Sensitivity,probabilistic and stochastic analysis of the thermo-piezoelectric phenomena in solids by the stochastic perturbation technique

The main aim here is to present the application of the generalized stochastic perturbation technique to thermo-piezoelectric analysis of solid continua. The general nth order Taylor series representation for all random input parameters and the state functions is employed to formulate the coupled thermo-electro-elasticity equilibrium equations of the additional order; a determination of any probabilistic moments and characteristics is described; the discretization of the problem in terms of the Stochastic perturbation-based Finite Element Method is also provided. Since this expansion includes the lowest order partial derivatives, the structural sensitivity analysis using direct differentiation is performed at the same time with probabilistic modeling contrasted with the Monte-Carlo simulation results. The probabilistic approach is extended here towards an accounting for the stochastic ageing processes, which appear frequently in aggressive external environments and under dynamic excitation. The two parametric stochastic process with Gaussian initial value and ageing velocity is tested for this purpose. The entire procedure is tested on the example of the thermo-electro-elastic pulsation of the beam modeled analytically using the symbolic software MAPLE, where polynomial approximations, design sensitivities, probabilistic moments and their histories are computed and visualized.     

On-Chip Electrostatically Actuated Bending Tests for the Mechanical Characterization of Polysilicon at the Micro Scale

The issue of mechanical characterization of polysilicon used in micro electro mechanical systems (MEMS) is discussed in this paper. An innovative approach based on a fully on-chip testing procedure is described; two ad hoc designed electrostatically actuated microsystems are here used in order to determine experimentally the Young’s modulus and the rupture strength of polysilicon. The first device is based on a rotational test structure actuated by a system of comb-finger capacitors which load up to rupture a couple of tapered beams under bending in the plane parallel to the substrate. The second microsystem is based on a large plate with holes. It constitutes with the substrate a parallel plate capacitor moving in the direction orthogonal to the substrate itself. A couple of tapered beams placed at the centre of the plate is loaded up to rupture in bending in the plane orthogonal to the substrate. By means of the two devices, experimental data are obtained: they allow for a careful determination of Young’s modulus and rupture strength. The rupture values are interpreted by means of the Weibull approach; statistical size effects and stress gradient effect are taken into account thus allowing for a direct comparison between the data obtained from the two test structures.     

Numerical and experimental evaluation of the magnetic interaction for frequency up-conversion in piezoelectric vibration energy harvesters

Meccanica - The purpose of this work is to improve the modelling process for the application of permanent magnets in a frequency up-conversion (FuC) mechanism for piezoelectric energy harvesters....     

A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts

In this paper the effects of accidental impacts on polysilicon MEMS sensors are investigated within the framework of a three-scale finite element approach. By allowing for the very small ratio (on the order of 10⁻⁴) between the inertia of the MEMS and the inertia of the whole device, macro-scale analyses at the package length-scale are run to obtain the loading conditions at the sensor anchor points. These loading conditions are successively adopted in meso-scale analyses at the MEMS length-scale to detect where the stress level tends to be amplified by sensor layout. To foresee failure of polysilicon in these domains, as caused by the propagation of inter- as well as trans-granular cracks up to percolation, representative crystal topologies are handled in micro-scale analyses. In case of a uni-axial MEMS accelerometer falling from a reference drop height, results show that the crystal structure within the failing sensor detail can have a remarkable effect on the failure mode and on the time to failure. Conversely, through comparison with simulations where the MEMS is assumed to fall anchored to the naked die, it is assessed that packaging only slightly modifies failure details, without significantly reducing the shock loading on the sensor. F. Fachin is currently with: Technology Laboratory for Advanced Materials and Structures, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 (USA). F. Cacchione is currently with: ABB SACE, Viale dell’Industria 18, Vittuone, 20010 (Italy).     

On-Chip Mechanical Characterization using an Electro-thermo-mechanical Actuator

A new micro-system for the on-chip mechanical characterization of thin polysilicon films was designed, fabricated and tested. The device contains a micro electro-thermo mechanical actuator which is able to load a specimen until rupture in purely tensile conditions. The elongation of the specimen is measured during the test through the capacitance variation of a set of parallel plate capacitors, while the force in the specimen can be computed starting from the applied voltage. Through a unique loading cycle in which the voltage is first increased until specimen rupture and then decreased, the new device allows for the determination of the specimen elastic stiffness and nominal tensile strength. The obtained experimental results were compared with values previously obtained by means of different on-chip test devices. Multi-physics FE simulations were performed for additional comparison with analytical formulae used in the data reduction procedure and with the obtained experimental results.     

Optimal 2D auxetic micro-structures with band gap

A systematic investigation is presented that explores band gap properties of periodic micro-structures architected for maximum auxeticity. The design of two-dimensional auxetic cells is addressed using inverse homogenization. A non-convex optimization problem is formulated that is solved through mathematical programming. Different starting guesses are used to explore local minima when distributing material and void or two materials and void. The same numerical tool succeeds in capturing re-entrant, chiral and anti-chiral layouts with negative Poisson’s ratio, retrieving solutions originally found through other approaches as well as generating variations. A Floquet–Bloch approach is then applied to the achieved periodic cells to investigate possible band gaps characterizing the in-plane wave propagation. Directional and full band-pass filters are found in the case of micro-structures whose auxetic behavior comes from the arising of a rotational deformation of the periodic cell. Such kind of topologies could be exploited to design tunable wave guides and tunable phononic crystals, respectively.

     

A resonant micro accelerometer based on electrostatic stiffness variation

A new out-of-plane resonant micro-machined accelerometer has been designed, modelled and fabricated. The sensing principle is based on the variation of the electrostatic stiffness of two torsional resonators mechanically coupled with an inertial proof mass. The accelerometer, fabricated by the ThELMA^® surface micro-machining process of STMicroelectronics, constitutes a further step of a research focussing on the design of in-plane and out-of-plane resonant micro accelerometers. Preliminary electrostatic measures of the torsional resonators response have been compared with the theoretical predictions.