads to hardening behavior in the micro-switches, and also static deflection is decreased with respect to linear beam theory. The results also indicate that with an increase in the applied voltage, nonlinear strains increase and nonlinear effects caused by radius of curvature will be significant. For instance, when the stiffness parameter is increased from 0 to 10, maximum deflections of the micro-switches for applied voltages of 1V, 2V and 3V decreases about 7.7%, 35.8% and 48.6 %, respectively.