Parametric Excitation of Coupled Nonlinear Microelectromechanical Systems

The commencement of the semi-conductor industry in the second half of the last century gave a surprising new outlook for engineered dynamical mechanical systems. It enabled, thanks to the continuously evolving microfabrication methods, the implementation of Micro Electromechanical systems (MEMS) followed by their nano-counterpart or NEMS. Nowadays M/NEMS constitute a massive portion of the small-scaled sensors industry, in addition to electrical, optical and telecommunication components. Since these tiny dynamical electromechanical systems involve sometimes couplings between degrees of freedom as well as nonlinearities, the theory of stability in dynamical systems plays a significant role in their design and implementation. From a practical point of view, the approach to stability problems often takes two different perspectives. The first one, most commonly in linear systems, aims to avoid any instability which could cause destructive consequences for mechanical structures or for electrical and electronic components. On the contrary in nonlinear systems, the second perspective aims to drive the system into regions of instability for the trivial solution, while searching for stable nontrivial steady-state solutions of the underlying differential equations. With the advent of micro and nanosystems, the second perspective could acquire increased importance. This is attributed to their capability to exhibit typical nonlinear behavior and higher amplitudes at normal operation conditions, when compared to macroscale systems. Higher amplitudes, in this sense, allows for a better amplification of an input excitation, and thereby higher sensitivity for miniature sensors and measurement devices. In addition, if the system parameters were time-periodic, the trivial solution could turn to be unstable at the so called parametric resonances. Known as parametric pumping in micro and nanosystems, the system’s response is usually amplified at these resonance frequencies for higher sensitivity and accuracy. For these reasons, this work is mainly focused on parametrically excited nonlinear systems. Nevertheless, a systematic approach is followed in this thesis, where the origins of destabilization are surveyed in time-invariant systems before proceeding to carry out a theoretical study on time-periodic systems in general, and time-periodic nonlinear systems in particular. Through this theoretical study, a novel idea for the M/NEMS industry is presented, namely the broadband parametric amplification using a bimodal excitation method. This idea is then implemented in microsystems, by investigating a particular example, that is the microgyorscope. Given the low-cost of this device in comparison with other inertial sensors, it is being currently enhanced to reach a relatively higher sensitivity and accuracy. To this end, the theoretical findings, including the mentioned idea, are implemented in this device and prove to contribute effectively to its performance. Moreover, an experimental investigation is carried out on an analogous microsystem. Through the experimental study, an electronic system is introduced to apply the proposed bimodal parametric excitation method on the microsystem. By comparing the stability charts in theory and experiment, the theoretical model could be validated. In conclusion, a theoretical study is carried out through this work on parametrically excited nonlinear systems, then implemented on microgyroscopes, and finally experimentally validated. Thereby, this work puts a first milestone for the utilization of the proposed excitation method in the M/NEMS industry

Modeling and experimental characterization of belt drive systems in micro-hybrid vehicles

Belt Drive Systems (BDS) constitute the traditional automotive mechanism used to power the main internal accessories (such as the alternator, water pump and air conditioning pump) taking power from the engine's crankshaft rotational motion. BDS usually work in the severe ambient conditions of the engine compartment and are subject to highly dynamic excitations coming from the crankshaft harmonics. The substitution of the traditional alternator with an electric machine, namely Belt Starter Generator (BSG), is the most promising micro-hybrid technology towards a quick and effective satisfaction of the current regulations of fuel consumption and pollutant emissions reduction. The use of a BSG leads to increased stresses in the already complex front end accessory drive. As a matter of fact, a BSG is an electrical machine able to work both as motor and as generator and defines two distinct functioning modes of the drive, namely motor and alternator modes. The relative alternation of tight and slack spans profoundly changes the functionality of the overall drive and affects its transmissions capability and efficiency, furthermore resulting in NVH (noise vibration harshness) effects that need to be carefully addressed. Traditional automatic tensioners acting on the slack span of the alternator mode application are not capable of facing the irregular stresses of a BSG-based BDS which requires the use of a tensioning device capable of keeping the belt tension inside a safe range and of preventing slippage during all the operating conditions of the drive. With this goal many solutions are currently being investigated, such as the cooperation of two tensioners one for each span, active tensioners, double arm tensioners or hydraulic tensioners. The critical issues due to the involvement of BSG in BDS require a deep study focused on the tension conditions of the belt and its influence on the overall efficiency of the system. The aim of the research described in this thesis is to obtain a defined modelling approach of belt drive systems for micro-hybrid vehicles and to validate it through extensive experimental analysis. To obtain a reliable testing environment, a dedicated full-electric test rig was designed and realized. The test rig presented in this work is capable of assuring the repeatability and accuracy of the measurements leaving aside the uncertainties deriving from the irregularities of the ICE behaviour that usually affect the experimental activities conducted on front engine accessory drives. After providing both the modelling and testing environment as assets for the analysis, several experimental activities are carried out with the goal of assessing the dynamic behaviour of belt drive systems and their efficiency, comparing the performances of different tensioning solutions, understanding the behaviour in static and dynamic conditions of a traditional automatic tensioner and one example of an omega twin arm tensioner, which is the tensioning solution most explored by the manufacturers at present. The ultimate goal of gaining a complete understanding of belt drive systems in the special case of micro-hybrid vehicles is eventually fulfilled by an experimental validation of the static and dynamic models proposed

Advances of Italian Machine Design

This 2028 Special Issue presents recent developments and achievements in the field of Mechanism and Machine Science coming from the Italian community with international collaborations and ranging from theoretical contributions to experimental and practical applications. It contains selected contributions that were accepted for presentation at the Second International Conference of IFToMM Italy, IFIT2018, that has been held in Cassino on 29 and 30 November 2018. This IFIT conference is the second event of a series that was established in 2016 by IFToMM Italy in Vicenza. IFIT was established to bring together researchers, industry professionals and students, from the Italian and the international community in an intimate, collegial and stimulating environment

Dynamic stability of thin-walled structures : a semi-analytical and experimental approach

Buckling refers to a sudden large increase in the deformation of a structure due to a small increase of some external load. If this external load has a dynamic nature, (e.g. a harmonic load, shock load, a step load and/or a random load), such a sudden increase in deformations is denoted as dynamic buckling. Thinwalled structures are often met in engineering practice due to their favourable mass-to-stiffness ratio. Such structures are very susceptible to buckling and are often subjected to dynamic loading. However, fast (pre-) design tools for obtaining detailed insight in the dynamic response and the stability of thinwalled structures subjected to dynamic loading are still lacking. One of the research objectives of this thesis is, therefore, to develop (fast) modelling and analysis tools which give insight in the behaviour of dynamically loaded thinwalled structures. To illustrate and to test the abilities of the developed tools, a number of case studies are examined. The tools are developed for structures with a relatively simple geometry. The geometric simplicity of the structures allows to derive models with a relative low number of degrees of freedom which are, therefore, very suitable for extensive parameter studies (as essential during the design process of thin-walled structures). These models are symbolically derived using a Ritz method in combination with assumptions regarding geometric nonlinear (strain-displacement) relations and the effects of (in-plane) inertia. The resulting models, obtained from energy expressions, are sets of coupled ordinary differential equations which include stiffness nonlinearities and (sometimes) inertia and damping nonlinearities. The modelling approach is implemented in a generic manner in a symbolic manipulation software package, so that model variations can be easily performed. Furthermore, a set of designated numerical tools is combined (e.g. continuation tools for equilibria, periodic solutions and bifurcations, and numerical integration routines) to solve the analytically derived models in a computationally efficient manner. Using this semi-analytical (i.e. analytical-numerical) approach four case studies are performed which include the dynamic buckling of an arch type of structure due to shock loading, snap-through behaviour of a transversally, harmonically excited pre-buckled beam, and the dynamic buckling of a beam and a cylindrical shell structure, both with top mass, which are harmonically loaded in axial direction at their base. For all cases, the effects of several parameter variations are illustrated, including the effect of small deviations from the nominal geometry (i.e. geometric imperfections). For validation, the semi-analytical results are compared with results obtained using the computationally much more demanding finite element modelling technique. However, more important, for two cases (i.e. the axially excited beam and cylindrical shell structures carrying a top mass), the semi-analytical results are also compared with experimentally obtained results. For this purpose, a dedicated experimental set-up has been realized. For the beam structure, the experimental results are in good agreement with the semianalytical results whereas for the cylindrical shell structure, a qualitative match is obtained. It has been illustrated that the differences between the experimental results and the semi-analytical results for the cylindrical shell may be due to the strong dependency of the results with respect to the geometrical imperfections present in the shell. Next to the specific new insights obtained for each case considered, the major result of the thesis is the illustrated power of the semi-analytical approach to obtain practical relevant insights in the phenomena of dynamic buckling of thin-walled structures. In conclusion it can be stated that the semi-analytical approach is a valuable tool in the (pre-) design process of thin-walled structures under dynamic loading

Experimental and Numerical Studies on the Structural Dynamics of Flapping Beams

The nonlinear structural dynamics of slender cantilever beams in flapping motion is studied through experiments, numerical simulations, and perturbation analyses. A flapping mechanism which imparts a periodic flapping motion of certain amplitude and frequency on the clamped boundary of the appended cantilever beam is constructed. Centimeter-size thin aluminum beams are tested at two amplitudes and frequencies up to, and slightly above, the first bending mode to collect beam tip displacement and surface bending strain data. Experimental data analyzed in time and frequency domains reveal a planar, single stable (for a given flapping amplitude-frequency combination) periodic beam response with superharmonic resonance peaks. Numerical simulations performed with a nonlinear beam finite element corroborate the experiments in general with the exception of the resonance regions where they overpredict the experiments. The discrepancy is mainly attributed to the use of a linear viscous damping model in the simulations. Nonlinear response dynamics predicted by the simulations include symmetric periodic, asymmetric periodic, quasi-periodic, and aperiodic motions. To investigate the above-mentioned discrepancy between experiment and simulation, linear and nonlinear damping force models of different functional forms are incorporated into a nonlinear inextensible beam theory. The mathematical model is solved for periodic response by using a combination of Galerkin and a time-spectral numerical scheme; two reduced order methods which, along with the choice of the inextensible beam model, facilitate parametric study and analytical analysis. Additional experiments are conducted in reduced air pressure to isolate the air damping from the material damping. The frequency response curves obtained with different damping models reveal that, when compared to the linear viscous damping, the nonlinear external damping models better represent the experimental damping forces in the regions of superharmonic and primary resonances. The effect of different damping models on the stability of the periodic solutions are investigated using the Floquet theory. The mathematical models with nonlinear damping yield stable periodic solutions which is in accord with the experimental observation. The effect of excitation and damping parameters on the steady-state superharmonic and primary resonance responses of the flapping beam is further investigated through perturbation analyses. The resonance solutions of the spatially-discretized equation of motion (via 1-mode Galerkin approximation of the inextensible beam model), which involves both quadratic and cubic nonlinear terms, are constructed as first-order uniform asymptotic expansions via the method of multiple time scales. The critical excitation amplitudes leading to bistable solutions are identified and are found to be consistent with the experimental and numerical results. The approximate analytical results indicate that a second harmonic is required in the boundary actuation spectra in order for a second order superharmonic response to exist. The perturbation solutions are compared with numerical time-spectral solutions for different flapping amplitudes. The first-order perturbation solution is determined to be in very good agreement with the numerical solution up to 5° while above this angle differences in the two solutions develop, which are attributed to phase estimation accuracy

Analysis of Propellantless Tethered System for the De-Orbiting of Satellites at End of Life

The increase of orbital debris and the consequent proliferation of smaller objects through fragmentation is driving the need for mitigation strategies that address this issue at its roots. The present guidelines for mitigation point out the need to deorbit new satellites injected into low Earth orbit (LEO) within a 25-year time. The issue is then how to deorbit the satellite with an efficient system that does not impair drastically the propellant budget of the satellite and, consequently, reduces its operating life. In this contest a passive system, which makes use of an electrodynamics tether to deorbit a satellite through Lorentz forces, has been investigated. The system collects electrons from the ionosphere at its anodic end (the conductive tether itself left bare) and emits electrons through a plasma contactor at the cathodic end. The current that circulates in the tether produces the Lorentz drag force through the interaction with the Earth’s magnetic field. Power can also be tapped from the tether for running the cathode and other ancillary on-board equipment. The deorbiting system will be carried by the satellite itself at launch and it will be deployed from the satellite at the end of its life. From that moment onward the system operates passively without requiring any intervention from the satellite itself. This thesis summarizes the results of the analysis carried out to show the deorbiting performance of the system starting from different orbital scenarios and for satellite configurations, and describing the tethered system by means of different mathematical models in order to include the lateral flexibility and increase the accuracy of the results, which can be easily scaled. Moreover high-fidelity and latest environmental routines has been used for magnetic field, ionospheric density, atmospheric density and a 4×4 gravity field model, since the environment is very important for describing appropriately each external interaction, in particular the electrodynamic one. The electric properties of the wire depends on its temperature, which is computed dynamically by a thermal model that considers all the major input fluxes and the heat emitted by the tether itself. At last the electric current along the rope is constantly evaluated during the reentry, since large variations happens passing from sunlight to shadow regions, and vice-versa. Without any control the system goes rapidly into instability, because the electrodynamic torque pumps continuously energy into the system enlarging the libration of the tether. So ad hoc strategies must be thought and included. In the past several techniques have been proposed, but with a lot of assumptions and limitations. In this work a new concept has been implemented, mounting in the satellite at the basis of the tether a damping mechanism for dissipating the energy associated with the lateral motion. At last the whole deployment of a tape tether has been analyzed. Several configurations have been studied, and the tradeoff analysis concluded that a non-motorized reeling deployer is well suited for a 1-3 cm wide tape like the tapes. Optimal reference profiles have been evaluated for two class of tether (3 and 5km), and are then used to regulate the brake mechanism mounted on the deployer itself to control the deployment. Different conditions have been analyzed to demonstrate the capabilities of the control law to provide a successful deployment in the presence of various error

NASA Tech Briefs, February 1994

Topics covered include: Test and Measurement; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences; Books and Report

Dynamical systems : mechatronics and life sciences

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science

Aeronautical Engineering: A continuing bibliography with indexes, supplement 174

This bibliography lists 466 reports, articles and other documents introduced into the NASA scientific and technical information system in April 1984

Exploration of torsional actuation and twist to writhe transition in nanostructured hydrogels

Torsional artificial muscles are a branch of actuators that react to a stimulus by rotating. This rotation is driven by a change in volume and mechanical properties such as modulus and was shown to be extremely large in the case of twisted fibers due to their helical geometry. The following thesis introduces a new method of fabrication of nanofiber yarns and nanocomposites with the aim of making hydrogel torsional catch actuators that combine responsiveness to pH changes and a high torsional output as well as a systematic approach to the modeling of their behavior using the single helix theory