Modares Mechanical Engineering
Year:2019 | Volume:19 | Issue:11 |Papers Count:27

In this paper, a simple, practical and versatile model has been developed for a self-activated acoustic driven spherical swimmer that its surface may oscillate partially at dipole state (first mode of vibration). Regard to the nonlinear acoustic effects, the net acoustic radiation force exerted on the device is analytically derived and the non-zero states are approved. Considering hydrodynamics effects assuming low Reynolds number operating condition, the effects of active section angle and frequency of operation on the force, velocity and requirement power of swimmer are discussed. It is shown that comparing with many types of artificial and natural living matter swimmers, the swimming velocity of the developed model is satisfactory. The challenge of the random walk due to host medium fluctuations is discussed, and it is shown that the developed model can overcome the ubiquity of the Brownian motion, as well. Due to the simplicity of the developed model which leads to computing the swimmer features (such as force, velocity, etc. ) analytically, this study can be considered for development of contactfree precise handling, drug distribution and delivery systems, entrapment technology of active carriers and the self-propulsive controllable devices which are essential in many engineering and medicine applications.

In this paper nonlinear dynamic behavior of bending actuators of dielectric elastomer or Dielectric Elastomer Minimum Energy Structure (DEMES) is studied and the effects of viscoelasticity of dielectric film on system response are investigated. Considering hyperelasticity and viscoelasticity of dielectric film, the equation of motion of the actuator is extracted using Euler-Lagrange method. The natural frequency of small amplitude oscillations around the equilibrium state is calculated by linearizing the original nonlinear equation and the effects of dielectric film pre-stretch and excitation amplitude on natural frequency is investigated. The numerical simulation of the nonlinear equation of motion for periodic excitation shows that the system possesses harmonic resonances as well as sub-harmonic and super-harmonic resonances. By increasing the damping ratio of the dielectric film, resonance frequency increases for all harmonics and their excitation amplitude decreases. The analytical results show that excitation amplitude of harmonic resonance in chaotic behavior changes to a quasi-alternate and then an alternative behavior by increasing damping ratio.

In the present research, the effects of the internal overlap ratio on the performance of a two-blade vertical axis Savonius wind turbine is investigated using numerical simulation. Considerations are performed on both conventional and Bach-type rotors. For this purpose, the power characteristics of the wind turbine are examined under tip speed ratios ranging from 0. 2 to 1. 2 and wind speeds of 3, 5, and 7 m/s. In order to capture the turbulence characteristics, SST k-ω model is used and the obtained results are validated against the available data in the open literature. The instantaneous behavior of flow and the time-averaged data are presented for both conventional and Bach-type rotors. The obtained results of the research reveal that for all tip speed ratios and wind speeds, the optimum overlap ratio for conventional and Bach types rotors, respectively. On the other hand, regardless of the wind speed and overlap ratio, the maximum power coefficients are obtained in tip speed ratios of 0. 8 and 0. 7 for conventional and Bach-type rotors, respectively. Finally, it is found that in all tip speed and overlap ratios, in both rotors, the power coefficient increases with increasing the wind speed.

One of the most important applications of solar energy is its utilization in solar dryers to maintain agricultural products for long-term storage. These dryers work based on passing warm air through fresh materials by natural or forced convection. So, they have a direct dependence on the intensity of the sun’ s irradiance to their collector, which it disrupts the drying process in the absence of a thermal energy source in the hours when the sun is not available. In order to solve this problem, the phase change material (PCM) as thermal energy storage is used. The materials that have the capacity to absorb the thermal energy (charge phase) and, they release the absorbed energy (discharge phase) when the intensity of the solar radiation is low or during the night and cause the uniformity of the outlet temperature solar collector, and inside the drying chamber. As well as they provide the necessary thermal energy for hours when the sun is not available and increase the duration of use of the dryer. In the present research, the experimental studies have been carried out through designing and construction of an indirect cabin type solar dryer equipped with a heat pipe evacuated tube collector and using PCM material as energy storage in the expansion tank. In the present research, the experimental studies have been carried out through designing and construction of an indirect cabin type solar dryer equipped with a heat pipe evacuated tube collector and use of PCM material as energy storage in the expansion tank. The effect of various parameters such as inlet and outlet temperatures of the collector, temperature, and humidity of the drying chamber and ambient, the intensity of the solar irradiance on the drying process is investigated, with and without PCM and at two different speed of forced convection through the drying chamber. The results show that the effectiveness of forced convection on the drying process is more than the effect of PCM.

Despite the intense development of cable-driven robot in recent years, they have not yet been vastly utilized in their potential applications because of difficulties in their performing accurate installation and calibration. This paper aims to present a suitable control method, relieving the limitation of accurate calibration and installation requirement in the suspended cable-driven parallel robot. In this paper, kinematics and dynamics uncertainties are investigated and based on their bounds, a robust controller is proposed. The main innovation of this article is providing a new control method to cost reduction by eliminating accurate measurement tools such as a camera in position control of a deployable cable-driven robot. Using this approach, reducing costs in building a robot and increasing the speed of installation and calibration is achieved. Another problem investigated in this paper is the problem of joint space controllers applied to redundant cable-driven parallel robots, namely the loosened redundant cable. To solve this problem, the embedded force sensor and a new sliding surface for the controller is proposed. In fact, in this paper, the conventional joint-space controllers are modified to become applicable to the control of cable-driven robots. Finally, by conducting some experiments using ARAS suspended cable-driven parallel robot, the proposed algorithms are verified and it is shown that there are feasible solutions for stable robot maneuvers.

The material point method (MPM) is a numerical technique to modeling the large deformation and interaction between different phases of materials. MPM combines the best aspects of both Lagrangian and Eulerian formulations while avoiding some shortcomings of them. In MPM a body is modeled with the particles which carry all physical properties of the continuum such as mass, momentum, strains and stresses. The background mesh is used to solving the momentum equation. In the first phase, information is mapped from particles to nodes. In the second phase, momentum equations are solved for the nodes, and then the updated nodes are mapped to the particles to updating their positions and velocities. In the third phase the grid is reset. In numerical simulation of granular flows, large deformations and interactions between grain boundaries and buildings lead to the complexity in the structural behavior of the material and, as a result, the complexity of the simulations. From different numerical techniques, the material point method is a suitable method for simulating such problems. In this study, the problem of the collapse of a column of granular material on a rigid wall was simulated in two dimensions through material point method. The surface profile and displacement of the front were compared with the laboratory results which a good accordance is observed between them. The results show that the ratio of the initial column plays an important role in the development of granular mass.

In this study, a dynamic based control algorithm for six-link quadruped locomotion is proposed. Up to now, a lot of researches have been conducted in the field of quadruped locomotion but most of the researches are based on the detailed modeling of a robot and its surrounding. Such methods are not able to generate a stable locomotion when the surrounding changes. However, the main characteristic of vertebral motion is the adaptability of their motions. So this is important to propose a control algorithm based on the robot dynamics. The algorithms that can guarantee the stability are classified to two categories of dynamic based and trajectory based methods. The trajectory based algorithms need detailed information about gait which is not necessarily available. But the dynamic based algorithms use some geometric constraints to reach a stabilizer controller. These geometric constraints generate the proper gaits. So in this study by employing the dynamic based control algorithm, we proposed a controller for generating the Trot and Pace gait on a straight and flat path for quadruped robot locomotion. Given that the quadruped robot has four degrees of freedom, three geometric constraints are needed to provide rhythmic locomotion. In this study, the stability of quadruped locomotion has been proved using the Poincaré return map.

Abrasion in pipelines and fluid transfer equipment along with impurities in oil and gas and other industrial processes is one of the most important problems of oil, gas and petrochemical industries. Repair of this equipment is considered as one of the major challenges in industry. Wearing was created by the impact of solid particles with gas and liquid particles or by the collision of liquid droplets with the inner wall of the fluid passageway. This research aims to examine the factors affecting the rate of vane wearing including circulation speed of compressor vane, size of particles within methane, density of particles in compounds, angle of incidence and target metal stiffness. To obtain and analyze the rate of vanes’ wearing, degraded pieces of vanes’ substance were provided and were used as specimen according to the operational conditions, exploitation, and transfer of gas. During the experimental steps, the rate of wearing with varying conditions in solution and solid particles’ compounds was measured. According to the results, the speed rate of circulation of centrifugal compressor impeller is an important parameter in increasing efficiency. To obtain this parameter, the mechanical and metallurgical properties of the compressors should have a good quality. Also, considering the relationship with a parabola form, the abrasion increases with increasing the density of particle. The results of the research were compared to the existing standards and theories and the approaches were presented to decrease degradation and wearing in centrifugal compressors’ vanes.

This study aims to investigate the effect of nanoparticle deposition on the boiling surface in the presence of microchannel on the characteristics of boiling heat transfer. In this experimental study, the copper boiling surfaces including polished circular surface, rectangular and trapezoidal microchannels were used. The microchannels include feeding sub-channels perpendicular to the main channel, which increases the boiling surface and separates the downward cool fluid flow and upward hot bubbles. Nuclear boiling experiments on microchannel surfaces in the presence of a hybrid water-based nanofluid containing 70% titanium oxide and 30% OH-based multi-wall carbon nanotubes in volumetric concentrations of 0. 1% and 0. 5% have been conducted. The results of nanofluid boiling experiments on both microchannel surfaces show that with increasing concentrations, critical heat flux and heat transfer coefficient increases and the highest increase in critical heat flux and heat transfer coefficient is related to the hybrid nanofluid with 0. 5 % volumetric concentration on the surface with trapezoidal microchannel and their values are 64. 64% and 344. 76%, respectively, compared to pure water boiling on the polished copper surface. Also, in boiling of pure water on the deposited surfaces with nanoparticles, the greatest increase in critical heat flux and heat transfer coefficient is related to the surface with trapezoidal microchannels with 0. 1% volumetric concentration and 0. 5% and volumetric concentration and their values are 120. 16% and 149. 4% respectively, compared to pure water boiling on the polished copper surface.

Turbocharger turbine blade thickness is restricted by blockage and trailing edge losses and it is exposed to damage due to aerodynamic loads. Proper designing of the blade needs to full recognition of loads on the blade. Therefore, the force from the fluid to the blade should be calculated. Although, thickening the blade results to the more resistance to fracture and cracks, but it affects the aero-structural performance of each section of the blade differently. So, turbocharger turbine blades are exposed to pulsating flow which should be considered in thickness distribution selection. This article reports a comprehensive fluid-solid interaction study of the turbine blades with different thickness distribution which could beneficially investigates the effect of each part thickness on the aerostatic efficiency. Leading edge and trailing edge thickness, maximum thickness and its location, trailing edge shape, hub, and tip blade thickness were the variables which their effects were investigated. Using dual turbocharger turbines leads to lower dissipation of kinetic energy of pulsating charge from the engine. In such turbines, each sector of rotor accepts a different charge from upper and lower entries. The flow distribution of every passage is the difference from the others. Therefore, to the evaluation of the flow, modeling of the entire turbine is needed. 3D CFD model in ANSYS CFX for fluid side and an FEA model in ANSYS Static Structural module for the blade structural responses were used then the results were coupled. Validation was performed by reference to experimental data carried out in imperial college London on a dual turbocharger turbine.

Nowadays, metro system is widely used for public transportation. Its regular operation consumes large amounts of electrical energy in comparison to other urban systems, while a considerable part of its non-traction energy is consumed for air exchange and ventilation of tunnels and stations. In this research, the train movement inside the four stations and connecting tunnels of underground subway system is simulated. The tunnel and station models contain important units such as ticket hall, staircases, platforms and ventilation systems. The numerical model is validated by comparing the results with the experimental data available in the literature. The flow field inside the tunnel and stations induced by the train movement is calculated and compared in fan-off and fan-on conditions. The results show that the train movement changes the flow direction around the fans and grille openings and can severely affect the air-exchange performance. The flow field inside the tunnels and stations is completely dependent on the piston effect caused by the train movement. Because of the train movement, the volume OF flow exchange through station entrances, and also through station and tunnel inlets becomes ten times of that on the steady state condition with the stationary train. Also the air flow induced by the train movement is much higher than the flow generated by the air-exchange system. Therefore, the optimal use of the piston effect has a significant effect on reducing the energy consumption.

Beams are the basic geometries in engineering and many engineering issues are simplified as a beam problem. In this paper, the dynamics and vibration analysis of composite Timoshenko beam made of epoxy graphite layers with two piezoelectric layers on both sides have been investigated. Extraction of motion equations has been conducted based on the first-order shear deformation beam theory using the Hamilton principle. The partial differential equations were converted to the first-order coupled differential equations and then they were solved by fourth-order Runge– Kutta method. The effect of piezoelectric parameters on the vibrational and dynamic response of the beam has been investigated. The results show that the natural frequency of the beam decreases with increasing the length of the neam. Among piezoelectric parameters, the parameter of C11 has a lower effect than the effective transverse coefficient of e31 in the frequency response. As the ratio of the length of the beam is lower than the thickness, the effect of C11 will be greater on the natural frequency. The effect of the other piezoelectric parameters in the frequency response has also been evaluated very small relative to these two parameters.

In this paper, a sliding mode predictive control method is proposed for function improvement of affine discrete-time nonlinear systems using integral terminal sliding mode method (ITSMC). The proposed method is based on the integration of terminal integral sliding mode method and model predictive controller which leads to using the advantages of both methods. Indeed, in the proposed method, integral and terminal characteristics of terminal integral sliding mode method are used to design the sliding surface in order to reduce the error (in reaching phase) and to converge to the origin (in sliding phase). Moreover, the chattering phenomenon which usually exists in sliding mode based methods will be decreased using the model predictive controller. The proposed control method has the capability to eliminate the effect of external disturbances and uncertainties. In this paper, it is shown that the model predictive method decreases the chattering phenomenon more than using the saturation function in the control law of the sliding mode method. In addition, using numerical and functional examples, the performance of the proposed method in improving the quality of the system response in the presence of external disturbances and uncertainties is illustrated.

An analytical solution for the problem of time-dependent stress redistribution of a piezomagnetic rotating hollow cylinder subjected to an axisymmetric thermo-magneto-electro-mechanical loading is derived for the condition of plane strain. A differential equation containing creep strains is found using the constitutive equations, equilibrium equation and solving heat equation in plate strain. In the first step, eliminating creep strains in the differential equation, an analytical solution for the differential equation is obtained. Then, by adding creep strains and assuming constant thermal conditions, the creep stress rates and electric and magnetic potential are obtained using solving a differential equation. Lastly, the history of stresses, radial displacement, magnetic potential, and electric potential during the time can be obtained using an iterative method. In the numerical examples, the effects of time passing on the structure behavior and the effective parameters such as thermal boundary condition, angular velocity, and electromagnetic boundary condition were investigated comprehensively.

Porous biomaterials are known as one of the brand new materials which considering the specific mechanical properties such as hardness and density and enabling bone growth are considered for various applications of biological prostheses including bone replacement. It has been entrenched that porous biomaterials can be produced considering defined representative volume elements by recent developments in additive manufacturing using a 3D printer. In this research, a novel functionally graded porous material is introduced based on a new representative volume element. The theoretical solutions are developed to calculation of the mechanical properties including elastic modulus and yield stress of the orthotropic material. Furthermore, numerical modeling was performed using finite element software to validate the theoretical analysis results. The results show good agreement between the theoretical method and numerical modeling. The mechanical properties of each layer as well as the properties of the whole structure have been studied considering the three structures with different porosity. As the results show, the obtained properties of the proposed structures are suitable for the application of the bone implant. Finally, the effect of geometrical features changes of representative volume elements on the mechanical properties of the structures has been studied. The results show that these changes had a significant impact on the mechanical properties of the structure and the proper efficiency and distribution of the material properties for the considered applications can be achieved by correctly defining the geometrical features.

Origami, as a paper folding art and Japanese culture, has been utilized broadly in engineering areas. The exclusive features of origami such as negative Poisson’ s ration, lightweight, deployable and so forth, can be considered in the design of deployable space structures, expandable shelters, drug delivery, and robots. In this study, firstly, the continuum robot with six serial modules of origami parallel structure as its skeleton and the helical springs as the compliant backbone is studied, and constant curvature kinematics was implemented in order to simplify and approximate the kinematic model. Accordingly, the kinematic model of one module was derived. Then, the robot kinematics was obtained as a series of mentioned modules. Furthermore, the proposed continuum robot was modeled by an equivalent mechanism, and a comparison was conducted between the methods to obtain a workspace. Based on the results, the modeling of the equivalent mechanism has an advantage in terms of calculation’ s volume compared to the constant curvature method and the workspace obtained from both methods was the same. The Jacobian matrix was obtained through the constant curvature approximation methods, which can be considered for singularity analysis in specific conditions and the analysis reveals that the singularities occur when the curve and radius are equal and symmetry is created and the other is when the radius is equivalent to zero. The paper concludes a perspective on several of the themes of current research that are shaping the future of origami-inspired robotics.

In this study, a hybrid system of fuel cell/gas turbine was designed and simulated with the aim of coupling with desalination systems. This system was analyzed from the viewpoints of the first and second law of thermodynamics. A parametric analysis was also performed to the determination of the system optimal performance. The studied parameters are fuel utilization factor, compressor pressure ratio, pre-reforming percentage, and the steam to carbon ratio. The results show that for the design parameters, the net power is 1215kW, the overall efficiency is 81. 65% and the exergy efficiency is 60. 7%. Also, by analyzing the rate of exergy destruction, it has been determined that the stack of fuel cells, combustion chamber, and pre-reforming have the most part in the destruction of exergy. Parametric analysis results show that increases in pressure, pre-reforming percentage, and fuel utilization factor have a positive effect on the system performance to a certain extent and the suitable ranges of the fuel utilization factor are from 0. 8 to 0. 85. On the other hand, by analyzing the effect of pressure and temperature on the system, it is determined that the temperature of the fuel cell cannot be constant. It was also shown that the efficiency of the system decreases with increasing steam to carbon ratio.

In this research, the effects of partially austenitising time on the machinability of spheroidal graphite (SG) cast iron with ferrite-martensite dual matrix structure (DMS) were investigated to optimize its machinability. Specimens with non-alloy ferrite matrix structure were prepared by the casting process. Then the specimens were austenitized at temperatures of 900 oC at various times (5 to 25 min) and subsequently quenched into the water to produce DMS with martensite volume fractions. The Brinell hardness test method was used to determine the hardness of specimens. The machinability of the workpieces with ferrite and dual structures were investigated by measuring the surface roughness and primary cutting force. According to the results, the Johnson-Avram kinetic model was valid for correlation between the martensite volume fraction and autenitising time. The surface roughness was increased and the cutting force was decreased with increasing austentising time to 12 min, and consequently, with increase the hardness to 168 BHN. The heating at 900 oC for 12 min resulted in 16-20% and 15-23% improvement on the cutting force and specific cutting power, respectively, when compared to as-cast specimen, while the surface quality remained at the same level. The cutting force was correlated with feed rate as a power model with exponents of 0. 77 and 0. 73 for DMS (with 30% martensite) and ferritic as-cast samples, respectively.

In this research, an innovative approach has been proposed to the calculation of high order sensitivities and designing its guidance commands for an unmanned aerial vehicle landing strategy design. This method, which is called vectorised high order method, has been developed based on high order expansions method and its implementation using matrixbased mathematical calculations. In this research, a method is presented to design and extract the acceleration commands for landing maneuvers, by combining the vectorised high order expansions method and optimal control theory. Accordingly, the sensitivity variables for the given problem are calculated up to the 6th term and then the reference trajectory and acceleration command in the simulations are updated based on the initial deviations. In order to performance evaluation of the proposed method, 3 landing scenarios with the different initial deviations have been considered and the results of simulation of the proposed guidance law have been presented.

In the present work, the nonlinear finite element method is used to solve the phase field equations for phase transformations at the nanoscale. In the phase field theory, the evolution of a martensitic nanostructure is described in terms of several order parameters and the Ginzburg-Landau equation is a linear relationship between the of the change rate of an order parameter and the thermodynamic forces which are the variational derivative of the free energy of the system with respect to the order parameter. Since the free energy includes nonlinear terms of the order parameter, the thermodynamic forces are nonlinear functions of the order parameter. Therefore, the phase field equations are solved using the nonlinear finite element method and the self-developed code. The studied transformation is the conversation of cubic to tetragonal phase in NiAl by temperature changes and neglecting the mechanical effects. Therefore, the transformation is the induction temperature type and is defined using only one order parameter. To validate the numerical work, the profile, width, energy, and velocity of the austenite-martensite interface were calculated and compared to the previous works and a very good agreement is found between them. Also, various physical problems such as plane interface propagation, martensitic nucleation, and propagation undercooling, and reverse phase transformation under heating are simulated. The obtained results present a proper tool to solve more advanced phase field problems for phase transformations at the nanoscale including mechanics effects and complex initial and boundary conditions.

In this research, semi-constrained groove pressing (SCGP) as one of the severe plastic deformation techniques was investigated to achieve an ultrafine-grained structure in interstitial free steel sheets. The maximum of four semi-constrained groove pressing passes was successfully applied on the samples and the effects of the number of SCGP passes on the microstructure and mechanical properties of the samples were investigated. The microstructural investigations of the deformed specimens indicate that the semi-constrained groove pressing can effectively reduce the grain/crystallite size so that it ranges from about 41 μ m in annealed condition to 232 nm after four passes. The results also showed that the strength and hardness of the samples are increased significantly by applying the pressing process. The highest tensile and yield strengths were observed in the two-pass SCGP processed sample, which showed an increase of about 90% and 75%, respectively, compared to the initial sample. The maximum hardness value of 165 Vickers was obtained for a three-pass SCGP processed sample, which is about 68% higher than the annealed sample. Regarding the hardness tests results, the uniformity of deformation increased with increasing the number of SCGP passes. Finite element method was used to simulate the semi-constrained groove pressing, and the strain distribution was obtained for the deformed samples. The finite element simulation results correlated fairly well with the analytical results.

In this research, the heat sink performance of a laser diode with the different geometries was studied. A 3D simulation of flow and heat transfer has been used considering the natural convection. First, in order to test the validity, the simulation results were compared with the experimental results, which were in a good agreement. Then according to the chimney flow pattern, eight geometries were designed with two different heights of the fin and each one of them was evaluated by three heat fluxes of 200, 400 and 600 W/m^2. The aim of this research is to find the condition that minimizes the average temperature of the heat sink. The results showed that the average heat transfer coefficient in the heat sink is increased up to 40 percent by creating the slice in the fine. In the fins with the height of 21. 3 millimeters, the fin with two similar symmetric slices and in the fins with the height of 32. 6 millimeters and constant volume that the slices of fine are added to its teeth, for heat fluxes less than 400 W/m^2, symmetric fin with two similar slices in the middle section and a volume equal to the volume of the primary fin, had the best performance. For heat fluxes, more than 400 W/m^2, the average temperature of the symmetric fin with one slice in the middle and a volume equal to the volume of the primary fin was minimized. Fin average heat transfer coefficient, average Nusselt number, fin thermal resistance, fin average temperatures, flow streamline and isothermal contour plots in the fin plate were evaluated for each state.

The aim of this research is to design and fabricate an actuator, which operates based on reaction forces between current carrying stator coils and magnetic arrays (Halbach arrays) connected to the mover, in order to move a motion stage for positioning objects. Thus, according to the initial and intended position of the mover, current commutation in stator coils is changed in a way that required force for transporting the mover to the desired position is provided. In this research, the integration of two perpendicular synchronous linear motors is utilized in order to create the planar motion. The stator consists of two sets of rectangular coils, which are placed perpendicular to each other. Mover consists of four Halbach arrays, which two Halbach arrays are used for x-axis motion and the other two arrays are used for y-axis motion. First, the analytic relationship between the applied magnetic force and current commutation was introduced. Then, the design parameters such as mover dimensions and stator workspace were determined. Concerning these parameters, dimensions of cubic magnets for Halbach array fabrication were obtained and with respect to array dimensions, the dimensions and number of turns for stator coils were determined. Using these design parameters and commutation equations, the planar motion of the actuator was simulated. The simulation results showed good agreement with the analytical results. Experimental tests were conducted in order to investigate the positioning capabilities and 2 dimensional motion. The precision of the fabricated actuator is 5mm and the minimum response time of actuator is 0. 5sec. The minimum position error occurs at 25mm position that is due to the closeness to motor magnetic period.

In this paper, the new theory is proposed to investigate the fracture behavior of cracked composite materials. Based on this theory, crack is created and distributes in the isotropic matrix. Therefore, contrary to the previous fracture theories of composite materials presuming that crack growth occurs in anisotropic homogenous material, the new theory assumes that crack growth occurs in the isotropic matrix. It states that the isotropic matrix is affected by fibers in the composite structure of the material. In this approach, fibers are considered as isotropic matrix reinforcements and the reinforcement effects are defined as coefficients in stress state of the isotropic matrix. The coefficients are called reinforcement factors and derived via three different approaches to study the arbitrary crack in 2D materials. The reinforcing effects of fibers are obtained when tension across and along fibers and shear loadings exerted on the body. The three methods demonstrate that the reinforcement factors depend on elastic properties, crack growth location and the crack and fiber orientations. However, the method, derived from the micro-mechanic approach, displays their dependence on the fiber volume fraction. Comparing the results of these cofficients with the existing fracture theories illustrates the efficiency and ability of the reinforcement factors in investigation and explanation of the fracture behavior of orthotropic materials.

In this research, the free vibration of a sandwich plate made of smart magnetostrictive face sheets and polymer composite core is studied. The effective elastic properties of carbon nanotube-reinforced composite are obtained by the rule of the mixture and micromechanical approach. A feedback control system follows the magnetization effect of Terfenol-D films on the vibration characteristics of a sandwich plate. Considering velocity feedback control gain value, the dimensionless frequency of sandwich plate can be changed to desired values due to magneto-mechanical coupling in magnetostrictive materials. The equations of motions are derived using Reddy’ s third-order shear deformation theory, energy method, and Hamilton’ s principle. The differential quadrature method (DQM) as a numerical method is used for calculating the vibration frequency of the sandwich plate. This numerical method presents the optimal results using weighting coefficients. The findings of this study show the effect of the vibration control system and geometrical properties of the composite sheet on vibration frequency of structures. These findings can be used in marine, aerospace, and civil industries.