وحید عرب ملکی

This paper discusses the nonlinear dynamic behavior of nanocomposite microplates reinforced with carbon nanotubes in contact with static fluids. Equations of motion are derived using the first-order shear deformation theory of plates and considering the size effects and large deformations. Effective mechanical properties are determined by applying the law of mixtures. By use of the Galerkin method, the nonlinear equations governing motion are discretized and the numerical solution is obtained. The results have been verified and the effect of micro-plate geometrical characteristics, small size parameter, fluid height and weight fraction of the carbon nanotubes studied on natural linear and nonlinear frequencies and the dynamic response has been evaluated. The results indicate that the natural frequency of the system decreases with increasing fluid height. The reinforcement of microplates by carbon nanotubes also results in a softening of the stiffening behavior of the spring and a substantial bending of the response curve. Depending on the excitation frequency, this bending may result in jump instability. By examining the time response, phase, and Poincaré map of the system, periodic, quasi-periodic, and chaotic vibration behavior can be observed.

In this paper flexural vibration and buckling analysis of the viscoelastic nanotube under electromagnetic force is investigated analytically. In order to consider more realistic assumptions, the linear solid viscoelastic model is used. The differential equations of motion are derived via the nonlocal Timoshenko beam theory. The Lorentz magnetic force is obtained from the Maxwell's relation. The analytical method is used to obtain nonlocal natural frequencies and buckling load of the system. The influence of magnetic field, aspect ratio and nanoscale effects on the natural frequencies and buckling load are studied. Then the results are validated and illustrated with appropriate figures and tables.

In this paper, the energy harvesting by porous beams exposed to the external fluid flow is studied. The electromechanical nonlinear differential equations of the transverse vibration behavior of porous beams exposed to external fluid flow are derived using the Euler-Bernoulli beam theory. A porous beam with concentrated mass which is equipped with a piezoelectric layer at its upper surface is considered energy harvesting. After numerically solving the governing nonlinear equations, the effect of different parameters on the generated energy is investigated. The results show that in the lock-in area, the maximum amount of energy is taken. Also, the porosity distribution has a significant effect on the maximum amplitude of the oscillations as well as the energy harvesting by the porous beam. In addition, for electrical resistance of 1000 kΩ, the maximum voltage generated for the beam with symmetrical porosity distribution in the form of wall stiffness, asymmetric porosity distribution, and uniform porosity distribution is equal to 0.39 V, 0.44 V, and 57 V, respectively, which indicates the highest energy harvesting capability of the beam with the porosity distribution of the third type.

In this paper large amplitude vibration analysis of a porous FG-beam rested on a Winkler foundation and subjected to a harmonic loading is analytically investigated. The material properties of the porous FG beam are assumed to vary continuously according to a simple power law. Employing Von Karman’s geometric nonlinearity, implementing the Galerkin’s method and assuming doubly clamped immovable end boundary conditions, the governing nonlinear partial differential equation is reduced to a nonlinear ODE. Because of the large coefficient of the nonlinear term and due to existence of the external harmonic loading effect, none of the traditional perturbation methods leads to a valid solution. So, in order to solve this nonlinear nonhomogenous equation, the modified homotopy perturbation method is developed and it is called developed homotopy perturbation method (DHPM). For validating, the time response results obtained by DHPM and numerical methods are compared for various values of excitation amplitudes and frequencies. The increasing of nonlinear frequency obtained by DHPM with those of existence literature revealed a good agreement with a desired accuracy. Finally, the frequency response curves are presented for different values of volume fraction exponent together with porous volume fraction and the effects of nonlinearities on the frequency response curves are discussed in detail.

In this paper, by using a semi analytical method the effect of dynamic vibration absorber on amplitude reduction of fluid conveying pipe is investigated. Considering the Euler-Bernoulli beam theory, the governing equations of motion are derived. By using the first four vibration modes of the fluid conveying pipe, the Galerkin method is applied to discretize the equations, and then the discretized equations are solved numerically. Moreover, simple approximate analytical expressions are proposed for prediction of the natural frequencies of the simply supported fluid conveying pipe and the dynamic vibration absorber parameters. After validating the results of the proposed method, some proper curves are plotted to characterize the effects of system parameters on reduction of pipe vibration amplitude. The results indicate that around the first critical fluid velocity, by using an appropriate vibration absorber, the vibration amplitude can be reduced by 80%. Therefore, this type of absorber due to its simplicity of installation and high energy absorption capacity, can be considered as a benefit method to reduce/eliminate unwanted vibrations of the fluid conveying pipes.

In this paper, applying the general form of the viscoelastic model, vibration characteristics of viscoelastic fluid conveying pipes are investigated. By considering various viscoelastic constitutive equations, the equation governing the motion of the fluid conveying pipes is obtained, and by introducing a new analytical method, the exact mode shapes of the system are derived. Then, the effect of various system parameters on the complex eigenvalues and the instability of kind divergence and flutter are studied. The results show that for a pipe with viscoelastic behavior, the natural frequencies decrease and at the higher modes, the divergence critical fluid velocity increases dramatically. As a new result, it is observed the viscoelastic fluid conveying pipes with certain values of viscoelastic parameters, can experience the flutter instability before the divergence one. In addition, because the viscoelastic behavior does not affect all the vibration mode shapes in the same manner, therefore, the coupled-mode flutter does not take place.

The fluid induced vibration in fluid conveying pipes can cause fatigue and failure in the system. Therefore, controlling these unwanted vibrations and suppressing the vibrations of the fluid conveying pipe is important. In this paper by considering the passive vibration absorber for the fluid conveying pipe, the influence of the vibration absorber parameters on the dynamic behavior of the system is investigated. The governing equations of motion are obtained via the Newton’s second law, and analytical solutions for the characteristic equation and mode shapes of the system are obtained through the power series method. After verifying the obtained results, the effect of the vibration absorber parameters and the fluid flow velocity on the vibration behavior of the fluid conveying pipe have been investigated. Results show that by increasing the absorber mass, the effect of absorber on decreasing the oscillations amplitude is diminished. At different fluid velocities, the oscillation amplitude of the system can be reduced considerably by specifying proper values of the absorber parameters. At velocities near the critical velocity, where the oscillation amplitude reaches a maximum value, using a suitable vibration absorber may reduce the maximum oscillations amplitude of the system by 98%. The method presented in current study can be easily generalized to design passive vibration absorber for fluid conveying pipes with different boundary conditions.

This paper investigates the vibration behavior of fluid conveying viscoelastic pipe rested on non-uniform elastic Winkler foundation. The Kelvin-Voigt model is employed to consider the viscoelastic behavior of the pipe. Using the Galerkin’s method, the eigenvalue problem for the simply supported fluid conveying viscoelastic pipe is extracted. The effects of the fluid velocity, the viscoelastic constants and the foundation parameters on the complex eigenvalues and the divergence and the flutter instability of the fluid conveying viscoelastic pipe are studied and discussed. It is found that including the viscoelastic behavior to the pipe material alters the trend of the instability of the fluid conveying pipe, i.e., the first and the second modes divergence and the coupled mode flutter for the elastic pipe change to the first mode divergence, the second mode flutter and the second mode divergence for the viscoelastic pipe, respectively. The structural damping causes the velocity of the divergence instability at the higher modes to be increased. Also, because the viscoelasticity of the pipe affects the different vibration modes in different manner, therefore, the pipe dose not exhibit a coupled-mode flutter. Moreover, the non-uniformity of the foundation stiffness alters the first divergence velocity. The results are verified through comparing them with those reported in the literature.

Piezoelectric layers have significant effect on the vibration behavior and buckling capacity of the structures. For optimum usage of piezoelectric materials, it is possible to use the piezoelectric patches instead of the piezoelectric layers. In this paper, the effects of piezoelectric patches and boundary conditions on the buckling and vibration behaviors of Euler-Bernoulli beams is investigated. The piezoelectric stress resultants are introduced in terms of Heaviside discontinuity functions and the characteristics equation is obtained via Galerkin method. The effects of variation of location, length of the piezoelectric patches and the applied voltages on the natural frequencies and critical buckling loads of beam with different boundary conditions are investigated. Results show that the natural frequencies and critical buckling load are dependent on the voltage, length and location of the piezoelectric patches and the axial load. Also, patches have a considerable effect if they placed at the beam center.

In this research, firstly, the vibrational behavior of a cracked short cantilever beam under the axial load is investigated, and then, an analytical approach for the crack identification based on the vibration analysis is proposed. The cracked section of the beam is considered as a flexible element, which divides the beam into two segments. Using the fracture mechanics theory, the local flexibility of the crack is modeled as a mass-less tensional spring. By applying the boundary conditions and the inner conditions at the crack location, and taking into account the effects of shear deformation and rotary inertia, the governing equation of motion for the cracked beam is derived. The influence of the axial load and the crack parameters on the vibration behavior of the cracked beam is studied by establishing and solving the corresponding eigenvalue problem, directly. Then in order to predict the crack depth and location through the known natural frequencies of the cracked beam, which are obtained by the experimental tests, the corresponding inverse problem is established and solved analytically. The Results have been validated by the experimental and theoretical data reported in the literatures.

In this paper، a new analytical method is proposed to study the effect of crack and axial load on vibration behavior and stability of the cracked columns. Using the local flexibility model، the crack has been simulated by a torsional spring with connecting two segments of column in crack location. By solving governing eigenvalue equation، the effect of crack parameters and axial load on the natural frequencies and buckling load as well as buckling load are investigated. The results show that the presents of crack cause to reduction in natural frequencies and buckling load whereas this reduction is affected by the location and depth of the crack. Furthermore، the tensiel and compressive axial load increase and decrease the natural frequencies، respectively. In addition، as the compression load approaches to certain value، the fundamental natural frequency reaches zero and instability occurs. The accuracy of the model is validated through the experimental data reported in the literature.

In this paper, using the Hu-Washisu principle, the equation governing the lateral vibration of a pipe with a breathing crack has been derived. The crack is modeled as a continuous disturbance function in stress and displacement fields. In order to obtain the natural frequencies of the pipe with a breathing crack, a new model is introduced for the bilinear stiffness of the pipe at each lateral vibration mode. Using this model, the governing equation of motion is converted into the standard form which can be analyzed by the Lindstedt-Poincar’ method. Then the natural frequencies of the cracked pipe are derived. The first term of the solution is the response of the corresponding linear system with a stiffness equal to the mean value of the cracked pipe stiffness in fully open and fully closed cases of the crack, and the remaining terms represent the effect of nonlinearity due to the opening and closing the crack. The results reveal that the reduction in the natural frequencies for the case of breathing crack is less than that for open crack. The accuracy of the model is verified by comparing the theoretical results with the experimental data reported in the literature.

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

In this paper, the continuous model for vibration analysis of a cracked beam developed by Shen and Pierre is modified. For this end, by some realistic assumptions, new functions for displacement and stress fields are proposed. Then, the equation of motion of the cracked beam with breathing crack is obtained via the Hu-Washizu variational principle. The new obtained equation of motion is self-adjoint. Moreovers, by employing the Galerkin method, the modes shape of beam with a breathing crack are obtained. Then, in order to obtain the time response of the cracked beam, a new bilinear model is introdused for the stiffness corresponding to each mode. Using this model, the governing equation of motion is converted into the standard form which can be analyzed by Lindstedt-Poincar’ method. The results show that response obtained throught the perturbation metod (Lindstedt-Poincar method) is composed of two parts. The main part is the response of a system with the equivalent stiffness, whith is equal to the main value of the stiffness corresponding to the fully open and fully close crack cases. The remaining part of the response consistence of the correction terms, which reflects the effect of opening and closing the crack during vibration. The results show that for a given crack parameters, redaction in natural frequencies for a fatigue-breathing crack are smaller than the ones caused by open cracks. Also, the results have been validated by the experimental and theoretical data reported in the literature. There is a good agreement between the results obtained through the proposed method and those obtained from the reported experimental data.

In this research, a new continuous model for vibration analysis of a simply support cracked Euler Bernouli beam is proposed. The effect of the crack on the stress, strain and displacement field is modeled as a continuous disturbance function. The equation of motion and the corresponding boundary conditions for bending vibration of a cracked beam with an open edge crack, are derived by using Hu-Washizu variational principle. By employing the Galerkin method, the natural frequencies and mode shapes are obtained, and the influence of the crack parameters (crack depth and location) on the vibration behavior of the cracked beam is studied. The results have been validated by the experimental and theoretical dada reported in the literature. There is a good agreement between the results obtained through the proposed method and those obtained from the reported experimental data.