We present analytical formulations to calculate the induced resonance frequency shifts of electrically actuated clamped-clamped microbeams due to an added mass. Based on the Euler-Bernoulli beam theory, we investigate the linear dynamic responses of the beams added masses, which are modeled as discrete point masses. Analytical expressions based on perturbation techniques and a one-mode Galerkin approximation are developed to calculate accurately the frequency shifts under a DC voltage as a function of the added mass and position. The analytical results are compared to numerical solution of the eigenvalue problem. Results are shown for the fundamental as well as the higher-order modes of the beams. The results indicate a significant increase in the frequency shift, and hence the sensitivity of detection, when scaling down to nano scale and using higher-order modes.

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of an in-plane clamped-clamped microbeam, bridge, and resonator compressed by a force due to electrothermal actuation. We demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally, by passing a DC current through it. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and to simulation results of a multi-physics finite-element model. A good agreement is found among all the results.

We demonstrate experimentally internal resonances in MEMS resonators. The investigation is conducted on in-plane MEMS arch resonators fabricated with a highly doped silicon. The resonators are actuated electrostatically and their stiffness are tuned by electrothermal loading by passing an electrical current though the microstructures. We show that through this tuning, the ratio of the various resonance frequencies can be varied and set at certain ratios. Particularly, we adjust the resonance frequencies of two different vibrational modes to 2:1 and 3:1. Finally, we validate the internal resonances at these ratios through frequency-response curves and FFTs.

This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity profiles and integrity charts are drawn. The curves of constant percentage of integrity measure are detected, highlighting that they provide valuable quantitative information about the changes in the structural safety. Robustness as well as vulnerability to disturbances is examined. The practical range of existence of each branch is observed to be smaller, and sometimes remarkably smaller than the theoretical one. The issue of the dynamical integrity analysis in the AFM design is addressed, showing that these curves may be used to establish safety factors in order to operate the AFM according to the desired outcome, depending on the expected disturbances. Physical meaning and practical relevance of the nonlinear phenomena in the AFM engineering design are discussed.

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated MEMS arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and results of a multi-physics finite-element model. A good agreement is found among all the results. The electrothermal voltage is applied between the anchors of the clamped-clamped MEMS arch beam, generating a current that passes through the MEMS arch beam and controls its axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to increase in its curvature, thereby increases the resonance frequencies of the structure. We show here that the first resonance frequency can increase up to twice its initial value. We show also that after some electro-thermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators.

We present a method to determine accurately the position and mass of an entity attached to the surface of an electrostatically actuated clamped-clamped microbeam implemented as a mass sensor. In the theoretical investigation, the microbeam is modeled as a nonlinear Euler-Bernoulli beam and a perturbation technique is used to develop a closed-form expression for the frequency shift due to an added mass at a specific location on the microbeam surface. The experimental investigation was conducted on a microbeam made of Polyimide with a special lower electrode to excite both of the first and second modes of vibration. Using an ink-jet printer, we deposited droplets of polymers with a defined mass and position on the surface of the microbeam and we measured the shifts in its resonance frequencies. The theoretical predictions of the mass and position of the deposited droplets match well with the experimental measurements.

Microplates are building blocks of many Micro-Electro-Mechanical Systems (MEMS). It is common for them to undergo imperfections due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat plates and cannot be modeled using the governing equations of flat plates. In this article, we adopt the governing equations of imperfect plates employing the modified von-Karman strains. These equations then are used to develop a Reduced Order Model based on the Galerkin procedure to simulate the static and dynamic behavior of an electrostatically actuated microplate. Also, microplates made of silicon nitride are fabricated and tested. First, the static behaviour of the microplate is investigated when applying a static voltage Vdc. To study the dynamic behaviour we apply a harmonic voltage, Vac, superimposed to Vdc. Simulation results show good agreement with the experimentally measured responses.

Soot formation process was investigated for biomass-based renewable diesel fuel, such as biomass to liquid (BTL), and conventional diesel combustion under varied fuel quantities injected into a constant volume combustion chamber. Soot measurement was implemented by two-color pyrometry under quiescent type diesel engine conditions (1000 K and 21% O2 concentration). Different fuel quantities, which correspond to different injection widths from 0.5 ms to 2 ms under constant injection pressure (1000 bar), were used to simulate different loads in engines. For a given fuel, soot temperature and KL factor show a different trend at initial stage for different fuel quantities, where a higher soot temperature can be found in a small fuel quantity case but a higher KL factor is observed in a large fuel quantity case generally. Another difference occurs at the end of combustion due to the termination of fuel injection. Additionally, BTL flame has a lower soot temperature, especially under a larger fuel quantity (2 ms injection width). Meanwhile, average soot level is lower for BTL flame, especially under a lower fuel quantity (0.5 ms injection width). BTL shows an overall low sooting behavior with low soot temperature compared to diesel, however, trade-off between soot level and soot temperature needs to be carefully selected when different loads are used.

Direct use of naphtha in compression ignition (CI) engines is not advisable because its lower cetane number negatively impacts the auto ignition process. However, engine or fuel modifications can be made to operate naphtha in CI engines. Enhancing a fuel’s auto ignition characteristics presents an opportunity to use low cetane fuel, naphtha, in CI engines. In this research, Di-ethyl ether (DEE) derived from ethanol is used as an ignition enhancer for light naphtha. With this fuel modification, a “drop-in” fuel that is interchangeable with existing diesel fuel has been created. The ignition characteristics of DEE blended naphtha were studied in an ignition quality tester (IQT); the measured ignition delay time (IDT) for pure naphtha was 6.9 ms. When DEE was added to naphtha, IDT decreased and D30 (30% DEE + 70% naphtha) showed comparable IDT with US NO.2 diesel. The derived cetane number (DCN) of naphtha, D10 (10% DEE + 90% naphtha), D20% DEE + 80% naphtha) and D30 were measured to be 31, 37, 40 and 49, respectively. The addition of 30% DEE in naphtha achieved a DCN equivalent to US NO.2 diesel. Subsequent experiments in a CI engine exhibited longer ignition delay for naphtha compared to diesel. The peak in-cylinder pressure is higher for naphtha than diesel and other tested fuels. When DEE was added to naphtha, the ignition delay shortened and peak in-cylinder pressure is reduced. A 3.7% increase in peak in-cylinder pressure was observed for naphtha compared to US NO.2 diesel, while D30 showed comparable results with diesel. The pressure rise rate dropped with the addition of DEE to naphtha, thereby reducing the ringing intensity. Naphtha exhibited a peak heat release rate of 280 kJ/m3deg, while D30 showed a comparable peak heat release rate to US NO.2 diesel. The amount of energy released during the premixed combustion phase decreased with the increase of DEE in naphtha. Thus, this study demonstrates the suitability of DEE blended naphtha mixtures as a “drop-in” replacement fuel for diesel.

In this research, the flow and ignition properties of vegetable oil (VO) are improved by blending it with diethyl ether (DEE). DEE, synthesized from ethanol, has lower viscosity than diesel and VO. When DEE is blended with VO, the resultant DEEVO mixtures have favorable properties for compression ignition (CI) engine operation. As such, DEEVO20 (20% DEE + 80% VO) and DEEVO40 (40% DEE + 60% VO) were initially considered in the current study. The viscosity of VO is 32.4*10−6 m2/s; the viscosity is reduced with the increase of DEE in VO. In this study, our blends were limited to a maximum of 40% DEE in VO. The viscosity of DEEVO40 is 2.1*10−6 m2/s, which is comparable to that of diesel (2.3*10−6 m2/s). The lower boiling point and flash point of DEE improves the fuel spray and evaporation for DEEVO mixtures. In addition to the improvement in physical properties, the ignition quality of DEEVO mixtures is also improved, as DEE is a high cetane fuel (DCN = 139). The ignition characteristics of DEEVO mixtures were studied in an ignition quality tester (IQT). There is an evident reduction in ignition delay time (IDT) for DEEVO mixtures compared to VO. The IDT of VO (4.5 ms), DEEVO20 (3.2 ms) and DEEVO40 (2.7 ms) was measured in IQT. Accordingly, the derived cetane number (DCN) of DEEVO mixtures increased with the increase in proportion of DEE. The reported mixtures were also tested in a single cylinder CI engine. The start of combustion (SOC) was advanced for DEEVO20 and DEEVO40 compared to diesel, which is attributed to the high DCN of DEEVO mixtures. On the other hand, the peak heat release rate decreased for DEEVO mixtures compared to diesel. Gaseous emissions such as nitrogen oxide (NOX), total hydrocarbon (THC) and smoke were reduced for DEEVO mixtures compared to diesel. The physical and ignition properties of VO are improved by the addition of DEE, and thus, the need for the trans-esterification process is averted. Furthermore, this blending strategy is simpler and enables operation of straight run oils and fats in CI engine, replacing diesel completely.