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Abstract: The experimental study of structural vibration is often performed to determine the modal parameters of a structure or to verify the theoretical models and predictions. The first phase of this research involved the experimental determination of the modal properties of a rectangular steel tank with different levels of water. The natural frequencies obtained from the experiments were compared to those calculated by the analytical models. In the second phase, a procedure for computing hydrodynamic pressures in rectangular tanks is proposed. This procedure considers the effect of tank wall flexibility in determining the hydrodynamic pressures produced by the impulsive response. Based on a two-dimensional model of the tank wall, a dynamic time-history analysis was carried out. The results were compared with other models based on the current design practice codes and standards, which use a lumped mass approach. The comparison shows that, in most cases, the lumped mass approach overestimates the base shear. The effect of wall flexibility on wall displacements and base shears are also discussed.

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This paper introduces a new approach for the reduction of sound radiation from the mechanical structures. A combination of genetic algorithm method and geometry modification concept minimizes the root mean square level of structure borne sound for a square plate over a specific frequency range. The structure’s local geometry modification values at the selected surface key-points considered as design variables. The model is under three non-symmetric harmonic excitations. An iterative approach is used to develop new modified model until when a termination criterium is rached. The results show that this approach could produce significant reduction in the value of radiated sound power level of the structure.

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In this paper elastoplastic buckling of thin rectangular plates are analyzed with deformation theory (DT) and incremental theory (IT) and the results are investigated under different loads and boundary conditions. Load is applied in plane and in uniform tension and compression form. The used material is AL7075T6 and the plate geometry is . The Generalize Differential Quadrature method is employed as numerical method to analyze the problem. The influences of loading ratio, plate thickness and various boundary conditions on buckling factor were investigated in the analysis using both incremental and deformation theories. In thin plates the results obtained from both plasticity theories are close to each other, however, with increasing the thickness of plates a considerable difference between the buckling loads obtained from two theories of plasticity is observed. The results are compared with those of others published reports. Moreover, for some different situations new results are presented. Some new consequences are achieved regarding the range of validation of two theories.

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Due to the energy concerns, it is always desired to run the mechanical elements under optimized operating conditions. Many lubricated mechanical elements such as gears, rolling element bearings, cam and followers etc. usually operate under mixed-lubrication regime. In this regime, both the lubricant film as well as the asperities contribute in carrying the load. The life span of these elements is divided into two regimes: running-in and steady-state. In this research an efficient model has been presented to predict the variation in asperities height during running-in. The predicted results are verified with experimentally-obtained published data. A parametric study on the effect of operating conditions such as load and speed as well as initial surface roughness and material hardness on the roughness variation during running-in has been conducted.

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Ultrasonic technology has been applied in many industrial processes such as ultrasonic machining, welding, cutting, sewing, homogenizing, etc. In an ultrasonic system, acoustic horn transmits the vibration energy of ultrasonic transducer to the application area and amplifies the oscillation amplitude. Depending on the application and industrial operating conditions, different horns with different geometries and magnifications are required to be designed. In the present study exponential horns with rectangular cross-section for application in ultrasonic assisted grinding process are designed and analyzed. An analytical approach is applied to model this type of horns. For evaluating the analytical model, some acoustic horns are designed using analytical method and then analyzed by the finite-element method (FEM) in ANSYS. Then, their design parameters such as resonance frequency and amplification factor are compared and verified. A very good agreement is obtained between the results of analytical modeling and those of FEM simulation. Furthermore, geometrical modification was introduced as a solution to coincide the vibration related parameters of the horn to the desired design values. Moreover, a horn-workpiece assembly for applying in ultrasonic assisted grinding was simulated.

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Rrectangular plates-based resonant micro-sensors utilize the resonance frequency of electrically pre-deformed clamped micro-plates for sensing. Free vibration analysis of such systems in order to find their resonance frequency is the objective of present paper. For this aim, the modified couple stress theory (MCST) together with the Kirchhoff plate model is considered and the size-dependent equation of motion which accounts for the effect of axial residual stresses as well as the non-linear and distributed electrostatic force is derived using the Hamilton's principle. The lowest frequency of the system as the resonance frequency of these micro-plates is extracted using a single mode Galerkin based reduced order model (ROM). It is found that the fundamental frequency of the system is decreased with an increase of applied voltage and becomes zero when the input voltage reaches the pull-in voltage of the system. The findings of present paper are compared and validated by available results in the literature and an excellent agreement between them is observed. Also it is found that using the MCST in pull-in analysis of clamped rectangular micro-plates can remove the existing gap between the results of classical theory (CT) and available empirical observations. Furthermore, it is observed that accounting for the size-effect on free vibration analysis of electrostatically pre-deformed micro-plates is more essential than flat ones.

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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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In this study, static and free vibration behaviors of two type of sandwich plates based on the three dimensional theory of elasticity are investigated. The core layer of one type is functionally graded (FG) with the homogeneous face sheets where as in second type the core layer is isotropic with the face sheets FG material. Plate is under uniform pressure at the top surface and free from traction in the bottom surface. The effective material properties of FG layers are estimated to vary continuously through the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. State space differential equations are obtained from equilibrium equations and constitutive relations. The obtained governing differential equations are solved by using Fourier series expansion along the in plane directions and state space technique across the thickness direction. Accuracy and exactness of the present approach is validated by comparing the numerical results with the published results. Furthermore it is possible to validate the exactness of the conventional two dimensional theories. Finally the influences of volume fraction, width-to-thickness ratios and aspect ratio on the vibration and static behaviors of plate are investigated.

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Experimental investigation of two-phase air-water flow was conducted at consecutive inclinations of a large bend (with three equal slopes in respect to each other) and including the horizontal sections of the inlet and outlet of the bend. The results show that the elongated bubble regime flows without any effect of duct inclination change and consistent for all three zones of horizontal sections of before and after the bend and the bend itself. It was also noticed, as the duct inclination decreases along the route, vortex misty flow transmits to misty annular flow at higher gas flow rates. The annular flow regime was noticed only at the first slop of the bend. Slug flow was observed at the horizontal sections upstream and downstream of the bend. The slug flow at the upstream generated by the interfacial instabilities but at the downstream formed by Taylor bubbles. Slug flow area in the flow diagram increases as liquid flow rate increase at both horizontal sections. In addition, the void fraction change rate with phases mass flow rate was considered at the duct inlet.

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Micromechanical resonators are miniature devices that vibrate at high frequencies. Nowadays, with the recent advances in micro-electro-mechanical systems (MEMS) fabrication technology, micromechanical resonators are used widely in sensors, wireless communication and navigation systems. The commonly encountered energy loss mechanisms in micromechanical resonators include air damping, thermoelastic dissipation and anchor loss. In this paper, with regard to the dominated quality factor by anchor loss in some important applications including oscillators, electrical filters and gyroscopes, the closed-form expression is obtained for anchor loss quality factor in the plunging-mode vibrations of micromechanical rectangular-plate resonator with two support beams. The findings are validated by comparing with experimental data. As far as there is an acceptable match between the analytical and experimental results, the proposed model is confirmed. The results also show that the anchor loss quality factor increases with increasing substrate thickness. Moreover, a new design is proposed to enhance the anchor loss quality factor in the plunging-mode vibrations of micromechanical rectangular-plate resonators. For this purpose, the conventional support beams are replaced with T-shaped support beams. Besides, the results show that the anchor loss quality factor at the same resonant frequency is enhanced about 1.5 times.

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In this paper, two-phase air–water flow was investigated experimentally and simulated numerically using VOF method. The tests are conducted in Multiphase Flow Lab. of Tarbiat Modares University. In order to evaluate the rib effect on flow regimes, experimental investigation was conducted with ribs of different width and pitch where assembled on front and back side walls (side walls) of the duct during different test runs. The rib width and pitch were held constant during each test. The experimental work considered for different regimes of wavy, plug and slug which generated in the ducts with and without rib applying various phase velocities. The effects of using ribs on regime boundaries are presented in the flow diagrams and discussed in details. Compared to the smooth duct, the ribbed duct affects the different regime boundary positions noticeabily. The results showed that in the duct with small sizes ribs, the first slug initiates at longer time and distance in compare to the duct equipped with bigger size ribs. The results show that for normal operational flow velocities, the ribbed duct decreases the slug area on flow diagram map in compare to smooth duct. However, ribs facilitate the slug regime initiation for phase velocities in accordance with slug generation, which is not benefit of operational condition.

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In this paper, by expanding the Lekhnitiskii’s solution, the stress distribution around quasi-rectangular hole has been studied. Lekhnitiskii used complex variables analytic method for stress analysis of anisotropic plates with circular and elliptical hole. In order to extend the Lekhnitiskii’s analytical method for stress analysis of perforated symmetric laminates with non-circular holes, by means of conformal mapping, the area external to the hole can be represented by the area outside the unit circle. In this paper, try to study the effect of different parameters such as aspect ratio, stacking sequence, rotation angle of hole, bluntness and load angle on stress distribution around quasi-rectangular hole. The finite element method has been used to check the accuracy of analytical results. The analytical results are in good agreement with the numerical results. The results presented herein, indicated that the presented method can be used to determine accurately the stresses and stress concentration in composite plates with special shape cutouts .The results obtained clearly demonstrate the effect of these parameters on maximum stresses in perforated plates subjected to uni-axial tensile load. appropriate selection of bluntness and rotation angle of hole, can decrease stress concentration.

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In this paper, the behavior of copper and steel rectangular plates with clamped boundary conditions subjected to underwater explosion loading is investigated. Cavitation is a phenomenon that occurs in this process. During the cavitation, the total pressure of the explosion becomes zero, so that the governing equations of motion time will be different before and after the cavitation. As a result, in terms of analysis and design, the cavitation time is significant in studying the behavior of a rectangular plate at underwater explosive loading. To calculate the cavitation time, the equations of motion of a rectangular plate underwater explosive loading are derived first, based on Hamilton principle and variation method. Then, in order to obtain the forced response of the rectangular plate, the exact free vibration solution of the rectangular plate is derived for exact mode shapes. Then, the speed and generated stress of plate during cavitation time are calculated and compared with the yield stress of copper and steel rectangular plates. Using this method, one can distinguish the cavitation with in the elastic or plastic regimes. Results show that the cavitation time is on the order of microsecond.

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The main aim of this paper is to present the method to evaluate the stress distribution around quasi-rectangular hole in infinite isotropic plate subjected to uniform heat flow at infinity. The used method is the development of the Goodier and Florence’s method for the thermoelastic problem of uniform heat flow. Goodier and Florence used their solution for stress analysis of isotropic plates with circular and elliptical holes. In order to expand this method to solve the perforated plates with non circular holes, by means of conformal mapping, the infinite area external to the hole can be represented by the area outside the unit circle. In this paper, thermal-insulated condition along the hole boundary is assumed. Amongst the important parameters in hole geometry are rotation angle of hole, bluntness and aspect ratio of hole size. The results obtained demonstrate the effect of these parameters on stress distribution around quasi-rectangular hole and the correct selection of these parameters, lowest thermal stress rather than amount of stress corresponding to circular hole can be achieved. This method can be used for study of the stress analysis of plate with various holes.

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The main aim of this paper is to study the inelastic deformation of fully clamped rectangular plates under hydrodynamic loading by low rate with drop-hammer, both experimentally and analytically. In the analytic section, some models are presented for predicting the mid-point deflection by two methods consisting the plastic hinge and energy method. in the plastic hinge method, it is assumed that the used plate in the experimental analysis consists a central hinge and four decentralized hinge inside and also four hinges for fully clamed supported conditions; but in the energy method, the proposed model assumes the deformation in three directions and membrane and bending strain, besides the deformation profile and also the strain rate is assumed. To do this, in experimental section, some experiments were conducted on rectangular plates with different thickness, materials and different levels of energy in order to validate the obtained results from analytic results and also surveying the mechanical behavior of materials according to impacts. By comparing analytic and experimental results, it is obvious that results have satisfying accuracy, therefore using the presented analytic models is desired for predicting the mid-point deflection of rectangular plates under the hydrodynamic loading.

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In the design or analysis of structures for seismic loads, the effects of forces acting simultaneously in a member must be considered. The most common case is the interaction of bending moments and axial load in columns. The usual response spectrum method provides the maximum values of individual responses, but the critical combination of these responses may not involve any of these maxima. In this Paper, the response-spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is implemented. It is shown that, for an assumed orientation of the principal axes along which the ground motion components are uncorrelated, this envelope is an ellipsoid. For the case when the orientation of the principal axes is unknown, a ‘‘supreme’’ envelope is derived, which corresponds to the most critical orientation of the axes. The response envelope can be superimposed on the capacity curve to determine the adequacy of a given design. In the commercial softwares such as SAP and ETABS seismic designs of structures are based on rectangular spectrums that they are usually over estimated ones. Therefore, implementation of such accurate envelope instead of rectangular one is felt in design softwares. In the design or analysis of structures for seismic loads, the effects of forces acting simultaneously in a member must be considered. The most common case is the interaction of bending moments and axial load in columns. The usual response spectrum method provides the maximum values of individual responses, but the critical combination of these responses may not involve any of these maxima. In this Paper, the response-spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is implemented. It is shown that, for an assumed orientation of the principal axes along which the ground motion components are uncorrelated, this envelope is an ellipsoid. For the case when the orientation of the principal axes is unknown, a ‘‘supreme’’ envelope is derived, which corresponds to the most critical orientation of the axes. The response envelope can be superimposed on the capacity curve to determine the adequacy of a given design. In the commercial softwares such as SAP and ETABS seismic designs of structures are based on rectangular spectrums that they are usually over estimated ones. Therefore, implementation of such accurate envelope instead of rectangular one is felt in design softwares. It is shown that, for an assumed orientation of the principal axes along which the ground motion components are uncorrelated, this envelope is an ellipsoid. For the case when the orientation of the principal axes is unknown, a ‘‘supreme’’ envelope is derived, which corresponds to the most critical orientation of the axes. The response envelope can be superimposed on the capacity curve to determine the adequacy of a given design. In the commercial softwares such as SAP and ETABS seismic designs of structures are based on rectangular spectrums that they are usually over estimated ones. Therefore, implementation of such accurate envelope instead of rectangular one is felt in design softwares.

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In this paper, elastic-plastic buckling of a thick rectangular plate has been investigated based on both Incremental (IT) and Deformation (DT) plasticity theories. Uniform biaxial edge traction was assumed as the plate loading while simply supported as the boundary conditions. Integral uniqueness criterion has been minimized to determine the critical buckling traction. Based on Rayleigh-Ritz method, a linear combination of polynomial base functions, which satisfy the geometrical boundary conditions, has been used as the trial functions for rotations and transverse deflection. To validate the analysis, the results for the Mindlin plate theory have been compared with the previously published results and a very close agreement has been observed. Then the effects of thickness ratio, aspect ratio and also different biaxial traction ratios on the buckling traction have been investigated. The results show that for the problem considered here, very close critical buckling traction is predicted by the both Mindlin and sinusoidal plate theories. This implies that Mindlin plate theory is sufficiently accurate to predict critical buckling traction in this problem. Moreover when the loading is gradually changed from biaxial into uniaxial compression or when the thickness-ratio is increased, the difference between the two theories is also increased. Also for compression-tension loading case, the critical buckling traction predicted by deformation theory is much less than the incremental theory.

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In this paper, by expanding Muskhelishvili’s stress functions and with use of Schwarz’s alternating method, the stress distribution in a plate with two quasi-rectangular cut outs has been studied. Muskhelishvili represented the mentioned stress functions for studying the stress distribution in an isotropic plate with a circular or an elliptical cut out. In order to expand the Muskhelishvili’s analytical solution for deriving the stress functions related to quasi-rectangular cut outs, a conformal mapping function has been used. This conformal mapping transformed the area external of the quasi-rectangular cut out into the area outside the unit circle. Considering Schwarz’s alternating method, for calculating the stress distribution around two cut outs, complex series with unknown coefficients have been used. In this study, the effect of different parameters such as the location of the cut outs relative to each other, bluntness and aspect ratio of cut out sides on stress concentration factor can be investigated. The finite element method has been used to verify the accuracy of semi-analytical results. Comparison of two methods demonstrates the precision of obtained semi-analytical solution and indicates that it can be used for computing stress distribution in plates with two rectangular cut outs. Analysis of the proposed solution shows that the mentioned parameters have a significant effect on stress distribution and stress concentration factor decreases noticeably with selection of appropriate values of these parameters.

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The modeling and optimization of a rectangular finned multi stream plate-fin heat exchangers is presented in this paper. The proposed method for thermal modeling of this type of heat exchangers is based on uniform heat distribution along the plates. So, the heat streams are distributed along the multi stream heat exchanger based on two principles: equal quantity of stream channel distribution and uniform heat distribution in each of the channels. The geometric, thermal and hydraulic modeling and design of the multi stream heat exchanger is carried out based on rectangular fin specifications. The total annual cost (TAC), the summation of capital investment and operating and maintenance costs are regarded as objective function to be minimized. The main variables are heat exchanger core dimension such as length, width, height and the fin geometric parameters such as fin pitch and height. The genetic algorithm is utilized as optimization tool to minimize the total annual cost of the multi stream plate fin heat exchanger. The proposed method is applied to a case study. The results of the current method is compared with the literatures.

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In this study, the hydrostatic vibration analysis of an isotropic rectangular microplate in partial contact with a bounded fluid is studied. Modified couple stress theory based on the Kirchhoff plate assumptions are used to mathematically model the problem. The extended Hamilton’s principle is employed to drive the governing differential equation of motion and the corresponding boundary conditions. The transverse displacement of the microplate is approximated by a set of admissible functions which must satisfy the geometric boundary conditions. The fluid is assumed to be incompressible, inviscid and irrotational and the fluid velocity potential is obtained using the boundary and compatibility conditions. Natural frequencies of the microplate are calculated using the Rayleigh-Ritz method. To validate the present results, the natural frequencies of an isotropic macroplate in contact with fluid are compared with the available data in the literature and very good agreements are observed. Finally using the numerical data, the effect of different parameters such as thickness to length scale parameter, aspect ratio, length to thickness ratio and boundary conditions on the natural frequencies of the microplate are discussed in detail. We have observed that the difference between the natural frequencies predicted using the classical theory and the one evaluated by the modified couple stress theory is significant when thickness of the microplate is small, but diminishes as thickness increases.