Sharif Digital Repository

In this paper the static deflection and pull-in instability of electrostatically actuated microcantilevers is investigated based on the strain gradient theory. The equation of motion and boundary conditions are derived using Hamilton's principle and solved numerically. It is shown that the strain gradient theory predicts size dependent normalized static deflection and pull-in voltage for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. The results of strain gradient theory are compared with those of classical and modified couple stress theories and also experimental observations. According to this comparison, the... 

In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of... 

The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a... 

Functionally graded materials (FGMs) are inhomogeneous composites which are usually made of a mixture of metals and ceramics. Properties of these kinds of materials vary continuously and smoothly from a ceramic surface to a metallic surface in a specified direction of the structure. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are induced when two dissimilar materials with large differences in material properties are bonded. FGMs have extracted much attention as advanced structural materials in recent years. In this paper, free vibration of a rotating FGM cantilever... 

The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a... 

A part of resilience and sustainability in any urban environment is establishing and maintaining health. Sustainability in health is a dynamic process in which growth of physical, mental, and social health is guaranteed. A city is sustainable when all aspects of life, such as economy, environment, health, and infrastructure, are well defined and very often subjected to optimization  

Carbon nanotubes are widely used in the design of nanosensors and actuators. Any defect in the manufactured nanotube plays an important role in the natural frequencies of these structures. In this paper, the effect of vacancy defects on the vibration of carbon nanotubes is investigated by using an atomistic modeling technique, called the molecular structural mechanics method. Vibration analysis is performed for armchair and zigzag nanotubes with cantilever boundary condition. The shift of the principal frequency of the nanotube with vacancy defect at different locations on the length is plotted. The results indicate that the frequency of the defective nanotube can be larger or smaller or... 

In this study, the homotopy analysis method (HAM) is used to obtain an approximate analytical solution for geometrically non-linear vibrations of thin laminated composite plates resting on non-linear elastic foundations. Geometric non-linearity is considered using von Karman's straindisplacement relations. Then, the effects of the initial deflection, ply properties, aspect ratio of the plate and foundation parameters on the non-linear free vibration is studied. Comparison between the obtained results and those available in the literature demonstrates the potential of HAM for the analysis of such vibration problems, whose governing differential equations include the quadratic and cubic... 

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtained using the Homotopy Analysis Method (HAM) and Homotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%. © 2008 Elsevier Ltd. All rights reserved  

Electrostatically actuated beams are fundamental blocks of many different nano and micro electromechanical devices. Accurate design of these devices strongly relies on recognition of static and dynamic behavior and response of mechanical components. Taking into account the effect of internal forces between material particles nonlocal theories become highly important. In this paper nonlinear vibration of a microano doubly clamped and cantilever beam under electric force is investigated using nonlocal continuum mechanics theory. Implementing differential form of nonlocal constitutive equation the nonlinear partial differential equation of motion is reformulated. The equation of motion is... 

The dynamic pull-in voltage as a criterion for the system stability is one of the most important effects considered with the dynamics of microstructures. In this study effect of microbeam electrical resistivity on the pull-in voltage of an electrostatically actuated microbeam is investigated. Assuming Euler-Bernoulli theory for the microbeam, two coupled nonlinear partial differential equations are derived for the beam deflection and voltage. The one parameter Galerkin method is implemented to transform the equations to a set of nonlinear coupled ordinary differential equations. Obtained equations are solved implementing the differential quadrature method (DQM). Variation of dynamic pull-in... 

In this study vibration amplitude, frequency and damping of a microbeam is controlled using a RLC block containing a capacitor, resistor and inductor in series with the microbeam. Applying this method all of the considerable characteristics of the oscillatory system can be determined and controlled with no change in the geometrical and physical characteristics of the microbeam. Euler-Bernoulli assumptions are made for the microbeam and the electrical current through the microbeam is computed by considering the microbeam deflection and its voltage. Considering the RLC block, the voltage difference between the microbeam and the substrate is calculated. Two coupled nonlinear partial... 

Nonlinear vibration of a microbeam actuated by a suddenly applied voltage with considering the effect of voltage distribution on the beam due to electrical resistivity of beam is investigated. Homotopy perturbation method is implemented to solve the coupled nonlinear partial differential equations of motion. The vibration frequency variation and damping at various resistivities is studied. Considering resistivity, effect of applied voltage and beam length on the frequency shift and damping ratio is analyzed. Findings indicate there exists a jump in frequency shift and damping ratio at a critical resistivity. Variation of critical resistivity with respect to modulus of elasticity and beam... 

In this study, vibration of a microbeam excited by an ultrashort- pulsed laser considering the momentum and heating effect of the laser beam is investigated. When the laser impacts the microbeam, portion of the photons is absorbed by the beam and their energy will be transformed into heat while the others are reflected. The momentum change of the absorbed and reflected laser photons is considered and modeled as a distributed force on the beam. The absorbed thermal energy yields non-uniform thermal stress causing the beam to vibrate. According to short duration of laser pulse, the non-Fourier conduction equation which takes into account the finite propagation speed of thermal energy, is... 

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester... 

Application of piezoelectric materials in vibration energy harvesters is expanding rapidly, especially in MEMS-based devices, due to their uncomplicated fabrication processes and reasonable power generation potential. In addition to standard power extraction methods, nonlinear switched techniques with capability of generated power enhancement, are previously developed and extensively applied in energy harvesting using piezoelectric materials. In this article, vibratory behavior of bimorph resonant harvesters coupled to nonlinear circuits of energy harvesting including standard and switched techniques is investigated. An analytical approach employing some perturbation technique, is utilized... 

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester... 

As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and... 

Application of piezoelectric materials in vibration energy harvesters is expanding rapidly, especially in MEMS-based devices, due to their uncomplicated fabrication processes and reasonable power generation potential. In addition to standard power extraction methods, nonlinear switched techniques with capability of generated power enhancement, are previously developed and extensively applied in energy harvesting using piezoelectric materials. In this article, vibratory behavior of bimorph resonant harvesters coupled to nonlinear circuits of energy harvesting including standard and switched techniques is investigated. An analytical approach employing some perturbation technique, is utilized... 

Micro-scale piezoelectric unimorph beams with attached proof masses are the most prevalent structures in MEMS-based energy harvesters considering micro fabrication and natural frequency limitations. In doubly clamped beams a nonlinear stiffness is observed as a result of midplane stretching effect which leads to amplitude-stiffened Duffing resonance. In this study, a nonlinear model of a doubly clamped piezoelectric micro power generator, taking into account geometric nonlinearities including stretching and large curvatures, is investigated. The governing nonlinear coupled electromechanical partial differential equations of motion are determined by exploiting Hamilton's principle. A...