Showing 8 results for Microbeam
Ghader Rezazadeh, Morteza Sadeghi, Mohammad Fathalilou,
Volume 14, Issue 15 (3-2015)
Abstract
Size dependent behavior of materials appears for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. In these cases, ignoring this behavior in modeling may leads to incorrect results. In this paper, strong effects of the size dependence on the static and dynamic behavior of the electrostatically actuated micro-beams have been studied. The equilibrium positions or fixed points of the gold and nickel micro-beams have been determined and shown that for a given DC voltage, there is a considerable difference between the fixed points gained using the classic beam theory and the modified couple stress theory. In addition, it has been shown that the static and dynamic pull-in voltages gained using the couple stress theory are several times higher than those gained using the classic beam theory. Some previous studies have applied the classic beam theory in their models and introduced a considerable hypothetical value of residual stress to match their experimental and incorrect theoretical results. It has been shown that using the modified couple stress theory decreases considerably the difference with the experimental results.
Vahid Marefat,
Volume 16, Issue 10 (1-2017)
Abstract
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.
Amir Raheli, Saber Azizi, Shirko Faroughi,
Volume 17, Issue 5 (7-2017)
Abstract
In this research dynamic instability and nonlinear vibration of a clamped-clamped micro-beam sandwiched with piezoelectric layers based on parametric excitation in sub-harmonic region is investigated. The equation of motion is derived based on Hamiltonian principle, and non-dimensionalized using appropriate non-dimensional parameters. Applying a harmonic AC voltage to the piezoelectric layers results in the time varying of the linear stiffness of the micro-beam. The resultant motion equation in non-dimensional form is discretized to single degree of freedom model using Galerkin technique. The governing equation is a nonlinear Mathieu type ODE, and the periodic attractors are captured based on the shooting technique. The nonlinearity of governing equation is due to the geometric nonlinearity which originates from the clamped-clamped boundary conditions. The effect of various parameters including, magnitude of the nonlinear stiffness, damping coefficient, the frequency and the amplitude of the harmonic excitation on the parametric resonance region is investigated. The results depict that increased damping coefficient leads to the decreased aria of the parametric resonance region. It is concluded that the magnitude of the nonlinear stiffness, does not affect on the area of the resonance region, however it considerably influences on the amplitude of the parametric resonance.
Amir Veysi Gorgabad, Ghader Rezazadeh, Rasoul Shabani,
Volume 17, Issue 7 (9-2017)
Abstract
In this paper the nonlinear dynamic of an electrostatically actuated microbeam with viscoelastic-anelastic behavior considering size effect is studied. The micro-beam is deflected using a bias DC voltage and then driven to vibrate around its deflected position by a harmonic AC load. Regarding the stress-strain behavior of anelastic materials, the constitutive equation of microbeams is derived based on the modified couple stress theory (MCST). Assuming electrostatic and mid-plane stretching forces as the main sources of the nonlinearity and taking advantage of the Galerkin projection method, the partial differential equation is transformed to a set of nonlinear ordinary differential equation (ODE). Multiple scales method is used to obtain an approximate analytical solution for nonlinear resonant curves. The effect of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity, length scale parameter, anelastic relaxation time and relaxation intensity on the nonlinear vibration analysis are studied. The results demonstrate that there is very large dependence of resonance curves on the different mechanical behavior of materials. It is seen that there are special conditions which the elastic and anelastic models predict similar results while the predicted results from anelastic and viscoelastic models are different from each other. It is found that the relaxation intensity and anelastic relxation time can change the resonant curves significantly.
Mohammad Reza Salehi Kolahi, Hossein Moeinkhah,
Volume 17, Issue 12 (2-2018)
Abstract
In this research, the dynamic behavior and nonlinear vibration of a clamped-clamped initially curved microbeam under electrostatic step actuation is investigated. The initially curved microbeams under transverse loading may exhibit two different stable states and this is the basis of the emergence of bi-stable micro electro mechanical systems (MEMS). The equation of motion is derived based on energy method and Hamiltonian principle, and re-written in non-dimensional form by using appropriate non-dimensional parameters. The resultant equation of motion in non-dimensional form is discretized and converts to a system of nonlinear ordinary differential equations by using a reduced order model based on the Galerkin procedure. Runge-kutta method of order four is employed to solve the resulting system of nonlinear ordinary differential equations. COMSOL Multiphysics software is used for finite element simulation. Then, the effect of various parameters including voltage parameter, damping, initial midpoint elevation and gap length is investigated. It is concluded that the critical voltage of pull-in is decreased by increasing of the initial midpoint elevation. Also The results depict that by increasing of the damping parameter, the possibility of transition between two stable stats is eliminated.
Atieh Andakhshideh, Sattar Maleki, Hossien Karamad,
Volume 18, Issue 9 (12-2018)
Abstract
In this article, for the first time, the effect of non-uniformity of microbeam cross section and various boundary conditions on the nonlinear vibration of microbeam is investigated considering the size dependent behavior based on modified couple stress theory. Using the Hamilton’s principle, the governing equation of Euler–Bernoulli microbeam with von Karman geometric nonlinearity based on the modified couple stress theory is derived. The nonlinear vibration governing equation is then solved using the Generalized Differential Quadrature method (GDQ) and direct iterative method to obtain the nonlinear natural frequencies. In this step, the Galerkin method is used to reduce the nonlinear PDE governing the vibration into a time-dependent ODE of Duffing-type. The time domain is then discretized via spectral differentiation matrix operators which are defined based on the derivatives of a periodic base function. Next, the nonlinear parametric equation is solved using pseudo arc-length method and the frequency–response curves of microbeam nonlinear forced vibration is obtained. Finally, nonlinear natural frequency and frequency response of microbeam with various non-uniformity of cross sections and boundary conditions are obtained. Present results show that, the nonlinear free and forced vibration of microbeam is size dependent. Moreover, this size dependency is more significant for non-uniform microbeam and is deferent for various boundary conditions. The result of present method for simple case including uniform section and simply supported boundary condition is validated with that of exact method and have good agreement.
A. Nikpourian, M.r. Ghazavi,
Volume 19, Issue 2 (2-2019)
Abstract
Nonlinear behavior of an initially curved fully clamped microbeam is investigated in this paper. The microbeam is laminated between two thin piezoelectric layers along its length. Applying voltage to the piezoelectric layers induces a lengthwise force in the microbeam which, in turn, changes the initial rise and the bending stiffness of the microbeam. This feature is used to tune the frequency and the bistability band of the initially curved microbeam for the first time in this paper. The microbeam is electrostatically actuated as well. The governing equation of motion is obtained, using the Hamilton’s principle and the size effect is considered in the formulation of the problem utilizing the strain gradient theory. Static response of the system is obtained, using the Newton-Raphson numerical approach. The natural frequency of the system is obtained for various electrostatic voltages. The influence of piezoelectric actuation and size effect is studied on the static behavior and the frequency of the microbeam. Dynamic response of the microbeam in the vicinity of the primary resonance is obtained, using shooting technique and in some cases by the method of multiple scales. The effect of size and piezoelectric excitation on the primary resonance is investigated. The secondary resonance of the microbeam subjected to subharmonic resonance of order 1/2 and the influence of size on it is also studied.
E. Akrami Nia, H. Ekhteraei Toussi,
Volume 19, Issue 10 (10-2019)
Abstract
Microbeams are one of the most important members of microelectromechanical systems (MEMS) which contrast of electrical and mechanical forces in them cause pull-in instability. One of the proposed mechanisms for controlling this instability and enlarging the stable range of system are initially curved microbeams. Despite studying various pull-in instability in straight elastic or viscoelastic microbeams, the instability of curved microbeams has been investigated only within the range of elastic behavior. Therefore in the present study, assuming a clamped-clamped viscoelastic initially curved microbeam, the effect of viscoelastic behavior on the instabilities called snap-through and pull-in, was investigated. The viscoelastic behavior was simulated by the standard anelastic linear solid model. The governing differential equation was obtained based on the modified couple stress theory and by use of Hamilton’s pull-in instability principle. By using the Galerkin method, the governing equation was converted to a nonlinear ordinary differential equation and solved by MATLAB sofware. The structure behaviors are compared in two extreme situations before and after the viscoelastic relaxation by drawing diagrams. The results show when the time of structure relaxation increases, viscoelastic behavior causes more decreasing in instabilities voltage, but its effect on the position of instability will depend on the axial load. In this way, in the presence of tensile load, viscoelastic behavior increases the snap-through position and decreases the pull-in position, but in the presence of compressive load, snap-through occurs at smaller deflections and pull-in occurs at larger deflections.
