جستجوی مقالات مرتبط با کلیدواژه « ارتعاشات غیرخطی » در نشریات گروه « مکانیک »

The non-linear vibration analysis of a clamped circular nano-plate is performed using the nonlocal strain gradient model. For this purpose, a combination of the differential form of the nonlocal elasticity theory and strain gradient model, along with Hamilton’s principle, are used in conjunction with the von Kármán nonlinear strain-displacement relationships and Galerkin weighted residual method to discretize the governing equations. The analysis has focused on the effect of nonlocal and material parameter, initial conditions, and frequency number, on the overall behavior of the nano-plate. Using Galerkin method, the system of non-linear differential equations is obtained and the natural non-linear frequencies, as well as the mode shapes, are determined. Results indicate that increasing the parameters of nonlocal and material has a decreasing and increasing effect (respectively) in the frequency ratio in all modes. This indicates that these parameters have a softening and hardening behavior on the plate vibrational behavior respectively. Also, increasing the initial value of deflection produces a rising trend in the frequency ratio for all modes, nonlocal parameter λ and material parameter Ls.

In this paper, using homotopy analysis method, an analytical solution for the nonlinear free vibrations of the functionally graded porous micropipes conveying fluid flow is presented. The equations of motion are obtained based on Euler-Bernoulli beam theory and modified couple stress theory with consideration of geometric nonlinearity. It is assumed that the micropipe is porous and the porosity distribution is in three forms; uniform, non-uniform symmetric, and non-uniform asymmetric distributions. The Hamilton principle is used to obtain the governing equations of motion. Also, the Galerkin method is used to convert partial differential equations to ordinary differential equations. Finally, by considering immoveable simply-supported boundary conditions and using the homotopy analysis method, the analytical solution for the governing equations is performed. The results obtained from this method has been verified by the Runge-Kutta numerical method which shows that the homotopy analysis method has good accuracy by considering two terms of the Taylor series. The results showed that between the proposed porosity distribution schemes in the micropipe, the non-uniform asymmetric distribution pattern is the most suitable, because the microtube becomes unstable at a higher fluid velocity.

Purpose of paper is to use a nonlinear dynamic absorber as beam with concentrated mass at its end to reduce the amplitude of resonant nonlinear oscillator vibration. Primary vibration system consists of mass, nonlinear spring, and viscous damping, and harmonic force is applied to it and causes the system to intensify. Nonlinear dynamic absorber has been used to reduce vibration amplitude. First, the kinetic energy and potential energy of system are calculated, and then governing equations of the system are extracted using Lagrange's equations. To solve the governing equations, the method of multiple scales is used. Numerical solution, in the negligible case of considering the mass of the absorber and the stiffness of the nonlinear Duffing spring, the validation of results is done. The effect of nonlinear dynamic vibration absorber on reducing the amplitude of resonant oscillator vibration can be seen well. Influence of the main parameters of the nonlinear dynamic absorber on vibration amplitude of primary system is investigated.

According to the wide presence of beams in engineering structures, it is very useful to understand how the beams vibrate nonlinearly in conditions where they oscillate with a large amplitude. In this paper, the nonlinear vibrations of an Euler-Bernoulli beam under finite strain are investigated. In this study, unlike other papers, in order to obtain the governing equations of beam, the field-displacement relationship has been done without approximation. Based on this, the strain-displacement relations are calculated using the Green Lagrange strain and the nonlinear form of the equations is obtained by using the Hamilton method. In order to solve the partial differential equation, using the Galerkin method, the equation has been converted to an Ordinary differential equation and finally solved using the multiple scale method and compared with the Rung-Kutta numerical method. To evaluate the accuracy of the method and the validity of the modeling, the obtained results are compared with the Euler–Bernoulli beam theory and the Von-Karman nonlinear model. The results show that the present method in low vibration amplitudes is consistent with the model of Euler-Bernoulli and Von-Karman, but with increasing amplitude of oscillations, the results of these models will be significantly different from each other, which is as expected.

In recent years, the vibrations control of beams has been significantly considered by researchers and a lot of research has been done in this field. Given that the material of studied beams was mostly metal or composite, so in this study, in order to increase the physical and thermal resistance, the studied beam was considered as functional graded (FG). In this paper, the active control of nonlinear vibrations for an FG beam with different boundary conditions under external loading is investigated. Two piezoelectric layers are connected to the upper and lower surfaces of the beam to be used as sensors and actuators. To discretize the equations of motion, Glerkin method is used, and the numerical simulation is utilized to solve the discretized equations. In order to control the vibrations of the beam, the feedback linearization control and the sliding mode methods have been used. The time-amplitude and time-voltage curves are shown for five boundary conditions, including, clamped- clamped, free-clamped, simply-clamped, free-free and simply-supported ends. The results of the mentioned control methods are compared for all boundary conditions in the presence and absence of uncertainty.

In this article, the nonlinear forced vibrations of carbon nanotubes conveying magnetic nanofluid under a longitudinal magnetic field have been investigated. Using Von Karman's nonlinear strain field and the Euler-Bernoulli beam theory, the equations governing the nonlinear vibrations of carbon nanotubes are extracted. Using the method of multiple scales, the frequency response in primary resonance, superharmonic resonance, and subharmonic resonance is obtained. In order to consider the effects of small size, a stress-driven non-local integral model has been used. In the end, the effect of magnetic fluid and magnetic field intensity on frequency response and force response has been investigated. From the results, it can be seen that the presence of a magnetic field causes the system's vibration amplitude to be unstable and have a limited cycle. In this condition, the vibration response is quasi-periodic. However, the presence of magnetic fluid causes the vibration amplitude to be stable and the time response to alternate; In such a way that the Poincaré diagram shows a point in the phase plane. In the primary resonance, with the presence of the longitudinal magnetic field, as the excitation amplitude increases, the frequency response curves include two sub-amplitudes. One is an asymptotic curve with a horizontal axis and the other is a closed curve.

In the recent years, double-walled carbon nanotubes (DWCNTs) have been used for different indusrial applications such as separation and purification technology. So, the main purpose of this paper is to analyze the bifurcation behavior of double-walled carbon nanotubes conveying fluid with considering van der Waals nonlinear forces. The internal flow is considered to be pulsating. In the framework of the Von Karman's theory and the Euler-Bernoulli beam model, the nonlinear governing equations of motion are developed using the Hamilton's principle. The governing partial differential equations are discretized by means of the assumed modes method and solved by the Rung-Kutta method. Then, the effects of flow velocity and pulsation frequency on the dynamic behavior of the system are investigated by the bifurcation diagrams, phase plan portrait, time series and Poincar'e maps. The results indicate that the flow velocity and pulsation frequency have significant effects on the dynamic responses of the system. Also, the results of analysis reveal a variety of nonlinear behavior such as periodic, multi-periodic and chaotic motions that can give some insight to researchers in designing and studying these systems in the future.

In the analysis of many offshore structures such as oil columns and structures, oil rig abutments and towers surrounded by water, the single-beam model is usually used. These models usually bear the weight of a concentrated mass, and the response amplitude of these structures is of particular importance during design.In this paper, a nonlinear beam immersed in a fluid with a concentrated mass under the effects of the harmonic flow of water has been studied. Using the harmonic balancing method, the response of a nonlinear beam with three nonlinear terms is determined in the first four modes. Examination of the frequency response by analytical solution and numerical simulation shows that the jump phenomenon occurs in the triple response zone between the bifurcation points. The jump phenomenon is hardening in the first mode and softening in the second to fourth modes. Each of the nonlinear sentences has different effects on the vibrational behavior of the system and the jump phenomenon. The behavior of the beam in the state space along with the time response and Poincaré mapping shows that the path of the phase curve has different stability points. Finally, the phenomenon of chaos in the nonlinear beam was studied. At the bifurcation points, the behavior of the system is chaos, and the geometric nonlinear sentence has the most effective effect on the response disorder.

Frequently used thin walled beams have low torsional stiffness and their torsional deformations may be of such magnitudes that it is not adequate to treat the angles of cross section rotation as small. In this paper, nonlinear torsional vibrations of thin walled beams will be investigated. The method of multiple scales will be implemented as a solution method and different nonlinear phenomena will be studied. The obtained results are compared with the available results in the literature which reveals an excellent agreement between different solution methodologies. The outcomes of this study show that beam nonlinear torsional dynamics and the related phenomena could influence the linear torsional dynamic of beams under axial load, e.g. rotating beams. Forced torsional vibrations of a beam with the excitation in the form of primary resonance of the first and second modes have been investigated. It has been demonstrated that in the case of the beam with two ends clamped boundary conditions, three-to-one internal resonance will appear. The primary resonance of the first and second modes has been solved in two sets of boundary conditions, torsionally clamped-fixed and torsionally fixed-fixed. Nonlinear response, amplitude-phase equations, fixed points, and their stability have been studied.

The free and forced vibration analysis of a rotating large flexible structure with a single crack is investigated using the Homotopy Perturbation Method (HPM). The crack is modeled with a torsional spring element on a structure that follows the Euler-Bernoulli theory. The nonlinear equations of motion of the co-rotational system considering centrifugal forces are derived using the calculus of variation and the Assumed Mode Method (AMM). Applying the Galerkin method, the spatial domain is extracted and the time domain is transformed into a second-order nonlinear differential equation. The results of time response, phase plane, and bifurcation diagrams for different functional parameters variations such as base angular velocity, crack position and stiffness have been analyzed. Moreover, it is shown that as the base angular velocity increases, a tensile force appears along the cracked structure axis, stiff it, and shifts the backbone to the right, this can highly affect the nonlinear features of the system.

One of the most common defects in rotary equipments is cracks. Creation and growth ofcracks can cause irreparable damages as well as occurrence of unwanted vibration in rotatingequipments. On the other hand, increasing the damping of the system is one of the mostpractical solutions to control vibrations in rotating equipment. One of the most importantmethods to increase the damping is the use of squeeze film dampers. Despite the highefficiency of these elements in controlling the amplitude and damping of system vibrations,their nonlinear behavior has created many limitations in the use of this equipment.In this paper, the bifurcation analysis of a flexible rotor with a floating-ring squeeze filmdamper with centralizing spring and considering the occurrence of cavitation in the damper oilfilm and transverse cracks in the shaft is been investigated.

For the modelling of marine structures, such as the oil columns and structures, the terminal and base of oil platforms and the towers surrounded by water usually a cantilever beam or rod is used. These models are subjected to random excitation and the response amplitude of these structures is of particular importance during design. In this paper, a nonlinear cantilever beam immersed in a fluid with a concentrated mass under a narrow band random excitation has been studied and its response has been analyzed. With the development of the harmonic balance method, the variance of the random system response has been determined and the phenomenon of jumping and random jumping has been investigated. The analytical solution and the numerical simulations show that in comparison with the deterministic response, the random excitation increases the amplitude of the random response between the bifurcation points of the beam. As the intensity of the random excitation increases, the steady response changes from a circular to a cyclic state. The results also show that the random jump phenomenon occurs in the area where there are three states for the system. Finally, the results of analytical and numerical modeling indicate that there is a very good agreement between the data and the results of these two methods.

Nonlinear phenomena widely exist in engineering applications. A common example of this phenomenon in aerospace structures is the creation of fatigue cracks that open and close continuously under dynamic loads during the vibration cycle, causing a bilinear behavior in the structure. Late detection of such cracks can lead to a catastrophic failure. Therefore, identifying the nonlinear behavior of the cracked structure is very important for the prevention of structural failures. In this study, the nonlinear vibration behavior of a cantilever beam with a transverse breathing crack with bilinear behavior has been studied. For this purpose, we first estimate the polynomial function equivalent to the bilinear function of the beam stiffness. Then, using the well-known perturbation method, the method of multiple scales, the nonlinear equation of the beam is solved, and the frequency response equations for both harmonic and superharmonic resonances are extracted. Then, the sensitivity of the responses to the crack parameters such as depth, location, excitation force, and damping coefficient are investigated. The beam frequency response curves in the main resonance have become highly nonlinear due to the increase of the crack parameters and causes softening of the curves. Also, according to the results of the beam vibrations in superharmonic resonance, it was observed that the behavior of the beam in superharmonic resonance has a higher sensitivity to the existence of the breathing crack.

In this study, nonlinear vibrations of simply-supported pipes conveying fluid made of multilayer graphene reinforced composite materials have been investigated analytically and based on the Euler-Bernoulli beam theory. The constituent layers of the pipe wall thickness are considered to be made of polymer and graphene platelets and the reinforcing graphene platelets are varied by layers in the pipe wall thickness direction. Four different patterns for distribution of reinforcing graphene platelets, large deformations, and Von-Karman nonlinear strain field are considered. The nonlinear governing equations are derived by the Hamilton principle, they are converted to the ordinary differential equations by the Galerkin method and then are solved analytically using the homotopy analysis method. The variations of the first nonlinear natural frequency of the system with respect to the variation of initial amplitude, fluid velocity, fluid density, pipe length, and also time response of the nonlinear vibrations of the system are presented for different distribution patterns V, X, O and U of the graphene platelets. The results show that the first nonlinear natural frequency of the system for all distribution patterns of graphene platelets is decreased by an increase of pipe length, fluid velocity, and density but increasing the initial amplitude increases the first nonlinear natural frequency and also the distribution pattern V has the highest nonlinear frequency comparing with the other distribution patterns.

In the present study, a proper analytical model is developed for investigating nonlinear vibration behavior of asymmetric and symmetric rotors under unbalanced and misalignment induced forces in rotating coordinates. The rotor is connected to a motor through an asymmetric coupling. For a more accurate vibration analysis, Timoshenko's beam theory is applied and for a better modeling of misaligned coupling forces, Gibbons’ equations are used. The equations of motion are discretized by Rayleigh-Ritz method and derived from Hamilton's principle, thereafter. According to this investigation, for asymmetric rotors as opposed to symmetric rotors, a frequency range is detected in which resonance and instability occurs. Also, the dynamic behaviors of the symmetric and asymmetric rotors are analyzed at the same rotational speed to indicate specifically the effects of different parameters on both rotors. For investigating the vibration behaviors of the rotors more accurately, their time-domain vibration responses are plotted and then their Fast Fourier Transform (FFT) are presented to determine the vibration frequencies of the rotors, so the effects of different parameters can be well observed. As a whole, in this study, the effects of each of the defects such as shaft asymmetry, misalignment, mass unbalance and also nonlinear terms are investigated on the dynamic behavior of the rotor system.

In this study, the nonlinear vibration of the annular sector plate in contact with fluid is investigated. The displacements in polar coordinates are considered in terms of the first order shear deformation theory. The strains are determined based on Von-Karman relationships. By considering the kinetic and potential energies and the Hamilton principle, the governing equations of motion are determined. The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. The shape modes are considered based on linear vibration modes. By using shape modes and Galerkin method, the governing equations have become nonlinear differential equations based on time. The nonlinear differential equations solved based on perturbation method and nonlinear natural frequency is determined. At the end, the numerical results are presented for a sample plate and the effect of parameters such as aspect ratio, sector angle, boundary conditions, fluid density and fluid height have been investigated. Also, the results obtained are verified with the current research (DQM method) and FEM, which shows good convergence.

Graphene Sheets are used in this paper to design a high-sensitivity mass sensor. For this purpose, the nonlinear vibrations of carbon nanoplates on the Winkler and Pasternak foundation are investigated for use as a mass sensor. Kirchhoff's nonlocal plate theory is used to model the sensor's nanoplate, and the effect of concentrated masses on the arbitrary points of the plate is considered, then the Galerkin method is used to transform the partial governing equation into the ordinary differential equation. Next, the nonlinear frequency response of the system is obtained by the series method with multiple time scales. The nonlocal parameter that plays an important role in the behavior of the nano system is determined by comparing the results with other studies, and the natural frequency of the carbon nanoplate is verified with the molecular dynamic results. The dimensions of the nanoplate and the characteristics of the foundation used are such that the designed sensor is capable of detecting a single mass in the nanoplate center with five zeptograms. This ability to detect in different mass configurations has also been investigated and compared.

In this research, secondary superharmonic frequency analysis of a truncated conical shell, reinforced with stringer and ring stiffeners, under external load is presented. The stiffened shell is subjected to the transverse harmonic external load and the nonlinear governing equations of motion are extracted. Using Donnell-Mushtari-Vlasov theory and Airy stress function, the governing differential equations of motion, which are a system of coupled nonlinear partial different equations, are obtained. The nonlinear Galerkin method along with homotopy perturbation method (HPM) have been applied to solve the equations of motion. A parameter study is performed to show the effects of the various parameters, such as conic apex angle, thickness of the shell, number of rings and stringers, on the frequency responses of secondary resonances. Based on the results, increase of the number of stringers and increase of the shell thickness cause a deviation of frequency response to the right which indicates an increase in the amount of the rigidity of the structure. Further, increase of the number of rings leads to the deviation of frequency response to the left which reveals the reduction in the value of the rigidity of the stiffened shell.

In this paper, nonlinear vibration analysis of a microbeam on Winkler type of foundation and subjected to an axial compressive load on its both ends is investigated. The partial differential governing equation of motion in transverse direction for the Euler-Bernoulli microbeam considering the Hook’s law based on the couple stress theory and applying the Hamilton principle is derived. Using Galerkin method, the partial differential equation of vibration in lateral direction is converted to an ordinary differential equation and then is analytically solved using the He’s nonlinear method to obtain frequency response of the microbeam. Effect of changes of various parameters such as geometrical size scale of microbeam, stiffness of Winkler foundation and axial compressive load on the nonlinear and linear natural frequencies are all investigated. It is seen that by increasing the axial compressive load, the dimensionless ratio of nonlinear frequency to linear frequency increases and the value of this ratio for the pinned-pinned microbeam is greater than the one for a clamped-clamped microbeam.