The problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically-actuated microcantilever beam as a typical configuration utilized in microcantilever-based sensing is being investigated. The actuation and sensing are both facilitated through bonding a piezoelectric layer (here, ZnO) on the microcantilever surface. Considering different geometrical configurations for the beam, it is demonstrated that how beam geometry or piezoelectric properties can bring different nonlinear coupling terms into the equations. An experimental setup consisting of a commercial piezoelectric microcantilever installed on the stand of an ultramodern laser-based microsystem analyzer is designed and utilized to verify the theoretical developments. First and second flexural natural frequencies are experimentally obtained, which are shown to be in good agreement with their theoretical values. Both linear and nonlinear simulation results are compared with experimental results and it is observed that nonlinear modeling response matches the experimental findings very closely. More importantly, it is disclosed that the initial twisting in the microcantilever can influence the value of the flexural vibration resonance. Such unique and unexplored coupling effect may lead to the possibility of indirectly measuring small torsional vibration without the need for any angular displacement sensor. This observation could significantly extend the application of friction force microscopy to measure the friction of a surface indirectly.

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A general nonlinear-comprehensive modeling framework for piezoelectrically-actuated microcantilevers is developed and validated both analytically and experimentally. The proposed model considers both longitudinal and flexural vibrations of the microcantilever sensor and their coupling in addition to the ever-present nonlinearities due to geometry of the microcantilever. More specifically, it is demonstrated that the electromechanical coupling in these sensors is also nonlinear which appears in quadratic form. Through extensive experimental measurements, the coefficient of such quadratic nonlinear term is determined which compares well with both analytical and numerical results. Taking into account the inextensibility feature of such sensors, the coupled longitudinal and flexural equations of motion are reduced to one nonlinear flexural equation. The resultant nonlinear equation of motion is then solved using the method of Multiple Scales to arrive at the frequency response of the system, analytically. Consequently, the system response to a number of periodic excitations with different amplitudes is experimentally and analytically investigated. Using the experimental values of the linear damping and material nonlinearity coefficient, the frequency-response curves are generated via analytical equation. These curves are compared to the experimental data, demonstrating excellent agreement everywhere in the frequency range and not only at the peak frequencies. Finally, the frequency response results clearly demonstrate the presence of nonlinear quadratic term in electromechanical coupling in these sensors. This is a critical observation when designing and employing such sensors for practical applications.

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We are developing closed-form distributed-parameters based modeling framework for a self-sensing piezoresistive microcantilever sensor. Such microcantilevers have recently received widespread attention due to their extreme sensitivity and simplicity in a variety of sensing applications. Current modeling practices call for a simple lumped-parameters framework rather than modeling of the piezoresistive microcantilever itself. Due to the applications of the piezoresistive microcantilevers in nanoscale force sensing or non-contact atomic force microscopy with nano-Newton to pico-Newton force measurement requirements, precise modeling of the piezoresistive microcantilevers was essential. Instead of the previously used lumped-parameters modeling, a distributed-parameters modeling framework is proposed and developed here to arrive at the most complete model of the piezoresistive microcantilever with tip-mass, tip-force and base movement considerations. In order to have online control and real-time sensor feedback, a closed-form model of the piezoresistive microcantilever which expresses the microcantilever's piezoresistive output voltage as a function of tip force and the base motion is highly desirable. Along this line of reasoning and utilizing a novel approach, a closed-form model for the piezoresistive microcantilever is presented. Following mathematical modeling, both numerical simulations and experimental results are presented to demonstrate the accuracy of the proposed distributed-parameters model when compared with the previously reported lumped-parameters modeling approach. It is shown that by utilizing the distributed-parameters model rather than lumped-parameters approach and by predicting the exact motion of each point on the microcantilever, the precision of the piezoresistive microcantilever's model is significantly enhanced.

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We are developing new modeling frameworks for microcantilever biosensors utilized in surface stress measurements. It is more common to measure the static deflection of the microcantilever for the surface stress measurements. We noticed that this method is applicable only if one side of the microcantilever is bio-functionalized. Moreover, there were some other shortcomings related to the static deflection detection mode. Therefore, we have come up with the idea of utilizing dynamic detection mode for the surface stress measurements. As the frequency response of the system may be best related to the equation of motion of the vibrating microcantilever beam, we have generated nonlinear equation of motion of the microcantilever with a piezoelectric (here, ZnO) layer of actuation and adsorbed biological layer on its surface. A modeling for the arrangement of the adsorbed biological species was needed in order to formulate the potential energy of their molecular interactions and resultant surface stress. In our work, we have focused on the attraction/repulsion forces and have tried to model these interactions using the Lennard-Jones potential equation. Based on the Lennard-Jones relation and considering a monolayer of the adsorbed biological species, we have been able to formulate the general nonlinear equation of motion of the microcantilever biosensors with the adsorbed biological species and the PZT layer.
A new approach was introduced for the solution of nonlinear equation of motion of the microcantilever beam. In this method, nonlinear vibration of the microcantilever biosensor is modeled as the linear vibration around its static deflection. This way, a new method of formulating the adsorption induced surface stress as a function of the static deflection of the microcantilever has been introduced. This method of formulating the static deflection is a powerful method as it formulates all the intermolecular forces causing the surface stress into the general equation of motion of the microcantilever. It is easy and straight forward to bring the forces into the equation of motion of the microcantilever by just knowing its potential. The sensitivity of the static detection mode (based on the abovementioned method) has been compared to that of the dynamic mode and it has been shown that the dynamic mode of biosensing is much more sensitive, compared to static mode, to change in properties of the adsorbed biological species.

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The piezoelectrically driven microcantilevers have recently attracted much attention for sensing of verity of physical parameters such as force, mass, temperature, and various chemical and biological agents. It is shown that in such applications, a part of cantilever is covered by the piezoelectric layer which creates jumped non-uniformity in the beam cross section. Moreover, in order to enhance the sensitivity of measurement, the tip section was fabricated with smaller width compared to the rest of beam. We noticed that these abrupt changes in the cross section may significantly alter the configuration of beam mode shapes. For this purpose, using a state of the art Micro System Analyzer, the MSA-400 manufactured by Polytec Inc., the natural frequencies and mode shapes of the beam were obtained. These results were compared with the commonly used theory of forced vibration of beam with uniform cross section. It was demonstrated that the modal response of the beam obtained by theory cannot predicate the actual microcantilever mode shapes. Along this line of reasoning, we intend to acquire a comprehensive and straightforward method to predict the response of piezoelectrically-driven microcantilevers with multiple jump discontinuities in cross section.

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A three degree of freedom (3 DOF) nanomanipulator with revolute revolute prismatic (RRP) actuator structure, named here MM3A, can be utilized for a variety of nanomanipulation tasks. We are working on developing mathematical modeling and a memory-based robust adaptive controller for the nanomanipulator driving principle. Unlike widely used Cartesian-structure nanomanipulators, the MM3A is equipped with revolute-piezoelectric actuators which result in outstanding performance in controlling the nanomanipulator's tip alignment during the nanomanipulation. However, the RRP structure of the nanomanipulator introduces complicity in kinematic and dynamic equations of the system which needs to be addressed in order to control the nanomanipulation process. Dissimilar to the ordinary piezoelectric actuators which provide only a couple of micrometers working range, the piezoelectric actuators utilized in MM3A, namely Nanomotors, provide wide range of action (120 degrees in revolute actuators and 12mm in prismatic actuator) with sub-nanoscale precision (0.1 mu rad in revolute actuators and 0.25 nm in prismatic actuator). This wide range of action combined with sub-nanoscale precision is achieved using a special stick/slip moving principle of the Nanomotors. However, such stick/slip motion results in stepping movement of the MM3A. Hence, due to the RRP structure and stepping movement principle of the MM3A nanomanipulator, development and implementation of an appropriate controller for such nanomanipulation process is not a trivial task. In this research, a novel memory-based robust adaptive controller is proposed to overcome such shortfalls. Following the development the controller, numerical simulations are preformed to demonstrate the positioning performance capability of the controller in a variety of nanomanipulation tasks.

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Funded by the Department of Commerce through National Textile Center, we are currently investigating polymeric fibrous materials with sensing and actuation capabilities. The ability to manipulate (thru a robot with proper grippers) and characterize these fibrous materials can result in different functions, and henceforth, lay the foundation for new structure design and manufacturing. Along this line, we are extending our currently funded project to explore and exploit the properties of active polymeric fibrous materials through an automated manipulation. Our currently funded project has yielded functional fabrics using a novel automated electrospinning method. The automated manipulation proposed in his work will utilize multiple active probe-based manipulators (as grippers attached to the end of robot arms) in combination with the 3D visual feedback from a stroboscopic video microscopy (SVM). As a demonstrable device fabrication, we aim to create complex 2D and 3D twisted fiber structures for different textile related applications.

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We are working on developing a linearized micro/nano-scale positioning through inverse model-based feedforward tracking control of piezoelectrically-driven nanostages with application to tracking of surface topographies similar to those scanned through Scanning Probe Microscopy (SPM). More specifically, utilizing a modified version of the Prandtl-Ishlinskii hysteresis operator, an inverse model-based feedforward controller is designed and integrated in series with piezoelectric actuator to cancel out the effect of hysteresis nonlinearity and achieve a linear input/output response. This controller was implemented on a 3D XYZ PZT-driven nanostage and the trajectory tracking results for Y- and Z-axes were attained with 1.3 % and 4.1% tracking errors, respectively.

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We have investigated the implementation of a robust Sliding Mode Control with Perturbation Estimation (SMCPE) strategy to achieve a precise positioning and tracking control of piezoelectrically-driven nanostagers against parameter uncertainties and ever-present unmodeled dynamics. The stability of the closed-loop system has been guaranteed in the Lyapunov sense, and the controller has been implemented on a single axis PZT-driven nanostager with high resolution capacitive position feedback for different low- and high-, and multiple-frequency desired trajectories. The tracking results indicate that controller is able to accurately track the desired trajectories in lower frequencies. However, achieving high speed multiple-frequency trajectory control with small tracking error enables fast and accurate positioning, scanning, and manipulating objects through SPM, using the proposed controller.

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With a surge in technological advancements and the needs of diverse communities such as consumers, military and navy communities, the textile industry is shifting its focus to fabrication of next-generation textiles that not only meet the basic conventional requirements, but also serve a host of other functions. Along this line, this project proposes the development of functional fabrics (named here electronic textile or e-textile) utilizing carbon nanotube (CNT) composites. The proposed area of research in e-textile is primarily motivated by the discovery of bond extension in charged nanotubes (i.e., piezoelectric effect in nanotubes). On the other hand, the textile industry has already demonstrated a remarkable capability to incorporate both natural and manmade filaments into yarns and fabrics to satisfy a wide range of physical parameters that survive the manufacturing processes and are tailored to specific application environments. Hence, our proposed nanotube-based fabrics could become an enabling technology for a variety of macroscopic textile related applications such as distributed sensing and actuation, rechargeable battery and flexible storage devices using e-textile, energy harvesting, vibration dampening, pressure sensors and shape modification of membrane structures.

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The major findings in this section are related to our continuum and molecular level modeling of CVD-based carbon nantube (CNT) fabrication process and can be divided into the following subsections.

Continuum Level Modeling: Based on our CVD system modeling, which contains fully coupled gas phase and surface chemical reaction modeling along with heat transfer and nonisothermal fluid dynamics, the highest concentration of surface chemical components during CNT synthesis occurs near the tip edge (the silicon edge which is closer to CVD inlet) of silicon substrate and the minimum amount of concentration is observed at the tail edge of the substrate. Therefore, it can be expected that the growth rate of the CNTs at the tip edge posses a higher value compared to fabricated CNTs at the tail edge.Molecular Level Modeling: Molecular Dynamics (MD) technique was utilized to investigate carbon diffusivity into FeO and Fe2O3 nanoparticles that can be used during CNT fabrication process for the temperature range where single-walled CNT (SWCNT) or multi-walled CNT (MWCNT) can be produced. Three distinctive regions were observed in diffusivity diagrams as follow:

 MWCNT synthesis region: After initial increase, a reduction in diffusivity rate was observed. This region is located in the temperature limits required for MWCNT synthesis.

Also, silicon molecular structure was added to the simulated nanoparticles. The comparison results show a decrease in carbon diffusivity from the simulation case without silicon substrate. This decrease is more distinctive in higher temperatures. Also, it was observed that the effect of silicon on FeO is less than Fe2O3 nanoparticle.

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A novel configuration for microcantilever beam actuation using nanotube-based piezoelectric actuators has been introduced here. The study demonstrated that BNNTs with (9,0) chirality are one of the best candidates as nanotube actuators. The model was used to study the tip mass and tip heat source effects on microcantilver vibration made of aluminum or titanium.

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In this research work, we proposed a semi-active control approach in which applied electrical loading to piezoelectric polymeric matrix such as Polyvinylidene Fluoride (PVDF) and reinforced with nanomaterials results in radial displacement of piezoelectric polymer corresponding to the direction and magnitude of electrical load. This leads to control of restriction effect of nanotube on the polymer segments, and consequently results in tunable interfacial adhesion between piezoelectric polymer and nanomaterials with faster response time. For this purpose, a shear lag model was obtained for a nanotube reinforced piezoelectric polymer under electro-thermo-mechanical loadings. Results indicate that as the electrical load increases, the relative displacement between nanotube and polymer increases which mean the possibility for slippage increases. Furthermore, results indicate that stiffer structures have potential to show more switched stiffness capability for future semi-active vibration control implementation.

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In this work, the buckling behavior of boron nitride nanotube (BNNT)-reinforced piezoelectric polymeric composites was investigated when subjected to combined electro-thermo-mechanical loadings. For this, the multi-walled structure of BNNT was considered as elastic media and a set of concentric cylindrical shell with van der Waals interaction between them. Using three-dimensional equilibrium equations, Donnell shell theory was utilized to show that the axially compressive resistance of BNNT varies with applying thermal and electrical loads. Also, a new equivalent spring constant model of piezoelectric matrix under electro-thermo-mechanical loadings was developed according to the concept of Whitney-Riley model. Results indicate that the support of piezoelectric matrix significantly enhances the buckling resistance of BNNT. Alternatively, the effect of BNNT piezoelectric property on the buckling behavior of the composites was demonstrated. Furthermore, it was demonstrated that the supporting effect of elastic medium depends on the direction of applied voltage and thermal flow. More specifically, it was shown that applying direct and reverse voltages to BNNT changes the buckling loads for any axial and circumferential wavenumbers. Such capability could be uniquely utilized when designing BNNT-reinforced composites

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