We analyze transient finite electroelastodynamic deformations of a perfect electrically conducting undamped clamped–clamped beam, a clamped–clamped parabolic arch and a clamped–clamped bell-shaped arch suspended over a flat rigid semi-infinite perfect conductor. The pull-in instability in a beam and the pull-in and the snap-through instabilities in the two arches due to time-dependent potential difference between the two electrodes have been studied. The potential difference is applied either suddenly or is increased linearly in time. Since the time scale of the transient electric forces is very small as compared to that of the mechanical forces, inertia effects only in the mechanical deformations are considered. Effects of both material and geometric nonlinearities are incorporated in the problem formulation and solution; however, damping due to the interaction of the structure with the surrounding medium is neglected. The coupled nonlinear partial differential equations for mechanical deformations are solved numerically by the finite element method and those for the electrical problem by the boundary element method. The Coulomb pressure due to the potential difference between the two electrodes is a nonlinear function of the a priori unknown distance between them. The potential difference that induces either the pull-in instability in a beam or the snap-through followed by the pull-in instabilities in an arch has been computed. Wherever possible these results are compared with those available in the literature. With a decrease in the rate of the applied potential difference, the pull-in and the snap-through parameters approach those for a static problem. Also, for large rates of increase in the potential difference between the two electrodes, the snap-through instability in an arch is suppressed and only the pull-in instability occurs.

Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-relays, micro-valves, optical switches and digital micro-mirrors. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability and the pull-in instability of a bi-stable arch-shaped MEMS under static and dynamic electric loads. Unlike a mechanical load, the electric load is a nonlinear function of the a priori unknown deformed shape of the arch. The nonlinear partial differential equation governing transient deformations of the arch is solved numerically using the Galerkin method and a time integration scheme that adaptively adjusts the time step to compute the solution within the prescribed tolerance. For the static problem, the displacement control and the pseudo-arc-length continuation methods are used to obtain the bifurcation curve of the arch's displacement versus a load parameter. The displacement control method fails to compute the arch's asymmetric deformations that are found by the pseudo-arc-length continuation method. For the dynamic problem, two distinct mechanisms of the snap-through instability are found. It is shown that critical loads and geometric parameters for instabilities of an arch under an electric load with and without consideration of mechanical inertia effects are quite different. A phase diagram between a critical load parameter and the arch height is constructed to delineate different regions of instabilities. We compare results from the present model with those from a continuum mechanics based approach, and with results of other models and experiments available in the literature.

This paper presents the results of a combined experimental and computational research program to investigate turbine vane and blade material surface deterioration caused by solid particle impacts. Tests are conducted in the erosion wind tunnel for coated and uncoated blade materials at various impact conditions. Surface roughness measurements obtained prior and subsequent to the erosion tests are used to characterize the change in roughness caused by erosion. Numerical simulations for the three-dimensional flow field and particle trajectories through a low-pressure gas turbine are employed to determine the particle impact conditions with stator vanes and rotor blades using experimentally based particle restitution models. Experimental results are presented for the measured blade material/coating erosion and surface roughness. The measurements indicate that both erosion and surface roughness increase with impact angle and particle size. Computational results are presented for the particle trajectories through the first stage of a low-pressure turbine of a high bypass turbofan engine. The trajectories indicate that the particles impact the vane pressure surface and the aft part of the suction surface. The impacts reduce the particle momentum through the stator but increase it through the rotor. Vane and blade surface erosion patterns are predicted based on the computed trajectories and the experimentally measured blade coating erosion characteristics.

Ion bombardment causes surface instabilities on a range of materials including metals, semiconductors, and insulators. However, the proposed mechanisms for these instabilities have yet to explain the rich range of nanometer-scale patterns that are observed experimentally. Here we show that smoothing balanced by impact angle dependent mass redistribution explains the atomistic origin of ripple formation and orientation, particularly angle dependent transitions between different orientations. A competition between the mass accumulated on the surface and the hole created on the surface determines the orientation of ripples. Results are consistent with experimental observations for a range of ions, ion energies, and targets.

This paper presents the results of a combined experimental and computational research program to investigate turbine vane and blade material surface deterioration caused by solid particle impacts. Tests are conducted in the erosion wind tunnel for coated and uncoated blade materials at various impact conditions. Surface roughness measurements obtained prior and subsequent to the erosion tests are used to characterize the change in roughness caused by erosion. Numerical simulations for the three dimensional flow field and particle trajectories through a low pressure gas turbine are employed to determine the particle impact conditions with stator vanes and rotor blades using experimentally-based particle restitution models. Experimental results are presented for the measured blade material/coating erosion and surface roughness. The measurements indicate that both erosion and surface roughness increase with impact angle and particle size. Computational results are presented for the particle trajectories though the first stage of a low-pressure turbine of a high bypass turbofan engine. The trajectories indicate that the particles impact the vane pressure surface and the aft part of the suction surface. The impacts reduce the particle momentum through the stator but increase it through the rotor. Vane and blade surface erosion patterns are predicted based on the computed trajectories and the experimentally measured blade coating erosion characteristics.