IMECE2011-63108 ANALYTICAL SOLUTIONS FOR THE STATIC INSTABILITY OF MICRO/NANO MIRRORS UNDER THE COMBINED EFFECT OF CAPILLARY FORCE AND CASIMIR FORCE

ABSTRACT This paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and Casimir force. At the First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained. The dependency of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of casimir force can considerably reduce the stability limits of nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the casimir force applied to the mirror. Finally analytical tool Homotopy Perturbation Method (HPM) is utilized for prediction of the mirror's behaviour under combined capillary and casimir forces. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this paper can be used for successful fabrication of nano/micromirrors using wet etching process where capillary force plays a major role in the system.

IMECE2011-63112 CLOSED FORM SOLUTIONS FOR THE PROBLEM OF STATICAL BEHAVIOR OF NANO/MICROMIRRORS UNDER THE EFFECT OF CAPILLARY FORCE AND VAN DER WAALS FORCE

ABSTRACT The current paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and van der Waals force. First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained using the newtons first law of motion. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of vdW torque can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW toque applied to the mirror. Finally analytical tool Homotopy Perturbation Mehtod (HPM) is utilized for prediction of the nano/micromirror behaviour under combined capillary and vdW force. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this paper can be used for successful fabrication of nano/micromirrors using wet etching process where capillary force plays a major role in the system

Optimization of acoustic performance of EPDM-based foams using Taguchi design of experiments: Appropriate content of additives

Novel EPDM-based polymer foams were prepared using a combination of nanomaterials, namely nano silica, nano clay, and graphene nanoplatelets. In order to achieve optimal acoustic performance, the Taguchi design (TD) technique was applied to reduce the number of experiments and optimize the formulation. By employing an orthogonal array of L9(34), four controlled factors, including content of the three nanomaterials and the blowing agent (Unicell D200A), were chosen. In practice, the acoustic properties of the nine suggested experiments with TD were examined with an impedance tube, and the signal-to-noise ratio analysis revealed two more optimal formulations for foam composites. Further experiments for the last two formulations compared to the nine Taguchi tests, showed an improvement of 13.04 and 19.68%, respectively, for noise reduction coefficient (NRC) and average transmission loss (ATL). It seemed that the idea of using multiple nanomaterials simultaneously is to be an effective way. Besides, the SEM images of nine samples proved that the smaller cell size of the foam were achieved using the higher concentration of nanoparticles. These findings are in accordance with the acoustic results, as the sample with larger cell size and more open cells (C3) showed higher NRC and the sample with larger cell size and closed cells (B2) showed higher ATL values. To complete the study, some blank samples with zero level or only one type of the nanomaterial were also investigated. Interestingly, the obtained results indicated that the formula should contain more than one type of nanoparticle to achieve a better acoustic performance. Comparing the result obtained in this study for EPDM foam with the same EVA foam in our previous work, it can be seen that EPDM showed an increase of 15.56% in NRC and a slight decrease of 2.5% in ATL. This behavior could be due to the difference in their morphology, in which the EPDM has probably more open cells and thinner cell walls

IMECE2009-12186 APPLICATION OF THE EXTENDED KANTOROVICH METHOD TO THE VIBRATIONAL ANALYSIS OF ELECTRICALLY ACTUATED MICROPLATES

ABSTRACT This paper presents an extended Kantorovich approach to investigate the vibrational behavior of electrically actuated rectangular microplates. The model accounts for the electric force of the excitation and for the applied in plane loads. Starting from a one term Galerkin approximation and following the extended Kantorovich procedure, the partial differential equation governing the microplate vibration, is discretized to two ordinary differential equation with constant coefficients. These equations are then solved analytically and iteratively with a rapid convergence procedure for finding microplate natural frequencies and modeshapes. Results in some specific cases are validated against other theoretical results reported in the literature. It is shown that rapid convergence, high precision and independency of initial guess function make the EKM an effective and accurate design tool for design optimization

Vibration Suppression of MR Sandwich Beams Based on Fuzzy Logic

In this paper, the vibration suppression capabilities of magnetorheological (MR) layer in smart beams is investigated. A three-layered beam including MR elastomer layer sandwiched between two elastic layers is considered. By assuming the properties of MR layer in the pre-yield region as viscoelastic materials behavior, the governing equations of motion as well as the corresponding boundary conditions are derived using Hamilton’s principle. Due to field-dependent shear modulus of MR layer, the stiffness and damping properties of the smart beam can be changed by the application of magnetic field. This feature is utilized to suppress the unwanted vibration of the system. The appropriate magnetic field applied over the beam is chosen through a fuzzy controller for improving the transient response. The designed fuzzy controller uses the modal displacement and modal velocity of the beam as its inputs. Free and forced vibration of smart sandwich beam is investigated using numerical simulations. The results show that the magnetorheological layer along with the designed fuzzy controller can be effectively used to suppress the unwanted vibration of the system. The qualitative and quantitative knowledge resulting from this research is expected to enable the analysis, design and synthesis of smart beams for improving the dynamic performance of smart engineering structures

CHARACTERIZATIO OF STATIC BEHAVIOR OF ELECTROSTATICALLY ACTUATED MICRO TWEEZERS USI G MODIFIED COUPLE STRESS THEORY

Abstract In this paper, static behavior and pull-in of micro tweezers is studied. The micro tweezer is modelled as two cantilever beams. Static behavior of the micro tweezer under the effect of electrostatic actuation is modelled using the Euler-Bernoulli beam theory. In order to capture size effects on the behavior of micro tweezers, modified couple stress theory is utilized. It is shown when the voltage between two electrodes increased from some specific value, micro beams adhere to each other and it is observed that the pull-in voltage predicted by the modified couple stress theory considerably differs with that of the classical theory of elasticity. Results of this paper can be used for accurate design, synthesis and optimization of micro tweezers

Photogrammetry and Optical Methods in Structural Dynamics - A Review

Many of energy harvesting devices use piezoelectric elements to convert mechanical vibrations into usable electrical energy. The input excitation is usually assumed to be a deterministic harmonic wave, while in practical situations; the mechanical excitation of the media is a random signal. The objective of this research is to study the energy harvesting in piezoelectric devices using the random vibration theory. At the first step a lumped parameter physical model of the device is presented. A mathematical model is then developed by obtaining the normalized differential equations governing the voltage induced in the energy harvesting circuit as well as the length of the piezoelectric material. The random vibration theory is then utilized to derive analytical expressions for the statistical properties of the voltage, power and the length of the piezoelectric material in terms of the statistical properties of the excitation which is assumed to be a band limited white noise. It is shown that with proper selection of the system parameters, the expected value of the harvested power can be effectively maximized. The qualitative and quantitative knowledge resulting from this effort is expected to enable the analysis, optimization, and synthesis of piezoelectric energy harvesting devices

On the Effects of Structural Coupling on Piezoelectric Energy Harvesting Systems Subject to Random Base Excitation

The current research investigates the novel approach of coupling separate energy harvesters in order to scavenge more power from a stochastic point of view. To this end, a multi-body system composed of two cantilever harvesters with two identical piezoelectric patches is considered. The beams are interconnected through a linear spring. Assuming a stochastic band limited white noise excitation of the base, the statistical properties of the mechanical response and those of the generated voltages are derived in closed form. Moreover, analytical models are derived for the expected value of the total harvested energy. In order to maximize the expected generated power, an optimization is performed to determine the optimum physical and geometrical characteristics of the system. It is observed that by properly tuning the harvester parameters, the energy harvesting performance of the structure is remarkably improved. Furthermore, using an optimized energy harvester model, this study shows that the coupling of the beams negatively affects the scavenged power, contrary to the effect previously demonstrated for harvesters under harmonic excitation. The qualitative and quantitative knowledge resulting from this analysis can be effectively employed for the realistic design and modelling of coupled multi-body structures under stochastic excitations