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- In this paper vibration frequency characteristics of functionally graded cylindrical (FGM) shells are investigated using the differential quadrature method (DQM). The essence of the differential quadrature method is that the partial derivative of a smooth function with respect to a variable is approximated by a weighted sum of function values at all discrete points in that direction. Its weighting coefficients are not related to any special problem and only depend on the grid points and the derivative order. The material properties are graded in the thickness direction of the shell according to the volume fraction power law distribution. The fast convergence behavior of the method is demonstrated and its accuracy is verified by comparing the results with those of other shell theories obtained using conventional methods and also with those of ABAQUS software. Effects of the exponential volume fraction law on the natural frequencies of FGM cylindrical shells for classical boundary conditions (all possible combinations of clamped (C) and simply supported (S) boundary conditions) are studied against circumferential wave number, length to radius ratio and thickness to radius ratio for different values of power law exponents

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In this paper, free vibration analysis of moderately thick smart FG rectangular plate is presented on the basis of Mindlin plate theory. This structure is composed of a host FG plate and two bonded piezoelectric layers. The plate has two opposite edges simply supported (i.e., Levy-type rectangular plates). The closed circuit piezoelectric layers can be used as an actuator. According to a power-law distribution of the volume fraction of the constituents, material properties vary continuously through the thickness of host plate. Using Hamilton's principle and Maxwell electrostatic equation, six complex coupled equations are introduced. These equations are exactly solved introducing the new potential and auxiliary functions as well as using separation of variables method. The accuracy of the frequencies is verified by the available literature and the finite element method. The present exact solution can accurately predict not only the out of plane, but also the in-plane modes of FG plate. Finally, the effects of various parameters such as boundary conditions, gradient index and thickness of piezoelectric layers on the natural frequency are investigated.

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in this paper natural frequencies of a rectangular mindlin plate with surface bounded piezoelectric patches is obtained. Simply supported boundary condition is imposed at the plate edges. Ritz approach based on the principle of minimum potential energy is applied to obtain the frequency parameters of rectangular plate. Since displacement fields of the plate are postulated by trigonometric series function, solution is a semi analytical one. For verifying the accuracy of this method, results are for the isothropic and piezoelectric plates are compared with those reported in the literature. As we see a good conformance is derived from the obtained results and the exact solution. At the end, natural frequencies of a rectangular mindlin with surface bounded piezoelectric patches is obtained.

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In this paper, the effect of the crack on the vibration behavior of a thick-walled cracked pipe conveying fluid is investigated. The presence of a crack on the pipe introduces considerable local flexibility at the crack location. This flexibility is modeled by the fracture mechanics approach. The accuracy of the model is validated through the experimental data reported in the literature. Then, by using the mentioned model, the vibration analysis of the cracked pipe conveying fluid has been accomplished. Moreover, in order to solve the equation governing the vibration of the cracked pipe conveying fluid, a new analytical technique based on the power series method is proposed. Then, by applying the boundary conditions and the compatibility conditions at the crack location, the frequency equation is obtained. The results are presented by appropriate curves showing the variation of the natural frequency of the cracked pipe conveying fluid in terms of the crack depth and the fluid flow velocity. Also, the results show that for a cracked pipe with a given depth and location for the crack, by increasing the fluid flow velocity, the natural frequencies of the pipe decrease. Also, as the fluid velocity approaches to a certain value, the fundamental natural frequency approaches zero and instability occurs.

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Sensible vibration of steel beams in long spans is undesirable issue in the buildings. These beams may be vibrated during people passage, although the strength calculations of this beams to be performed, accurately and drift control index based on buildings codes to be considered. Iranian Steel Buildings Code has offered a formula for controlling of vibration of beams in building frames with pin connections in serviceability phase. However, this code has not presented criteria for beams include fixed connections. Since these beams have the considerable portion of building frames, their vibration control needs special attentions. The presented equations for determination of beams frequency are complicated and have been not used for control of buildings floor vibration. In this paper, the mentioned formula in forenamed codes has been discussed. The dynamic analysis, finite element method (FEM) and artificial neural networks (ANN) techniques have been adopted to constitute the frequency equations of the fix ends and cantilever steel beams. Comparison of resulted frequency from presented equations and ANN showed that the error is low. Furthermore, it is suggested that use proposed equations for determination of frequency of moment connection beams.

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Automotive crankshafts are subjected to fluctuating torques due to periodic strokes in the cylinder. The gas-forces and inertial-forces due to the reciprocating masses will contribute to the excitation forces on the crankshaft system. The forces cause alternative torque on the crankshaft and cause vibration on the motor which cause noise and shake in the vehicle. Therefore, it’s necessary that was determined crankshaft dynamic behaviour. Although most physical structures are continuous, their behaviour can usually be represented by a discrete parameter model. In this paper, torsional vibration was determined with theoretical, analytical and experimental analysis on the Peugeot and Renault vehicle. For Solution of theoretical analysis, was used of B.I.C.E.R.A formula [1] and natural frequency for analytical analysis obtained with ANSYS software. Then, theoretical and analytical procedure compared with the experimental model, to obtain optimization model and with the best model, influence of torsional vibration was determined on the engine speed.

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The current article presents an analytical approach, for determining the natural frequencies of a rotating cracked Euler–Bernoulli beam with a varying transverse cross-section, using the so-called differential transform method (DTM). First, the natural frequencies of the beam are obtained for different values of the crack position and depth. The results have been validated against those obtained from experimental modal test, Abaqus software and some other methods reported in the literature and a good agreement between the results is observed. Then, the inverse problem is investigated. For this reason, the position and depth of the crack of the rotating beam with a varying transverse cross-section are estimated using the genetic algorithm and then, the natural frequencies are obtained from the modal test. It is seen that the numerical results have a suitable agreement with the actual position and depth of the crack that indicates the effectiveness of this method in determining the parameters of the crack in the rotating beams.

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Conventional modal testing is a powerful tool for dynamic analysis of structures. One of the drawbacks of this technique is the problem of excitation of large structures such as: bridges, towers or trains. However, these structures are excited by ambient forces, such as wind, walking of people or passing the cars on bridges. Operational Modal Analysis (OMA) is the practical tool to overcome this problem. In OMA the structure is excited by ambient forces and only the responses are taken into account. In this article, the accuracy of one of OMA methods is investigated. The modal parameters of a cantilever beam are estimated both from Stochastic Subspace Identification–Covariance Driven (SSI-COV) method and Finite element method. The effect of noise and damping on the accuracy of modal parameters is investigated. Also, a crankshaft is considered for experimental investigation of the accuracy of SSI-COV method. The results show the applicability of SSI-COV method in practical cases.

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This paper studies the vibration characteristics of a cracked Timoshenko beam with a varying transverse cross-section using Differential Transform Method (DTM). The effects of the crack location and the crack size in calculating the natural frequencies and mode shapes are investigated. The result have been validated for a beam with and without the crack against those obtained from experimental modal test, Abaqus software and some other methods reported in the literature and a good agreement between the results is observed. The results show that the Timoshenko theory predicts fewer values for the natural frequencies because there is less rigidity, especially for large values of cross-section moment of inertia. Then, the inverse problem is investigated. For this reason, the position and depth of the crack of the beam with a varying transverse cross-section are estimated using the genetic algorithm and then, the natural frequencies are obtained from the modal test. It is seen that the numerical results have a suitable agreement with the actual position and depth of the crack that indicates the effectiveness of this method in determining the parameters of the crack in the Timoshenko beam.

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This study is investigated vibration analysis of a FG rectangular plate partially contacting with a bounded fluid. Wet dynamic transverse displacement of the plates is approximated by a set of admissible trial functions which is required to satisfy the clamped (CL) and simply supported moveable (SSM) and simply supported immoveable (SSI) geometric boundary conditions. The oscillatory behavior of fluid is obtained by solving the Laplace equation and satisfies the boundary conditions. The natural frequencies and mode shapes of the plate coupled with sloshing fluid modes are calculated by using the Rayleigh–Ritz method based on minimizing the Rayleigh quotient. The proposed method is validated with available data in the literature. In the numerical results, the effects of volume fraction coefficient, thickness ratios and aspect ratios of the FG plates and depth of the fluid, width of the tank, and boundary conditions on the wet natural frequencies are examined and discussed in detail.

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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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Bridges are exposed to damage during their service life which can severely affect their safety. Thus, it is important to monitor bridges for existence of damage. A damage in a structure alters its dynamic characteristics. Changes in properties such as the flexibility or stiffness matrices derived from measured modal properties and changes in mode shape curvature have shown promise for locating structural damage. Since damage alters the dynamic characteristics of a structure, namely its eigenproperties (natural frequencies and modes of vibration), several techniques based on experimental modal analysis have been developed in recent years. Therefore vibration characteristics of a structure can be used as the basis for vibration based damage detection (VBDD) techniques. These techniques have been recently subjected to a considerable amount of attention for damage detection due to their relative simplicity and the moderate cost of dynamic measurements. Damage detection methods based on the dynamic measurements of structures are one of the most important techniques for damage evaluation in bridges. VBDD methods use damage-induced changes to the dynamic properties of a structure to detect, locate, and sometimes quantify the extent of damage.VBDD methods are able to detect damage with information from the dynamic response of the bridge only. The performance of these methods for damage detection in bridges has not been fully proven so far and more research needs to be done in this direction. In this article a new method base on developing the Co-Ordinated Modal Assurance Criteria and Damage Inedx (DI) is present. For applying these methods, mode shapes and natural frequencies that came from health bridges model and damage bridges model are used. The bridges that used are a two-span bridge and a five-span bridge that modeled and verified. To verifying the models, five natural frequencies of the models that created with software, copmared to natural frequencies of the original models. In this article just one element defined as damage location. The damage created by redusing stiffness in one element near the abutments. The four level damage that considered are 15%, 30%, 70% and 90% reduce in module of elasticity. At first the unability of COMAC and DI methods to detecting the damage near the abutment is shown. Then the new method base on these method is presented. This new method is use of mode shapes that obtained from several longitudinal section instead of one longitudinal section. Results confirmed that if mode shapes are just extract from one longitudinal section like before, methods can not always detecting the damaged cross section or damaged longitudinal section. But if mode shapes obtain from several longitudinal sections, these methods will be able to assessment the damaged cross section plus damaged longitudinal section. Although in the most of the times these methods detecting the elements at the abutment as damage location wrongly. So it is necessarily to eliminate the result of the element at the abutment and then decided for the damage location. Besides it is concluded that for detecting the damage near the abutment, COMAC method has better

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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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Frame structures have several applications in industries. They are used to carry all types of loadings. Usually catastrophic failure in these structures initiate from small cracks. Catastrophic failure can be prevented by detecting the cracks early and replacing or repairing the cracked members. The change in dynamics and vibration characteristics is one of the consequences of cracks in structures. In this work, detection of surface cracks in frame structures with regards as the change in natural frequencies of the system is studied. The finite element has been used to compute the natural frequencies of cracked structures. Then, according to the difference in natural frequencies of intact and cracked structures the locations and depths of cracks have been determined by the solution of an inverse problem. For the inverse problem the ant colony optimization algorithm has been employed. It is shown that; while, the changes in natural frequencies are good means for crack detection in a separate beam, it is not sufficient for crack detection in a frame structure. It seems that, other characteristic of the system such as changes in natural modes must be considered.

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Free vibration analysis of a cracked rotating multi-span Timoshenko beam is studied in this article to determine the natural frequencies and mode shapes of this beam. First, the relationships between each two segments are obtained by considering the compatibility requirements in the frame angles and in the cracks. To determine the transformed compatibility requirements, the boundary conditions, and the vibrational equations, the so-called differential transform method (DTM) is used. Then, these equations are performed to determine the natural frequencies. The mode shapes of the beam are determined by using the inverse of differential transform method. The results have been validated against those obtained from Abaqus software for a rotating multi-span beam and the ones obtained from transfer matrix method for a non-rotating case that an appropriate agreement is observed. Finally, the effects of the angle of break, the rotational speed, and the crack location on the natural frequencies are investigated. It is shown that the natural frequencies will be increased by increasing the rotational speed. Also, it is seen that the first natural frequency will be increased by moving the crack location from the cantilever support to free support and the variations of other frequencies are dependent to the crack distance to the vibrational nodes. The validation results show the accuracy of DTM in the process of studying the free vibration of this problem.

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Free vibration characteristics of rectangular composite plate with constrained layer damping and magneto-rheological fluid (MR) core are presented.. Hamilton principal is used to obtain the equation of motion of the sandwich plate. Based on the Navier method, a closed-form solution is presented for free vibration analysis of MR sandwich plate under simply supported boundary conditions. The governing equation of motion is derived on the base of classical lamination theory for the faceplates. Only shear strain energy density of the core is considered. Using displacement continuity conditions at the interface of the layers and core, shear strain of the core is expressed in terms of displacement components of the base and constraint layers. The complex shear modulus of the MR material in the pre-yield region was described by complex modulus approach as a function of magnetic field intensity. The validity of the developed formulation is demonstrated by comparing the results in terms of natural frequencies with those in the available literature. The effects of magnetic field intensity, plate aspect ratio, thicknesses of the MR core, base layer and constrained layer for three different stacking sequences of composite faceplates on the fundamental frequency and loss factor of the first mode are discussed. The results indicate significant effect of physical and geometrical parameters on the natural frequency and loss factor associated with the first mode.

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Nowadays the Computer Aided Engineering (CAE) technique is widely used for improving Noise Vibration Harshness (NVH) performance of vehicles. High complexities in the Body In White (BIW) of vehicles lead the developed CAE models to become complex by which the optimization process will become very hard. Concept modeling could be a suitable replacement to overcome the mentioned limitations. Dynamic characteristics such as natural frequencies and mode shapes could be studied in the early phase of design with very low amount of calculations with the concept model. For this purpose, a developed concept model has been presented for the wheelhouse. The developed concept model uses approximated equivalent beam elements to model the beam like and panels of the structures. Also, the experimental test and numerical model have been utilized for the validation of the developed concept model. Two criteria of natural frequencies and corresponding mode shapes have been considered as the measure of validation. The results showed good correlation with corresponding advanced CAE models as well as experimental tests in low frequency range. The results showed that the developed concept model in this research is a powerful and effective tool to enhance and optimize the NVH performance of the vehicle in the early stage of design.

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A comparison between three different time domain MIMO modal identification techniques i.e. ERA, EITD and PRCE is performed. The comparison is executed for discontinuous (mass and spring) and continuous (beam) systems in two different cases; i. e. experimental and operational modal analysis techniques. For this purpose the modal parameters of the system are measured using both direct time history data of impulse response (EMA) as well as correlation function of random response of the structure (OMA). From the results it is noted that some parameters like sampling frequency and total recording time have effect on their accuracy. Sensitivities of the results due to these parameters are measured and reported for all three considered methods. For this purpose the effecting parameters are altered between a couple of values and the sensitivity of the results is studied for all methods in both EMA and OMA cases. Finally, a comparison between the results of different methods is done and the accuracy of the methods is studied. It is concluded that ERA is the most accurate and reliable method with the least sensitivity to effecting parameters in both EMA and OMA cases.

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In this paper, thermal and vibration response of cross-ply bi-stable composite laminated plates were studied using semi-analytical, finite element and experimental method. In order to evaluate the semi-analytical and finite element results, a bi-stable composite plate was manufactured using a special procedure. Next, geometrical characteristics and displacement of different paths on the plate were measured experimentally at room temperature. In semi-analytical approach, the two stable states and the first natural frequency of cross-ply laminates are calculated based on Rayleigh–Ritz approach combined with Hamilton’s principle. In this study, a modified shape function was introduced that allows the curvatures to vary in both longitudinal and transverse directions. Using the modified shape function, the displacement of the plate in its stable configuration and the first natural frequency of the plate can be more accurately predicted in compared to the Hyer’s shape functions. The obtained results from the proposed shape function are in good agreement with the finite element and experimental data. The proposed shape functions can also be used in dynamic and vibration analysis to determine the snap-through load of the cross-ply laminates.

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ََAbstract Recognition of the dynamical behavior and vibrations of marine structures, submerged in vicinity of the water free surface, is one of the most important issues in design of the marine structures. It is obvious that physical properties of the ambient fluid have some influences on vibrational frequencies of the structures. For the structures that have exposed under the influences of asymmetric environmental conditions, prediction of their dynamical behaviors is more complicated. In this paper the effects of immersion depth on first natural frequency of a bounded circular plate that was placed parallel in vicinity of the water surface, are studied numerically and experimentally. Based on the author’s knowledge, the techniques used for exciting the plate and measurements of natural frequencies are innovations of this research. Numerical solutions are done by using of the ABAQUS software. Comparisons of the numerical and experimental results show a good consistency. The investigations showed by increasing of the immersion depth, so the ratio of the depth to plate diameter reached to a certain value, the natural frequencies were also decreased. After that it remained constant while the immersion depths of plate were increased.