Sharif Digital Repository

In this study, the homotopy analysis method is used to obtain an accurate analytical solution for fundamental non-linear natural frequency and corresponding displacement of tapered beams. Comparison between the obtained results and numerical solutions shows that the first-order approximation of present study leads to accurate solutions with a maximum relative error less than 0.5%  

Modified couple stress theory is a size-dependent theorem capturing the micro/nanoscale effects influencing the mechanical behaviors of the micro- and nanostructures. In this paper, it is applied to investigate the nonlinear vibration of carbon nanotubes under step DC voltage. The vibration, natural frequencies and dynamic pull-in characteristics of the carbon nanotubes are studied in detail. Moreover, the effects of various boundary conditions and geometries are scrutinized on the dynamic characteristics. The results reveal that application of this theory leads to the higher values of the natural frequencies and dynamic pull-in voltages  

In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler-Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior... 

The objective of this work is to create an analytical framework to study the non-linear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton's principal is utilized to derive the equations governing the nonlinear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these non-linear partial differential equations are reduced to two coupled non-linear ordinary differential equations. These equations are solved analytically using combination of the method of multiple time scales and homotopy perturbation analysis. Closed-form, parametric analytical expressions are presented for the time domain response of... 

Although many researchers have studied the vibration and buckling behavior of porous materials, the behavior of porous nanobeams is still a needed issue to be studied. This paper is focused on the buckling and nonlinear vibration of functionally graded (FG) porous nanobeam for the first time. Nonlinear Von Kármán strains are put into consideration to study the nonlinear behavior of nanobeam based on the Euler–Bernoulli beam theory. The nonlocal Eringen’s theory is used to study the size effects. The mechanical properties of ceramic and metal are used to model the functionally graded material through thickness, and the boundary conditions are considered as clamped–clamped (CC) and simply... 

The current paper focuses on the non-linear torsional vibration of a one-stage transmission gear system. Four different methods have been applied for solution of the equation of motion; the discretization method, the perturbation method, the Ritz method, and the stepwise time integration of the equation of motion. The time and frequency results from these analyses have been compared with each other, as well as those reported in literatures. Although all of these methods are accurate and computationally effective for finding the main spectral contribution, however, only the discretization method and the step-wise time-integration model are able to identify the other frequency components. ©... 

A time domain approach is used to study the cutting conditions in reaming process that leads the system to regenerative chatter vibrations. The dynamic analysis of the system includes inertia of the tool, centripetal and Coriolis terms, damping and the first mode bending of reamer. A model of cutting forces proportional to chip cross sectional area and process damping proportional to cutting speed is considered. Numerical simulation based on the Euler integration scheme is carried out to obtain time domain solution of the equation. Despite linearization in force modelling, the model is nonlinear due to the change in the tool engagement area. Another nonlinearity included in the model jumping... 

The non-linear flexural vibration for a dagger-shaped atomic force microscope cantilever has been investigated using the Timoshenko beam theory. In this article, the normal and tangential tip-sample interaction forces are found from Hertzian contact model and the effects of the geometry, normal and lateral contact stiffness, height of the tip, thickness of the beam, the angle between the cantilever and the sample surface and breadth and height taper ratios on the non-linear frequency to linear frequency ratio have been studied. The differential quadrature method (DQM) is employed to solve the non-linear differential equations of motion. The results show that the softening behaviour is seen... 

The non-linear flexural vibration for a double-tapered atomic force microscope cantilever has been investigated by using the Timoshenko beam theory. In this article, the normal and tangential tip-sample interaction forces are found from the Hertzian contact model, and the effects of the contact position, normal and lateral contact stiffness, height of the tip, thickness of the beam, angle between the cantilever and the sample surface, and breadth and height taper ratios on the non-linear frequency to linear frequency ratio have been studied. The differential quadrature method is employed to solve the non-linear differential equations of motion. The results show that the softening behaviour... 

An efficient hybrid modal-molecular dynamics method is developed for the vibration analysis of large scale nanostructures. Using the reduced order method, presented in this paper, linear and nonlinear vibrations of a suspended graphene nanoribbon (GNR) carrying an electric current in a harmonic magnetic field are investigated. The resonance frequencies as well as the nonlinear vibration response obtained by the present technique and direct molecular dynamic simulations are in very good agreement. Also, the obtained results illustrate the hardening behavior of nonlinear vibrations which is diminished by stretching the GNR  

In this paper, the nonlinear forced-vibration of Euler-Bernoulli beams with large deflections is investigated based on the modified couple stress theory, a non-classical theory capable of capturing size effects. The classical theory is unable to predict the size effects. In systems with the dimensions in order of microns and sub-microns the size effects are very significant. For some specific beams subjected to a concentrated force at its middle as the harmonic exciter, the size-dependent responses are investigated for primary, super-harmonic and sub-harmonic resonances. The results show that the frequency-responses of the system are highly size-dependent  

In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity  

In this paper, we investigate the influence of nonideal boundary conditions on the nonlinear vibration of damped Euler-Bernoulli beams subjected to harmonic loads. These nonidealities allow for small deflections and/or moments at the supports of the beam. Using the iteration perturbation method, analytical expressions for the case of simply supported beams with immovable end conditions are provided. The results reveal that the first order of approximation obtained by the proposed method is more accurate than the perturbation solutions. Moreover, compared with the previous studies, some interesting phenomenon is predicted. We have shown that in some special combinations of the nonidealities... 

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions... 

In this paper, the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a traveling mass with variable velocity is investigated. The nonlinear coupled partial differential equations of motion for the bending rotation of cross-section, longitudinal and transverse displacements are derived using Hamilton's principle. These nonlinear coupled PDEs are solved by applying Galerkin's method to obtain dynamic response of the beam under the act of a moving mass. The appropriate parametric studies by taking into account the effects of the magnitude of the traveling mass, the velocity of the traveling mass with a constant acceleration/ deceleration... 

In this study, the nonlinear free vibration of conservative two degrees of freedom systems is analyzed using the homotopy analysis method (HAM). The mathematical model of such systems is described by two second-order coupled differential equations with cubic nonlinearities. First, novel approximate analytical solutions for displacements and frequencies are established using HAM. Then, the homotopy Padé technique is applied to accelerate the convergence rate of the solutions. Comparison between the obtained results and those available in the literature shows that the first-order approximation of homotopy Padé technique leads to accurate solutions with a maximum relative error less than 0.068... 

This paper theoretically finds the different parameters of shape memory alloys via strain rate. Finite element formulation for temperature rate, and produced latent heat due to phase transition have been derived. Moreover, the equivalent viscous damp coefficient is provided. In addition, the Devonshire coefficient has been theoretically found by simplifications. This method helps to predict the heat and temperature change in quasi-static and dynamic studies in NiTi. Furthermore, they could be used in high nonlinear and low elastic deflection of NiTi. Then, the nonlinear vibration of smart composite involved with NiTi from any kind and percent of Ni and Ti could be handled by results.... 

This paper presents the vibration and stability analyses of an unbalanced rotor mounted on high-static-low-dynamic-stiffness supports. The stiffness of the supports is modeled as symmetric of cubic order. Then a second-order multiple scales method is used for studying the primary resonance of the system. The types of singular points are investigated and phase-plane of the system is plotted using analytical and numerical methods. The difference between analytical and numerical solutions is less than 2 percent. © 2017 Elsevier Masson SAS  

Influence of backside coating parameters on dynamic response of AM-AFM is modeled. Timoshenko based beam model is used and the general nonlinear interaction force is enclosed. The coupled ODEs of motion are achieved. The mode shapes are determined for coated cantilever and the natural frequency of each mode is validated with experimental results. It is showed a shorter cantilever with tip mass have better accuracy and inelastic and massless assumptions are not proper choice for modelling of the coating. The assumed mode method is used to determine time response of system for faraway and scanning condition of AM-AFM. Amplitude of response is calculated by FFT of time domain. Sensitivity... 

Environmental issues and energy crisis have caused the world attention to the renewable energies; especially the wind power, since they have low cost and high reliability. To achieve higher capacity, wind turbines have increased in their size over the years. However, the large size of the modern turbines has exacerbated the problem of vibrations, which results in lower efficiency and power generation. Because of the large deformations, the conventional linear theories cannot model the blades accurately, due to the importance of nonlinear effects in large scale wind turbines. In this research, a nonlinear kinematic model of the wind turbine blade is developed using the Hamilton's principle....