Pratiher, Barun

The objectives of this present work is to study the stability and bifurcation control of an idealized electrostatically actuated microcantilever MEMS device that can widely observe in the field MEMS application. Here, the cantilever based device has been modelled as a spring-mass-damper system considering both the linear and nonlinear spring and damper. Simultaneously, the cantilever based device is excited harmonically by applied voltages. The method of multiple scales is employed to obtain the reduced order equations in terms of amplitude and phase those are directly used to determine the approximate the solutions for different resonance conditions. The catastrophic failure of the system may occur due to the presence of saddle-node and pitchfork bifurcation points as it leads the jump phenomenon. Basins of attractions are plotted in order to find the initial condition for a specific solution in a region having more than one solution. The obtained results can successfully be used in designing the microcantilever based devices that depict typical realistic nonlinear characteristics in the field of MEMS application. © 2012 The Authors. Published by Elsevier Ltd.

Nonlinear dynamic analysis of a Cartesian manipulator carrying an end effector which is placed at different intermediate positions on the span is theoretically investigated with a single mode approach. The governing equation of motion of this system is formulated by using the D'Alembert principle in addition to profuse application of Dirac delta function to indicate the location of the intermediate end effector. Then the governing equation is further reduced to a second-order temporal differential equation of motion by using Galerkin's method. The method of multiple scales as one of the perturbation techniques is being used to determine the approximate solutions and the stability and bifurcations of the obtained approximate solutions are studied. Numerical results are demonstrated to study the effect of intermediate positions of the end effector placed at various locations on the link with other relevant system parameters for both the primary and secondary resonance conditions. It is worthy of note that the catastrophic failure of the system may take place due to the presence of jump phenomenon. The results are found to be in good agreement with the results determined by the method of multiple scales after solving the temporal equation of motion numerically. In order to determine physically realized solution by the system, basins of attraction are also plotted. The obtained results are very useful in the application of robotic manipulators where the end effector is placed at any arbitrary position on the robot arm. © 2011 Springer Science+Business Media B.V.

Investigation of critical speeds and nonlinear free vibration analysis of a highly flexible rotor system have been studied. The rotary inertia and gyroscopic effect combined with inextensible geometric condition for pinned-guided shaft element have been taken into account to develop the governing equation of motion. The closed-form mathematical expressions have been derived for determining both linear and nonlinear natural frequencies and their behavioral patterns have been simultaneously demonstrated through time histories, FFTs and Poincare's maps upon changing the control parameters. The nonlinear natural frequencies have been found to be higher by about 4–6% as compared to the findings obtained via linear analysis. For lower spin speed of the shaft, both linear and nonlinear forward natural frequencies have been found to be dominant. The influence of rotary inertia on natural frequencies by considering Euler and Rayleigh beam elements, separately has been reported. The system response has been observed to be either periodic or quasi-periodic depending on the spin speed. Outcomes which were not explored earlier enable significant theoretical understanding of free vibration analysis and whirling speeds of rotating system which are of great practical importance for investigating further dynamic performance.

In the current study, CFD simulations and static structural analysis were carried out to estimate the wind loads for up and downstream wind directions on ground mounted arrayed solar panels. The goal of simulations is to estimate the loads (i.e. drag and lift forces and also moment coefficients) and wind pressure that act upon their surface. Static structural analysis coupled with CFD simulation is done to determine the total deformation due to wind loads on each panel. The motive of the study is to protect the integrity of the solar panels in a situation like cyclone and typhoon so that energy production is not hindered throughout their service life. Simulations were carried out on arrayed nine panels with changing various parameters (i.e. clearance height, inter row spacing between panels and panel inclination) that effect wind loading on the panels

The assessment of nonlinear phenomena with a focus on investigating the bifurcations and chaotic behaviour of an elastically induced flexible rotor-bearing system subjected to a harmonic ground motion has been studied. The higher-order Euler–Bernoulli deformation theorem has been adopted that governs the nonlinear dynamic characteristics of the rotating system. Nonlinear vibration analysis has been carried out to determine the critical speeds, i.e., Campbell diagram followed by demonstrating the inherent nonlinear signatures through the illustration of time history, Fourier spectrum and Poincare’s map upon varying the system design variables. The perturbation technique has been used to obtain the approximate nonlinear solutions from a set of polynomial algebraic equations under steady-state condition in various resonance cases. Further, stability analysis along with successive bifurcations of the solutions has been investigated. The present nonlinear model formulated based on Euler theory has been found to be capable enough to predict the correct value of critical speeds and dynamic responses in comparison with that of model developed based on Timoshenko theory. The present outcomes can offer immense practical importance for any application of the flexible rotor-bearing system when it performs high-speed operation.

The effect of all-inclusive generic offset payload characteristics on the modes of vibration and nonlinear characteristics of a rotating flexible manipulator with a revolute pair has been accomplished in the present article. A brief dynamic modelling and free vibration analysis to obtain the eigenspectrums of the system, whereafter nonlinear analysis of a manipulator with a general offset payload undergoing overall motion has been accomplished. Dynamic equation of motion and associated boundary conditions have been developed where the payload is considered as a mass whose center of gravity doesn’t coincide with the point of attachment with the manipulator. The effect of various system parameters such as offset mass, offset inertia, offset length, hub mass, actuated inertia and hub stiffness on eigenfrequency is well tabulated and the same effect on eigenspectrums is presented graphically. Further, MMS is employed to investigate the effect of parametric variation on the nonlinear behaviour and associated bifurcation of the rotating single-link flexible manipulator being harmonically driven at the joint under primary resonance considering the centrifugal forces acting on the link and payload as well. The present analysis indicated the pronounced effect of system mass, inertia, stiffness and rotating speed on the eigencharacteristics and bifurcations of a flexible manipulator with a rotating joint.

A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

A detailed numerical investigation on stability and bifurcation analysis of a highly nonlinear electrically driven MEMS resonator has been established. A nonlinear model has been developed by using Hamilton’s principle and Galerkin’s method considering both transverse and longitudinal displacement of the resonator. The special care has been paid by incorporating higher order correction of electrostatic pressure. The pull-in results and consequences of higher order correction on the pull-in stability have been investigated. Furthermore, investigation of nonlinear phenomenon for the consequences of air-gap, electrostatic forcing parameter and effective damping on overall responses has been thoroughly studied. The possible of undesirable catastrophic failure at the unstable critical points has been critically examined. Basins of attractions that postulate a unique response in multi-region state for a specific initial condition have been depicted. The obtained responses using first-order method of multiple scales have been cross compared with the findings obtained numerically. Findings from this work can significantly be adopted to identify the locus of instability in microcantilever-based resonator when subjected to AC voltage polarization. In addition, the present outcomes provide theoretical and practical ideas for controlling the systems and optimizing their operation.

The effect of squeeze air-film and AC actuation voltage on dynamic stability of microswitch actuated electrostatically has been investigated in squeeze film domain. The dynamics of the device has been developed considering the load arising from the squeezed air film between the microcantilever attached plate and the grounded substrate. Using trajectories in phase plane and time history, characteristics of the pull-in phenomena have been studied in the presence of DC voltage combined with AC component. Pull-in voltage is observed to be less as compared to the conventional micro-cantilever devices which are actuated only due to DC loading. Furthermore, the dynamic pull-in voltage tends to approach static pull-in voltage, when the squeeze film damping is considered. The study indicates that although electrostatic forces cause softening characteristics, geometric nonlinearity produces a stiffening effect on the microstructure and the nonlinearities play a significant role when pull-in occurs. The ability to resist the bending deformation has become higher as the overall damping has been enhanced due to the effect squeeze film damping. The consideration of higher order nonlinearities while modeling electrostatic forces, predicts more accurate response. This research gives a desirable insight of dynamic behavior of MEMS device under the influence of squeeze film effect.