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In this article, analytical solutions of low velocity transverse impact on a nanobeam are presented using the nonlocal theory to bring out the effect of the nonlocal behavior on dynamic deflections. Impact of a projectile (mass) on simply supported and clamped nanobeams are investigated using nonlocal Timoshenko beam theory. In order to obtain an analytical result for this problem, an approximate method has been developed wherein the applied impulse is replaced by a suitable boundary condition and initial momentum of projectile and nanobeam. A number of numerical examples with analytical solutions for nonlocal nanobeam and classical beam (steel and aluminum) have been presented and discussed. When the value of the striker mass is increased, the frequencies are decreased and the maximum dynamic deflection at the center of the beam is increased for both of the simply supported and the clamped-clamped nanobeams. The inclusion of the nonlocal effect increases the magnitudes of dynamic deflections and decreases frequencies. Furthermore, the mass and the velocity of the nanoparticle (striker) have significant effects on the dynamic behavior of nanobeam.

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In this paper, thermal effect on deflection, critical buckling load and vibration of nonlocal Euler-Bernoulli beam on Pasternak foundation using Ritz method is proposed. Equations of motion Euler-Bernoulli beam on Pasternak elastic foundation under thermal load is achieved by using energy method. Ritz method is used to solve the governing equations of motion. By this method, mass, stiffness and hardness buckling matrices are obtained. In this study, the effects of thermal, various boundary conditions, Winkler-type spring constant, Pasternak-type shear constant, non-local parameter on dimensionless deflection, critical buckling load, and natural frequency of Euler-Bernoulli beam theory are assessed. The obtained results indicate that with an increase of Winkler and Pasternak constants, the dimensionless natural frequency and critical buckling load increase, while the dimensionless deflection decreases. However, with increasing the temperature change in nonlocal Euler-Bernoulli beam on Winkler–Pasternak elastic foundation, the dimensionless natural frequency and critical buckling load decrease, while the dimensionless deflection increases. Moreover, with considering Winkler and Pasternak constants, the lower mode shape are removed and replaced with higher mode shapes.

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In this paper, the governing equations for a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. These equations which are a system of nonlinear partial differential equations with constant coefficients are solved analytically with the perturbation technique and the natural frequencies and the buckling load of the system are determined. A parametric study is performed and the effects of the geometrical and material properties on the natural frequency and buckling load are investigated and the effect of normal transverse strain and axial load on natural frequency are examined. Some results based on the first order shear deformation theory are consistent with classic theories of beams and some yield different results. Formulation presented to calculate the transverse frequency, determines the axial frequency too. Also, the natural frequencies and buckling load are calculated with the finite elements method by applying one and three-dimensional elements and the results are compared with the analytical solution.

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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 corrugated composite beam is actuated by shape memory alloy wire (SMAw). SMAw was placed on the surface of composite beam. Martensite to austenite transformation occurs by increasing of SMAw temperature. After transformation, SMAw length decrease and beam actuated. Beam displacement, force and current are measured and by A/D board transferred to computer. For evaluation of temperature in SMAw, the Heat transfer differential equation is used. Also Brinson’s model is used for modeling of SMA behavior. The results show that SMA behavior in Brinson’s model is good agreement whit experiments. But in lower temperatures than martensitic transformation state, the SMA stress is equal to zero in experiment unlike Brinson’s model. Also considering the SMA training and DSC test, for some temperatures in the experimental results, the start and end transformation temperatures are different to Brinson’s model. The results show as using SMAw in the corrugated composite, smart structures can be achieved that in corrugation direction is irritable, whereas in Perpendicular to the direction, corrugated composite bending strength is high that lead to using this structure in engineering application.

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In this study, the non-linear bending analysis of isotropic and orthotropic rectangular plates is performed by Dynamic Relaxation (DR) method. In order to model the plate, the four-variable refined plate theory, which is a new and simple higher-order shear deformation theory and has a good capability in analysis of thick plates, is adopted. Despite the first-order shear deformation plate theory; this theory does not need the shear correction factor, predicts shear strains and stress parabolically across the plate thickness and satisfies the zero stress conditions on free surfaces. The governing equations are obtained using virtual work principle and the Von-Karman nonlinear terms are considered in strain-displacement equations. The non-linear coupled governing equations are solved by DR method combined with finite difference technique, and for this purpose a computer code is provided in MATLAB software. In order to demonstrate the accuracy of present method, the numerical results are compared with the existing ones and very good agreement is observed. Also the effects of side-to-thickness ratio and boundary conditions on the results are examined. Finally, the variations of shear effects by changing the plate thickness and also changing the orthotropy ratio in orthotropic plates are investigated.

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The inseparable parts of any industrial unit are usually the rotary machines. Fans are categorized as a common type of rotary machines, which play an important role in the industry. In order to decrease the repairing costs and energy consumption, Fans have to operate without vibration. However, if the fan unit with an acceptable level of vibrations is installed on a huge structure, the vibration caused by the fan can develop complications for the structure as well as serious problems for the fan itself. A long-time operation of a faulty fan can cause failure in the fan motor and fatigue in the structure. Therefore, investigating the root causes of the vibrations of the fan and decreasing the vibrations is vital for increasing the operating time and the efficiency of the fans. This study is focused on identifying the root causes of excessive vibrations of one of the air fans in BualiSina petrochemical company. First, the main frequencies which are responsible for the increase in vibration levels are identified, by using ODS analysis. Then, the natural frequencies of the structure are derived using the operational modal analysis (OMA). Also, the finite element model of the fan unit and the structure is developed based on the most possible compatibility with the experimental data. Finally, a number of suggestions for reducing vibration amplitudes of the fan are proposed.

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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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Micro-milling is prominent among other micro-manufacturing processes due to their abilities in manufacturing of 3D features, high material removal rates and high precision. One of the most important challenges of this process is tool deflections which contribute even up to 90% of dimensional errors of the finished product. This paper addresses a novel method to estimate micro-milling tool deflections applicable in micro-milling machines equipped with linear motors. In this method, position feedbacks and inputs to the amplifiers are used to real-time estimation of cutting forces by applying Kalman filter. Outputs of the estimator include a resultant of all disturbing forces in servo control loop of the motors. Therefore, cutting forces need to be compensated for other disturbing forces that are mostly friction and force ripples in linear motors. To compensate them, neural networks were used. A neural network with a hidden layer and 16 nodes inside, and with two time-delayed lined (TDL) could well model friction and force ripples. Results showed that the proposed tool deflection method is able to estimate 22% of micro-milling tool deflections.

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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.

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In design of structures using force-based methods applied in current seismic codes, to obtain the nonlinear displacements of structures under the design earthquake, deflection amplification factor (C_d) is applied. In other words, the displacements obtained from elastic analyses under the reduced seismic forces are amplified by C_d to obtain the inelastic displacements under the design earthquake. Research studies showed that using a constant coefficient for estimating the inelastic displacements may lead to considerable overestimation or underestimation of the displacements in different stories of structures. Generally, in regular structures the inelastic maximum interstory drift ratio (IMIDR) occurs in lower stories. Investigating the seismic performance of structures with irregularity in their heights showed that the inelastic responses of these types of structures can differ significantly from the inelastic responses of regular structures. The present study investigates C_d for estimating IMIDR and inelastic maximum roof drift ratio (IMRDR) for steel special moment resisting frames (SMRFs) with vertical mass irregularity under the design earthquake. In addition, the variation of C_d with the variation of the location of the heavier story in the structural height, and mass ratio (i.e., the ratio of the mass of the heavier story to the mass of the adjacent story) is studied. For producing a heavier story, the dead and live loads of the story are multiplied by 2.0 and 3.0. Three different locations (i.e., bottom, mid-height and top story) for the heavier story, are assumed. For investigating the effects of mass irregularity, two regular 5- and 10-story structures are also considered. Therefore, 14 structures (i.e., two mass ratios × two building heights (5 and 10 stories) × three locations for the heavier story + two regular structures) are considered. To perform nonlinear dynamic analyses, 67 ground motion records are applied. The records are scaled such that the mean of the pseudo acceleration response spectra exceeds the design response spectrum for the period range of 0.2T₁ to 1.5T₁. The results show that using C_d = 5.5 recommended by Standard No. 2800 and ASCE 7 for steel SMRFs underestimates the IMIDR in most of the structures considered and their stories, under the design earthquake. When the heavier story is located in the first story, the lowest mean C_d is obtained in the first story. Because, increasing the mass of the story leads to an increment in the stiffness and strength demand of the story. When the heavier story is located at the roof, the lowest mean C_d is obtained for the top story. While the mean C_d in the first story increases significantly. Moreover, it is shown that C_d = 5.5 underestimates the IMRDR in the structures considered. Investigating the consideration of different values for C_d shows that using C_d = 7.5 leads to the lowest error in the estimation of IMIDR in the structures considered. In the case of estimating IMRDR, the displacement amplification factor is termed C_{d Roof}, and it is shown that using C_{d Roof} = 6.5 leads to the lowest error in the estimation of IMRDR. Therefore, C_d = 7.5 and C_{d Roof} = 6.5 are respectively proposed for more precisely estimating IMIDR and IMRDR in steel SMRFs with vertical mass irregularity.
 

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Response modification factors are used to reduce the lateral loads in "force-based design" method. Naturally the calculated lateral displacement (drift) of the structures in the linear static analyses is smaller than actual values. Hence, deflection amplification factor (C_d) is needed to consider a realistic estimation of nonlinear displacements. Most seismic design codes such as ASCE7 and standard No. 2800- 4^th version propose this factor for different lateral bearing systems. This paper evaluates the proposed deflection amplification factor for dual system of special reinforced concrete moment-resisting frame with/without shear wall. For this purpose, a set of 2D reinforced concrete frames with 3, 7 and 11 story are designed based on standard No. 2800 (4^th version) and implemented in Opensees software in each case without considering the soil- foundation- structure interaction. In this regard, beams and columns are modeled using concentrated plasticity method with “Elastic Beam Column Element” in the middle and “Zerolength Element” at the end of elements. Moreover, “SFI-MVLEM” element is used for modeling of shear walls. Nonlinear behavior in two ends of the beams and columns is assigned by “Modified Ibarra- Medina- Krawinkler Deterioration Model with Peak-Oriented Hysteretic Response” model which has been developed by Ibarra et al. (2005). This model is defined using the proposed equations by Haselto et al. (2007). Uniaxial behavior of steel reinforcements and concrete sections are simulated by Steel02 and ConcreteCM, respectively. Studied frames are verified using Hatzigeorgiou and Liolios (2010) and Liu et al. (2020) study for special moment-resisting frame with/without shear wall, respectively. In addition to linear static analysis (LSA), linear and nonlinear dynamic analyses (LDA and NDA) are applied to 3, 7 and 11 story frames with two lateral bearing systems. In this regard, 22 far-field ground motion records which have been introduced in FEMA P695 are used as seismic scenarios. These records are scaled based on Standard No. 2800 to have identical spectral acceleration with the design spectrum for the fundamental period (T) of each studied frames. For this purpose, each record is normalized to its peak ground acceleration and records are scaled so that the average acceleration spectrum of all records was above the design spectrum in 0.2T to 1.5T range. In order to evaluate the deflection amplification factor and C_d/R, maximum drift of roof and other stories is used for each frames due to concentration of structural damage in certain floors of a multi-story structures and, consequently, creating larger lateral displacements in those floors. The calculated C_d coefficients are compared to the proposed values in ASCE7 and standard No. 2800 (4^th version) for all special reinforced concrete moment-resisting frames with/without shear wall. This comparison shows that the C_d coefficients which have been proposed in above-mentioned seismic design codes are not appropriate and more realistic estimate of the structural performance in earthquake has demanded larger C_d values. Moreover, C_d and C_d/R values are changed with the height of special reinforce concrete frames with/without shear wall. Finally, adequate values of deflection amplification factors are proposed for these frames with/without shear wall in this paper.

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Most seismic hazard assessments are usually performed only with consideration of the initial shock in the technical literature of structural and earthquake engineering. While the magnitude of aftershocks that occur after the main earthquake, may be enough strong to cause a lot of damage to the structures. Most aftershocks increase the structural damage caused by the main earthquake because of cumulative damage and increased vulnerability may seriously threaten the safety of residents. The structures are designed for solely a single earthquake – design earthquake –  based on the existing seismic design codes. For example, these codes did not provide specific values for the actual relative displacement under successive earthquakes to assess the structural damages. Therefore, considering the effect of multiple shocks consist of fore-shock and main-shock or main-shock and after-shock seems necessary. Moreover, the construction of a new building is not economic and requires a lot of time, which is not easily available to many communities. Hence, the design of structures considering the some capabilities such as replacement of damaged elements can improved significantly the performance of structures after severe successive earthquakes. However, most of the proposed structural systems are not generally repairable while replacing several damaged members under the earthquake, can be very economic and applicable. The linked column frame (LCF) as a relatively modern lateral bearing system, is a type of dual systems; the recent emergence of this structural system has reinforced the need for multiple seismic studies. For this reason, LCF is selected in this paper and the deflection amplification factor (C_d) for this system is evaluated under critical earthquakes with seismic sequences. This coefficient is calculated based on the linear displacements obtained from linear static analysis and actual values from nonlinear analysis. In this regard, 18 steel frames equipped by the linked column frame as lateral bearing system, with 3, 7, and 11 stories are designed based on the Iranian earthquake design code (Standard No. 2800, 4^th version – 2014). These frames are implemented in Opensees software and have been subjected to linear static, linear, and nonlinear dynamic analyses using critical earthquakes with/ without seismic sequence phenomenon to calculate the deflection amplification factor (Cd) and Cd/R for each of them based on Uang methaod. In order to better investigation of the mentioned coefficient, the effect of various parameters such as the length of the connection beams as well as the flexural or shear behavior of the connection beams have been considered. Thus, after the evaluations, the findings indicate an increase in Cd and Cd / R values, for the linked column frame with the connected column exposed to successive earthquakes. The increase of this coefficient has been more in short-frame frames. So that the most increase which hase been related to the 3-story frame with shear behavior and 2-meter linked distance, is about 11 percentage under the successive earthquakes. Also, the average results which have been obtained from consecutive earthquakes reveal that the proposed values ​​for C_d coefficient in the technical literature are not sufficient, and larger values ​​have been demanded.

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