Sharif Digital Repository

Dynamic behavior of a electrostatically actuated MEMS resonator is investigated. A double clamped micro-beam under distributed DC and AC actuation is used. Corresponding single degree of freedom model is derived using Galerkin's decomposition method. Homotopy Perturbation Method (HPM) is implemented in order to derive analytical expression for frequency response of the micro-resonator. Comparison of the obtained results with the numerical simulations confirms that HPM agrees very well with numerical simulations for a wide range of parameters. Obtained analytical solution can be used for design and optimization of MEMS resonators  

This paper deals with the investigation of the size-dependent nature of nonlinear dynamics, in a doubly clamped shallow nano-arch actuated by spatially distributed electrostatic force. We employ strain gradient theory together with the Euler-Bernoulli and shallow arch assumptions in order to derive the nonlinear partial differential equation governing the transverse motion of the arch with mid-plane stretching effects. Using the Galerkin projection method, we derive the lumped single degree of freedom model which is then used for the study of the size effects on the nonlinear snap-through and pull-in instabilities of the arch nano-electro-mechanicalsystem (NEMS). Moreover, using strain... 

This paper aims to explore the dynamic behaviour of a nano-resonator under ac and dc excitation using strain gradient theory. To achieve this goal, the partial differential equation of nano-beam vibration is first converted to an ordinary differential equation by the Galerkin projection method and the lumped model is derived. Lumped parameters of the nano-resonator, such as linear and nonlinear springs and damper coefficients, are compared with those of classical theory and it is demonstrated that beams with smaller thickness display greater deviation from classical parameters. Stable and unstable equilibrium points based on classic and non-classical theories are also compared. The results... 

With the rapid development of micro/nano-electro-mechanical systems (MEMS/NEMS), arch shaped resonators are becoming increasingly attractive for different applications. Nevertheless, the dynamics of bistable resonators is poorly understood, and the conditions for their appropriate performance are not well known. In this paper, an initially curved arch shaped MEMS resonator under combined DC and AC distributed electrostatic actuation is investigated. A reduced order model obtained from first mode Galerkin's decomposition method is used for numerical and analytical investigations. We have used the Homotopy Analysis Method (HAM) in order to derive analytical solutions both for the amplitude and... 

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.... 

Conventional continuum theory does not account for contributions from length scale effects which are important in modeling of nano-beams. Failure to include size-dependent contributions can lead to underestimates of deflection, stresses, and pull-in voltage of electrostatic actuated micro and nano-beams. This research aims to use nonlocal and strain gradient elasticity theories to study the static behavior of electrically actuated micro- and nano-beams. To solve the boundary value nonlinear differential equations, analogue equation and Gauss–Seidel iteration methods are used. Both clamped-free and clamped–clamped micro- and nano-beams under electrostatical actuation are considered where... 

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... 

The nonlinear dynamics of a bistable micro/nano-electro-mechanical system resonator composed of an arch-shaped microbeam is investigated. The initially curved microbeam is actuated through a combined DC and AC electrostatic parallel plate field. A single degree of freedom model obtained using the Galerkin's decomposition method with distributed electrostatic force is implemented in order to investigate the resonator dynamics near its primary resonance. According to the shape of the potential energy function which depends on the system parameters, the nonlinear dynamics of the system are classified into certain categories. The appearance of various nonlinear phenomena including dynamic... 

Multi-application execution in Graphics Processing Units (GPUs), a promising way to utilize GPU resources, is still challenging. Some pieces of prior work (e.g., spatial multitasking) have limited opportunity to improve resource utilization, while other works, e.g., simultaneous multi-kernel, provide fine-grained resource sharing at the price of unfair execution. This paper proposes a new multi-application paradigm for GPUs, called NURA, that provides high potential to improve resource utilization and ensures fairness and Quality-of-Service (QoS). The key idea is that each streaming multiprocessor (SM) executes Cooperative Thread Arrays (CTAs) belong to only one application (similar to the... 

In recent years, extensive experiments have shown that classical continuum theory cannot predict the behavior of mechanical microstructures with small size. To accurately design and analyze micro- and nano-electro-mechanical systems, size-dependent continuum theories should be used. These theories model micro- and nano-electro-mechanical systems with higher accuracy because they include size-dependent parameters. In this paper, polysilicon nano-beam is modeled using modified couple stress and Eringen's nonlocal elasticity theories. First, partial differential equations governing the vibration of nano-beams are converted to a one D.O.F. differential equations using Galerkin method, resulting... 

With the successes in numerous applications from signal filtering to chemical and mass sensing, micro- and nano-electro-mechanical resonators continue to be one of the most widely studied topics of the micro-electro-mechanical systems community. Nonlinearities arising out of different sources such as mid-plane stretching and electrostatic force lead to a rich nonlinear dynamics in the time response of these systems which should be investigated for appropriate design and fabrication of them. Motivated by this need, present study is devoted to analyzing the nonlinear dynamics and chaotic behavior of nano resonators with electrostatic forces on both sides. Based on the potential function and... 

In this article, an analytical method for calculating pull-in voltage is proposed. This method can accurately predict pull-in voltage of clamped-free, clamped-clamped and curved micro- and nano-beams. In this study, mid-plane stretching, axial stress, initial deformation and the effect of size are taken into account. To achieve this goal, governing equation of beam based on modified couple stress theory was first derived and then transformed to a single degree of freedom (D.O.F) model by Galerkin method. In this model, electrostatic force appears in integral form which is approximated to non-integral form employing Genetic Algorithm. This single degree of freedom model provides means for... 

Presented herein is a comprehensive analysis on the size-dependent dynamic behaviors of electrostatically actuated nano-resonator including surface stresses effect. To this end, partial differential equation of nano-resonator based on Gurtin–Murdoch and Euler–Bernoulli theories is converted to ordinary differential equation utilizing assumed mode method. Effect of applied DC voltage on stability and bi-stability of nano-resonator is investigated and it revealed that surface elasticity and stress affect the bi-stability region of nano-resonator. By plotting frequency response of the resonator, hardening and softening behavior of nano-resonator are analyzed and it is shown that surface effect... 

Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the... 

Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the... 

Different nonlinearities in micro-electro-mechanical resonators lead to various nonlinear behaviors such as chaotic motion which can affect the resonator performance. As a result, it is important to properly identify and analyze the chaotic regions in resonators. In this paper, a novel method is proposed for prediction of the chaos in the micro- and nano-electro-mechanical resonators. Based on the proposed method, first an accurate analytical solution for the dynamics behavior of the nano-resonators is derived using the multiple scales method up to the second order. The results obtained by this analytical solution are validated by comparing them with the numerical ones. Using the analytical... 

In the present study, the effect of the number of stages of Tesla Micro-Valve (TMV), as well as the dependency of Reynolds number, Re, on the valve performance has been analyzed. For this purpose, different layouts include one to four-stage with different sizes are investigated numerically. The main criterion for evaluation of valves performance is diodicity, Di. Unsteady and steady flow in valve have been simulated and compared. It is shown that although there are some difference but the trend is similar for both responses. Finally, 2-D and steady state computations of the fluid flow have been utilized that reveal a strong dependence of Di on Re and pressure drop, ΔP. The results showed... 

In this study, the performance of Tesla-type microvalves, used in micropumps for low frequency driving force, is examined. Three-dimensional and unsteady numerical analysis of fluid flow inside a valveless reciprocating micropump in the range of low working frequencies is carried out. Reciprocating movement of flow actuator provides the actuation and pumping of the working fluid. Ferrofluidic valveless micropump is one practical sample of this kind of micropumps that operate in the range of low working frequencies. To model the reciprocating movement of flow actuator, two time varying functions that includes sinusoidal and step excitation are employed. Also, the performance of... 

In nanometer-scale process technologies, the effects of process variations are observed in Multiprocessor System-on-Chips (MPSoC) in terms of variations in frequencies and leakage powers among the processors on the same chip as well as across different chips of the same design. Traditionally, worst-case values are assumed for these parameters and then a deterministic optimization technique is applied to the MPSoC application under design. We show that such worst-case-based approaches are not optimal with the increasing variation observed at system-level, and instead, statistical approaches should be employed. We consider the problem of simultaneously choosing MPSoC architecture and task...