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In this research, the phenomenon of vortex-induced vibrations and the effect of control cylinders usage with different configurations on vortex formation, lift and drag coefficients, and fluctuations amplitude at the back of an elastically supported rigid circular cylinder subjected to a uniform fluid flow are studied. Results obtained in the absence of control cylinders are validated with experimental and numerical results of other researchers and a good conformity is reached. After ensuring simulation accuracy and precision, control cylinders of equal diameter with master cylinder are placed as linear and triangular arrangements at the back of master cylinder and the optimal configuration and location of control cylinders are defined. In linear arrangement, at first the effect of a control cylinder usage at 5 different distances from 1.5 to 3.5 times diameter of master cylinder and then two control cylinders with ratios of 1.5, 2 and 2.5 times diameter of master cylinder are studied. At the end, in triangular arrangement, control cylinders are located at intervals of 1, 1.5 and 2 times diameter of master cylinder.

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In this paper a two dimensional elasticity for free vibrations and the effect of elastic foundantion on a two-direction functionally graded beams with integrated surface piezoelectric layers with combination of differential quadrature method and space-state method is presented here. Differential quadrature method in axial direction and space-state method in transverse direction is used. It’s considered that two parameters model or winkler-pasternak for elastic foundation which has been considered two kinds of boundary conditions include simply support and clamped-clamped. Also, It is assumed that beam properties in thickness and axial direction varying exponentially and poison factor is constant which has been considered the effects of materials properties gradient index and number waves on free vibrations beams. The obtained results show that this method has good accuracy and high speed of convergence.

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In this paper, nonlinear free vibration of a Nano plates rectangular has been investigated. For this purpose, first, the equations of motion for Nano plate which is considered as a continuous system have been derived using Hamilton principle based on classical plate theory. Then, by definition an stress function and using Galerkin method the equations converted to an ordinary nonlinear equation and a compatible equations. Using multiple time scale method this equation has been solved and analytical relations for first nonlinear natural frequency and nonlinear mode shaped have been derived. Then for example, these relations have been studied for Graphen sheet in Armchair and Zigzag structure and the effect of aspect ratio and nonlocal elasticity parameter on natural frequency have been investigated.

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Buckling and vibration characteristics of thin symmetrically laminated elliptical composite plates under initial in-plane edge loads and resting on Winkler-type elastic foundation are presented based on the classical laminated plate theory. The governing equations are obtained from the variational approach and solved by the Ritz method. Extensive numerical data are provided for the first three natural frequencies as a function of in-plane load for various classical edge conditions (free, clamped and simply supported). Moreover, the effects of fiber orientation on the natural frequencies and buckling loads of laminated angle-ply plates with stacking sequence of [(β /-β / β /-β)]s, are studied for chosen foundation parameter. Also, selected deformation mode shapes are illustrated. The accuracy of calculations is checked by performing good convergence studies, and the correctness of results is established by comparison with the existing results in the literature as well as FEM data.

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Axially moving beams are extensively involved in various industries and have significant importance in many mechanical engineering problems. In this paper, the nonlinear forced vibrations of axially moving beam under harmonic force and thermal environment have been studied. In order to considering the effects of transverse shear deformation and rotary inertia, the Timoshenko beam theory has been used to model the axially moving beam. The nonlinear governing equations are derived with the help of Hamilton’s principle. Then the equations and boundary conditions are discretized through generalized differential quadrature method (GDQ) and its differential matrix operators, and accordingly the partial differential equations are converted into the ordinary differential equations. To study the frequency response of the system, the harmonic balance method is used. Also the time responses of the axially moving beam are obtained by the Runge-Kutta method. In a case study, the effects of various parameters such as the axial speed, transverse force acting on the beam, damping coefficient and temperature change on the frequency responses of the axially moving beam with both end simply supported boundary conditions are discussed. The results show that the dynamic behavior of system is significantly affected by any of the mentioned factors.

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The accurate evaluation and experimental investigation of the gear dynamic response have indicated some interesting nonlinear phenomena such as bifurcation and chaotic behavior on some system parameters. The chaotic motion is an unusual and unpredictable behavior and has been considered as an undesirable phenomenon in the nonlinear gear vibration systems. Therefore, in order to design and develop an optimal gear transmission system, it is important to control and eliminate these nonlinear phenomena. This paper presents the design of a gear system in order to control and suppress the chaos. A generalized nonlinear dynamics model of a spur gear pair including the backlash and the static transmission error is formulated. The idea behind the design of this control system is applying an additional control excitation force to the driver gear. The parameter spaces of the control excitation force are obtained analytically by using the Melnikov approach. The numerical simulations including the bifurcation diagram, the phase portrait, and the time history are used to confirm the analytical predictions and show effectiveness of the proposed control system for chaos suppression in nonlinear gear systems.

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In recent years,the need for low power electronic circuits like sensors and wireless systems, has been considered by many researchers.Excessive weight, limited lifetime of the batteries and also having problem in replacing them, are the main reasons for harvesting energy from ambient vibrations. Among the various sources of environmental energy, mechanical vibrations, has gained popularity due to the availability. Among the different methods of ambient vibration energy harvesting, piezoelectric method, is one of the good ways to harvest energy due to the favorable effects of electromechanical coupling. The most common means of harvesting energy from vibrations, is a unimorph or bimorph cantilevered beam. In the present paper, electrical energy harvesting from Euler-Bernoulli trapezoidal cantilevered unimorph beam with base excitation using distributed parameter method has been considered. First, equations of motion analytically obtained and then using Assumed modes method(for rectangular beam), system’s natural frequencies is calculated and output voltage, current and power diagrams are presented. For verifying results, presented voltage, current and power diagrams for trapezoidal configuration close to rectangular configuration that it’s results are published in references, will be compared. Then, functional parameters for trapezoidal energy harvester, with resistance value changes for energy consumer has been analyzed.

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In this paper, the effect of passengers on the chaotic vibrations of the full vehicle model is investigated. The vehicle system is modeled as a full nonlinear seven-degrees of freedom with an aditional one -degree of freedom for each passenger. Four passengers are added sequentially to the vehicle that produces eight, nine, ten and eleven degrees of freedom models, respectively. The effect of passengers on the chaotic vibrations of vehicle is studied for the above mentioned cases. The nonlinearities of the system is due to the nonlinear springs and dampers that are used in the suspension and tires. Roughness of the road surface is considered as sinusoidal waveforms with time delay for tires. The governing differential equations are extracted by Newton-Euler laws and are solved numerically via forth-order Runge-Kutta method. The analysis is conducted first by detecting the unstable regions of the system and then followed by a specific excitation frequency, where there is possibility of chaos. The dynamic behavior of the system is investigated by special nonlinear techniques such as bifurcation diagram, power spectrum, pioncare section and maximum lyapunov exponents. The obtained results represents different types of nonlinear dynamic absorbers in the vehicle with and without passengers. Consideration the passengers and increasing the mass of the system can resultes in a significant changes in the dynamic behavior where improves the chaotic vibration of the vehicle.

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This paper deals with the nonlinear transient vibration of composite sandwich plates with an electrorheological (ER) fluid core. The initial excitation is a distributed transverse load or the flutter instability due to supersonic airflow. The Bingham plastic model is adopted to accurately model the post-yield behavior of the ER material. . The first order piston theory is used for evaluating the aerodynamic forces. The von Karman strain-displacement relations are employed to account for moderately large deflection. The Hamilton’s principle is applied in conjunction with the finite element method to derive the equations of motion. The solution is then obtained through use the Newmark time integration scheme. Numerical investigations are conducted to study the effect of ER core layer on the vibration characteristics of the sandwich plate. The influence of the electric filed strength, ER core thickness, initial excitation and the boundary conditions on the settling time of transient vibration are also examined. The results show that the damping of transient vibration is significantly improved as the electric field applied to the ER layer, but the amplitude of post-flutter oscillations remains unchanged.

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In this study, the vibrations of carbon nanotube are investigated in which the inner fluid flow with constant velocity and the widespread external harmonic force is applied to it. Also the nanotube is embedded in an elastic visco-Pasternak medium and the boundary conditions at two ends of nanotube are simply supported. In order to analyze the system and considering the small scale effects, the couple stress theory is employed and the Timoshenko beam theory is used for modeling the nanotube. The Hamilton's principle is written with taking into account all energies and external works of system and consequently the nonlinear motion equations of the system are achieved. Then with help of generalized differential quadrature method, the obtained partial differential equations are converted to ordinary differential equations and the domain of the beam is discretized. From the MatCont package in MATLAB software, the frequency responses of nanotube are examined. To this aim, the second order differential equations are turned to first order ones with appropriate transformations. So the small scale effect or equivalently the differences between present approach and classical Timoshenko beam theory are presented. Furthermore the effects of the size of nanotube, fluid velocity, applied transverse force and the elastic foundation parameters are studied. It is observed that the dependency of frequency response on each of these parameters is different and it significantly changes with these factors.

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The objective of this paper is to analyze the nonlinear vibrations of simply supported pseudoelastic shape memory alloy (SMA) cylindrical shell under harmonic internal pressure based on Donnell-type classical deformation shell theory. The pressure is a function of time and space. The behavior of pseudoelastic SMA is simulated via the Boyd–Lagoudas constitutive model numerically implemented by the Convex Cutting Plane Mapping algorithm. The Hamilton’s principle is employed to obtain the equations of motion. Differential Quadrature Method (DQM) and Newmark time integration scheme are applied to get the time and frequency responses of the cylinder. Also, the natural frequencies of the shell are obtained for the case of pure austenitic phase to compare the frequency response of the present nonlinear system (phase transformation –induced material nonlinearity) with the linear one around them. Results indicate that the strength of the material will decrease during the phase transformation. This fact is proved by the softening behavior observed in the frequency response of the system due to the phase transformation. Further, the pure austenitic phase shell is simulated in ABAQUS to verify the results. A good agreement is found between two outcomes.

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In this study out of plane active vibration control of a laminated composite rectangular plate with intermediate line support coupled with piezoelectric patches on both sides, upper and lower surface of the plate, is presented based on First order shear deformation plate theory (FSDT). Is this study, the piezoelectric patch is used as a sensor. In the relation of piezoelectric, electrical potential in the transverse direction earned by satisfaction of electric boundary conditions (open circuit) and Maxwell's electricity equation. The Rayleigh-Ritz approach is used to obtain natural frequencies and vibration mode shapes of the plate. Forced vibration response is obtained by using by the modal expansion method.In this paper, the Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) and Fuzzy Logic Controller (FLC) are used to control and reduce the amplitude of the transversely deformation of a laminated composite rectangular plate which is excited by external forced. In the numerical results, the effect of various inputs, e.g. positions of the external forced, on the responses of the system are examined and discussed in detail. The proposed analytical method is validated with available data in the literature.

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When two bodies slide on each other the asperities are engaged and friction is created. By superposing ultrasonic vibrations to one of the bodies, the friction force is reduced .This phenomenon is widely used in metal forming and metal cutting. In this research, experimental study of the effect of ultrasonic vibrations has been on sliding friction force in longitudinal direction. For this purpose, set-up was designed and fabricated. The main components of the set-up, including generators, transducers, first engaged body and second engaged body. The Set-up was installed on the machine lathe for investigation of the effect of ultrasonic vibrations on sliding friction force in longitudinal direction. The experiments were performed for eight different performance conditions. Next, the effect of each parameter ultrasonic wave velocity, roughness and material of contact surfaces were studied on the reduction of the friction force due to addition of ultrasonic vibrations. The result show that range of reduction friction force due to addition of ultrasonic vibrations in longitudinal direction is between 40 to 100% for the different performance conditions also friction force significantly reduced by increasing ultrasonic wave velocity so that friction force can be brought to zero by significant increase in ultrasonic wave velocity. The results also show that friction force has a more reduction for the surface has a less roughness. Aluminum-aluminum surfaces can be more reduction friction force from aluminum – steel surfaces.

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In this paper, the nonlinear free vibrations of a bimorph piezoelectric nanoactuator is studied based on nonlocal elasticity. The Euler-Bernoulli beam theory and Hamilton’s principle are used to derive the equation of motion of the actuator. In order to obtain the reduced-order form of equations, the Galerkin method is used. The mode shapes of a multi-span beam are used for a faster convergence. The nonlinear natural frequencies are obtained by using He’s variational approach. Equations are solved for clamped-clamped boundary conditions, and the effects of values of DC voltage, actuator length and thickness, length of piezoelectric layers and nonlocal parameter on the nonlinear natural frequencies are studied. The results show that applying a DC voltage induces a static deflection and an increase in the stiffness of the actuator. Therefore, the natural frequency increases. Moreover, increasing the nonlocal parameter decreases the rate of change in frequency variation. An increase in the nonlocal parameter or the length of the actuator increases the nonlinear to nonlinear natural frequency ratio. Finally, the effect of the middle layer material of the actuator on the frequency ratio is studied.

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nowadays, bridges play important roles in transportation. Due to their structural shape, bridges often have a wide and thin deck and so, they are prone to vibration in the vertical direction. Vertical vibrations of bridge deck resulting from passing vehicles, can affect the security and service of these structures. Using of control systems is one of the main strategies to reduce the vertical vibrations in bridges. In general, control systems can be classified into three categories: passive, active and semi active control systems. In this study, the reduction of vertical vibrations in bridges are investigated using the passive tuned mass dampers control systems. Passive tuned mass dampers contain a relatively small mass (compared to the mass of the bridge), a spring and a damper which are installed and operated to reduce the dynamic response of the bridge deck and their Performance principally depends on the energy dissipation of the deck vibrating motion by the oscillating motion of the mass damper. Thus, tuned mass damper frequency is proportional to the frequency of the dominant vibration modes of the bridge structure (usually the first mode) and when this frequency is excited, the tuned mass damper begins to vibrate in the opposite direction of the bridge vibration and the bridge energy is dissipated by the force of inertia inserted to the bridge by damper. Therefore, the inertia force of the passive tuned mass damper is the main cause of energy dissipation in the deck. Dynamic characteristics of tuned mass damper (including mass, damping percentage and frequency settings), installation location of tuned mass damper, speeds of the passing vehicles, are effective parameters influencing tuned mass damper performance in reducing vertical vibrations of bridge deck under traffic loads. In the first part of this study, the effect of mass on the performance of tuned mass damper is investigated by assuming other parameters to be fixed. Then, the effect of damping percent and setting frequency on reducing vibrations of different sections of bridges and different places where tuned mass damper is installed is investigated. In the second part, tuned mass damper performance in different speeds of vehicles is investigated.
The results show that TMD mass is more effective in reducing vertical vibrations in comparison with the damping percentage. Also, it is found that TMD is extremely sensitive to its regulatory frequency, in such a manner that with a little deviation from set frequency, its performance decreases. The effect of TMD is positive and considerable in certain speeds and certain TMD placement locations. Furthermore, the results reveal that the most important effect of TMD on reduction of the vibration response of the bridge deck structure occurs in the free vibration response. For the mentioned bridge with TMD, the maximum reduction of 24% and 59% in the dynamic response of the bridge deck occur for forced and free acceleration amplitude respectively, and the maximum reduction of 13% is obtained in the maximum displacement of the bridge deck, that these results are related to the occurrence of resonance in the bridge deck.

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Harvesting energy by piezoelectric materials is nowadays an efficient way for powering low-power electric devices. Required energy for sensors which are used in condition and health monitoring of bridges and other civil infrastructures can be examples of the energy harvesters. This study aimed to improve the piezoelectric-based energy harvesting on civil infrastructures, especially on bridge structures. In this investigation, harvesting energy from the vibrations of a bridge under moving consecutivemasses is studied. Harvesting energy iscarried out through a cantilever beam with piezoelectric patch which is installed atthe middle of a simply supported bridge. Governing equations for vibration of an Euler-Bernoulli beam under moving consecutivemasses arederived. The effects of inertial, centrifugal and coriolis forces areconsidered. For verifying, the results of the numerical solution of the moving mass problem are compared to the experimental tests data of the litterature. The harvester is modelled by a cantilever beam with piezoelectric patch under base excitations which are calculated from vibrations of the bridge mid-point. The obtained equations are then solved in MATLAB environment by using the forth order Runge-Kutta method. The calculated induced voltages are compared with those obtained from experiment. A good degree of accuracy is observed.

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Rotating cylindrical shells are applied in different industrial applications, such as gas turbine engines, electric motors, rotary kilns and rotor systems. So, it is of great interest to conduct some researches to improve the understanding of vibrational characteristics of rotating cylindrical shells. Grid stiffened laminated composite cylindrical shells are used as components of aerospace, marine industries and civil engineering structures. In this research free vibration of rotating grid stiffened composite cylindrical shell with various boundary conditions using the Fourier series expansion method is presented. Smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole structure. The stiffeners are considered as a beam and support shear loads and bending moments in addition to the axial loads. Strain displacement relations from Sanders's shell theory are employed in the analysis. Using the Fourier series expansion and Stokes’ transformation, frequency determinant of laminated cylindrical shells is derived. The effects of shell geometrical parameters and changes in the cross stiffeners angle and axial loading on the natural frequencies are investigated. Results given are novel and can be used as a benchmark for further studies.

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In this paper a nonlinear controller is going to be designed for micro-beam’s deflections under mechanical shock effects. The micro-beam is supposed to undergo mechanical shocks. Mechanical shocks are one of the failure sources and the controller is to considerably suppress shock’s unfavorable effects. Half-Sine, rectangular and triangular pulses are chosen as reference shock signals to represent true complicated shock signals in nature which consist of different harmonics. Two layers of electrodes are placed in both sides of the micro-beam and they are used to actuate the micro-beam by different voltage levels. Upper layer is specifically meant for control purpose. Nonlinear equations governing micro-beam’s deflection dynamics are derived, discretized by Galerkin method to a set of nonlinear duffing type ODE and used to investigate micro-beams response to each shock input signal. Controller design is based on a simple nonlinear model formed by micro-beam’s first mode shape. Proper second order behavior is generated by feedback linearization method as controller logic. Finally controller performance and shock rejecting capability is evaluated by numerical simulations. Controller is shown to be very effective in diminishing shock unfavorable effects and postponing pull-in instability by numerical simulations.

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Conical shells are widely used in various engineering applications such as mechanical, civil and aerospace engineering. In the present paper, based on the first order shear deformation theory (FSDT) of shells, the nonlinear vibration behavior of truncated conical shells with different boundary conditions is investigated using a numerical approach. To this end, the governing equations of motion and corresponding boundary conditions are derived by the use of Hamilton's principle. After catching the dimensionless form of equations, the generalized differential quadrature (GDQ) method is employed to obtain a discretized set of nonlinear governing equations. Thereafter, a Galerkin-based scheme is applied to achieve a time-varying set of ordinary differential equations and a method called periodic grid discretization is used to discretize the equations on the time domain. The pseudo arc-length continuation method is finally applied to obtain the frequency-amplitude response of conical shells. Selected numerical results are presented to examine the effects of different parameters such as thickness-to-radius ratio, small-to-large edge radius ratio, semi-vertex angle of cone, circumferential wave number and boundary conditions. It is concluded that the changes of the vibrational mode shapes and circumferential wave number have significant effects on the nonlinear vibration characteristics and hardening effects.

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The composite conical lattice structure in this paper made of helical ribs and thin outer skin. In this research, free vibrations of these structures with and without outer skin were investigated. A smeared method is employed to obtain the coefficients of stiffness of conical shell. Theoretical formulations are based on sander thin theory of shell. For verification of the analytically obtained results, using ANSYS software the 3D finite element model of composite lattice conical shell is built and analyzed. To verify the accuracy of this method, comparison of the results are made with numerical results from ANSYS Software and show a good agreement between them. Also, some special cases as influences of the semi vertex angle and thickness of the outer skin on the natural frequencies of the conical shell are studied. It is concluded that, the increasing of the semi vertex angle leads to increasing the natural frequencies of conical shell. Moreover for outer shell thicknesses greater than a specific value, the increment of the thickness of the outer skin leads to decreasing the natural frequencies. Because of few researchers investigated merely vibrational behavior of the composite lattice cylindrical shell, the obtained results of this paper have novelty and can be used for further and future researches.