Sharif Digital Repository

In this paper, the tip tracking control problem of a Timoshenko micro-cantilever beam is investigated. The beam is actuated by a piezoelectric layer laminated on one side of the beam. Dynamic equations of the beam and piezoelectric layer are found using the Hamilton principle. By employing the Galerkin projection method, state space representation of the system is derived. Then, a cascade control loop is used for tracking control of the beam's tip. The cascade control structure consists of an inner loop stabilizer and an outer loop proportional-integral-derivative controller. The stabilizer has a linear feedback form whose states are obtained through a linear observer which is based on the... 

In this study tracking problem of tip of a micro cantilever, actuated by electrostatic, is investigated. Dynamic model of the system is a PDE. Using electrostatic actuation.introduced significant nonlinearity in dynamic model of the system. Control goals are achieved by means of backstepping for SI and feedback linearization for MI system. Performance of control system is inspected for some assumptions and simplifications. The results are in according to numerical simulations  

This study investigates the exact controllability problem for a vibrating non-classical Euler-Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur  

In this paper, a continuous model for flexural vibration of beams with a vertical edge crack including the effects of shear deformation and rotary inertia is presented. The crack is assumed to be an open-edge crack perpendicular to the neutral plane. A quasi-linear displacement filed is suggested for the beam, and the strain and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton principle. The equation of motion is solved with a modified weighted residual method, and the natural frequencies and mode shapes are obtained. The results are compared to the results of similar model with Euler–Bernoulli assumptions and finite element model... 

In this study, dynamic response of a micro- and nanobeams under electrostatic actuation is investigated using strain gradient theory. To solve the governing sixth-order partial differential equation, mode shapes and natural frequencies of beam using Euler–Bernoulli and strain gradient theories are derived and then compared with classical theory. Galerkin projection is utilized to convert the partial differential equation to ordinary differential equations representing the system mode shapes. Accuracy of proposed one degree of freedom model is verified by comparing the dynamic response of the electrostatically actuated micro-beam with analogue equation and differential quadrature methods.... 

The present study demonstrates numerically a novel approach to perform a controllable single-mode random laser, using stimulated Raman gain. Due to the narrow linewidth of the Raman line shape, only one of the modes of the passive random system can lase. The robust control on the emission spectrum was achieved through the selection of any desired quasi-modes, by adjusting the pump wavelength in order to place the center of Raman line shape on desired quasi-modes. This approach was proved using a developed nonlinear transfer matrix method for a 1D Raman random system. The proposed method includes the Raman gain saturation and the frequency-dependent index of refraction  

The classical continuum theory not only underestimates the stiffness of microscale structures such as microbeams but is also unable to capture the size dependency, a phenomenon observed in these structures. Hence, the non-classical continuum theories such as the strain gradient elasticity have been developed. In this paper, a Timoshenko beam finite element is developed based on the strain gradient theory and employed to evaluate the mechanical behavior of microbeams used in microelectromechanical systems. The new beam element is a comprehensive beam element that recovers the formulations of strain gradient Euler–Bernoulli beam element, modified couple stress (another non-classical theory)... 

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses  

The probability of occurrence of random cavities' resonance frequency in the Stokes bandwidth of the Raman active medium can cause Raman laser oscillation in the random structures. Due to the small bandwidth of Raman line shape, the probability of the simultaneous appearance of random cavity resonance frequencies in the cascade Stokes line shapes is small. As a result, the cascade Raman laser oscillation effects on the saturation behavior are negligible. The nonlinear transmission matrix method is employed to determine the statistical behavior of a Raman random laser. Our results showed that the statistical behavior depends on the position of the Stokes line shape relative to the center of... 

In this study, sandwich beam model (SM) is proposed for free vibration analysis of bilayer graphene nanoribbons (BLGNRs) with interlayer shear effect. This model also takes into account the intralayer (in-plane) stretch of graphene nanoribbons. The molecular dynamics (MD) simulations using the software LAMMPS and Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential are done to validate the accuracy of the sandwich model results. The MD simulation results include the two first frequencies of cantilever BLGNRs with different lengths and two interlayer shear moduli, i.e., 0.25 and 4.6GPa. These two interlayer shear moduli, 0.25 and 4.6GPa, can be obtained by sliding a small... 

This research presents an application of transparent lanthanum-modified lead zirconate titanate (PLZT) materials in micro light source tracking device, which is designed to function as a result of irradiation, having neither lead wires nor electric circuits. The focus of the paper is on the analytical and finite element investigation into ultraviolet photo-induced multi-physics responses of PLZT photocantilever and a comparison of the measured bending displacement to check the feasibility of these materials in design of micro light source tracking device. The finite element formulation of the transverse deflection for multi-physics analysis of PLZT ceramics by including the photovoltaic and... 

In this paper, considering horizontal components of seismic excitation, an algorithm for the nonlinear multi-component analysis of building structures by the Endurance Time (ET) method is proposed, and results of the ET method for various steel moment frames with one to seven stories are verified by comparing with the results from Nonlinear Time History Analysis with use of two different sets of ground motions. In addition, several parameters such as eccentricities and irregularities in structure, rotational and lateral stiffness, effect of hysteresis type and ductility have been considered for sensitivity analysis on results, obtained by ET method. Results show that on the basis of... 

Axial-torsional vibrations of rotating pretwisted thin-walled composite box beams exhibiting primary and secondary warping are investigated. Considering the nonlinear strain-displacement relations, the coupled nonlinear axial-torsional equations of motion are derived using Hamilton's principle. Ignoring the axial inertia term leads to differential equation of motion in terms of elastic torsion in the case of axially immovable beams. Centrifugal load in the presence of material anisotropy and pretwist angle leads to an induced static torque. The nonlinear equation should be linearized about the corresponding equilibrium state to obtain the linear differential equation of motion. Extended... 

A micro scale Timoshenko beam was modeled with strain gradient theory in "A micro scale Timoshenko beam model based on strain gradient elasticity theory" by Wang et al., European Journal of Mechanics - A/Solids, vol. 29, pp. 591-599, 7//2010. Looking at the modeling of the beam, a mistake in deriving the effect of classical moment has occurred. The classical boundary conditions of a Timoshenko beam could not be derived going backward from the strain gradient Timoshenko beam theory which has been presented in aforementioned paper. In this comment, the contradiction has been shown and the correct form of the boundary conditions and final equations has been derived  

Since the classical continuum theory is neither able to evaluate the accurate stiffness nor able to justify the size-dependency of micro-scale structures, the non-classical continuum theories such as the modified couple stress theory have been developed. In this paper, a new comprehensive Timoshenko beam element has been developed on the basis of the modified couple stress theory. The shape functions of the new element are derived by solving the governing equations of modified couple stress Timoshenko beams. Subsequently, the mass and stiffness matrices are developed using energy approach and Hamilton's principle. The formulations of the modified couple stress Euler-Bernoulli beam element... 

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration analysis of single and double tapered beams on elastic foundation. Geometric nonlinearity is considered using the condition of inextensibility of neutral axis. Moreover, the elastic foundation consists of a linear and cubic nonlinear parts together with a shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the second-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the nonlinear... 

This paper presents the dynamic response of uniform Timoshenko beams with arbitrary boundary conditions using Dynamic Green Function. An exact and direct modeling technique is stated to model beam structures with arbitrary boundary conditions subjected to the external load that is an arbitrary function of time t and coordinate x and the concentrated moving load. This technique is based on the Dynamic Green Function. The effect of different boundary conditions, load, and other parameters is assessed. Finally, some numerical examples are shown to illustrate the efficiency and simplicity of the new formulation based on the Dynamic Green Function  

This paper presents vibration and buckling analysis of functionally graded beams with different boundary conditions, using reproducing kernel particle method (RKPM). Vibration of simple Euler-Bernoulli beam using RKPM is already developed and reported in the literature. Modeling of FGM beams using theoretical method or finite element technique is not evolved with accurate results for power law form of FGM with large power of "n" value so far. Accuracy of the RKPM results is very good and is not sensitive to n value. System of equations of motion is derived using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of the beam are taken into account using... 

Conventional continuum theory does not account for contributions from length scale effects. Failure to include size-dependent contributions can lead to underestimates of deflection and stresses of micro and nanobeams. This research aims to use strain gradient elasticity theory to model size-dependent behavior of small beams. In this regard, Young's modulus and length scale parameters of poly silicon are estimated by fitting the predicted static pull-in voltages to the reported experimental results in the literature. The results demonstrate that decreasing the beam thickness results in higher pull-in voltage, lower deflection and lower sensitivity to axial stress and mid-plane stretching in... 

In this paper the free vibration of single walled carbon nanopeapods encapsulating C60 molecules is considered. The nanopeapod is embedded in an elastic medium and clamped at both ends. The Euler-Bernoulli beam model is used for the carbon nanotube and the C60 molecules are considered as lumped masses attached to the beam. Based on the nonlocal elasticity theory the governing equation of motion is derived and the resonance frequencies of the nanopeapod are obtained. The effects of small scale, foundation stiffness and ratio of the fullerenes' mass to the nanotube's mass on the frequencies are studied and some conclusions are drawn