Experimental modal analysis (EMA) was carried out on a micro-machined acceleration switch to characterize the motions of the device as fabricated and to compare this with analytical results for the nominal design. Finite element analysis (FEA) of the nominal design was used for this comparison. The acceleration switch was a single-crystal silicon disc supported by four fork-shaped springs. We shook the base of the die with step sine type excitation. A Laser Doppler Velocimeter (LDV) in conjunction with a microscope was used to measure the velocities of the die at several points. The desired first three modes of the structure were identified. The fundamental natural frequency that we measured in this experiment gives an estimate of the actuation g-level for the specified stroke. The fundamental resonance and actuation g-level results from the EMA and the FEA showed large variations. The discrepancy prompted thorough dimensional measurement of the acceleration switch, which revealed discrepancies between the nominal design and tested component.
The shape control of thin, flexible structures has been studied primarily for edge-supported thin plates. For applications involving reconfigurable apertures such as membrane optics and active RF surfaces, corner-supported configurations may prove more applicable. Corner-supported adaptive structures allow for parabolic geometries, greater flexibility, and larger achievable deflections when compared to edge-supported geometries under similar actuation conditions. Preliminary models have been developed for corner-supported thin plates actuated by isotropic piezoelectric actuators. However, typical piezoelectric materials are known to be orthotropic. This paper extends a previously-developed isotropic model for a corner-supported, thin, rectangular bimorph to a more general orthotropic model for a bimorph actuated by a two-dimensional array of segmented PVDF laminates. First, a model determining the deflected shape of an orthotropic laminate for a given distribution of voltages over the actuator array is derived. Second, symmetric actuation of a bimorph consisting of orthotropic material is simulated using orthogonally-oriented laminae. Finally, the results of the model are shown to agree well with layered-shell finite element simulations for simple and complex voltage distributions.
Mechanical dynamics can be a determining factor for the switching speed of radio-frequency microelectromechanical systems (RF MEMS) switches. This paper presents the simulation of the mechanical motion of a microswitch under actuation. The switch has a plate suspended by springs. When an electrostatic actuation is applied, the plate moves toward the substrate and closes the switch. Simulations are calculated via a high-fidelity finite element model that couples solid dynamics with electrostatic actuation. It incorporates non-linear coupled dynamics and accommodates fabrication variations. Experimental modal analysis gives results in the frequency domain that verifies the natural frequencies and mode shapes predicted by the model. An effective 1D model is created and used to calculate an actuation voltage waveform that minimizes switch velocity at closure. In the experiment, the switch is actuated with this actuation voltage, and the displacements of the switch at various points are measured using a laser Doppler velocimeter through a microscope. The experiments are repeated on several switches from different batches. The experimental results verify the model.
The primary goals of the present study are to: (1) determine how and why MEMS-scale friction differs from friction on the macro-scale, and (2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction. Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of 'pre-sliding tangential deflections' (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load. Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity. Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include the effect of roughness in such an analysis by using a homogenized contact and friction models. AFM measurements were made to determine statistical information on polysilicon surfaces with different roughnesses, and this data was used as input to a homogenized, multi-asperity contact model (the classical Greenwood and Williamson model). Extensions of the Greenwood and Williamson model are also discussed: one incorporates the effect of adhesion while the other modifies the theory so that it applies to the case of relatively few contacting asperities.
This report documents the results obtained during a one-year Laboratory Directed Research and Development (LDRD) initiative aimed at investigating coupled structural acoustic interactions by means of algorithm development and experiment. Finite element acoustic formulations have been developed based on fluid velocity potential and fluid displacement. Domain decomposition and diagonal scaling preconditioners were investigated for parallel implementation. A formulation that includes fluid viscosity and that can simulate both pressure and shear waves in fluid was developed. An acoustic wave tube was built, tested, and shown to be an effective means of testing acoustic loading on simple test structures. The tube is capable of creating a semi-infinite acoustic field due to nonreflecting acoustic termination at one end. In addition, a micro-torsional disk was created and tested for the purposes of investigating acoustic shear wave damping in microstructures, and the slip boundary conditions that occur along the wet interface when the Knudsen number becomes sufficiently large.
The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured adequately through direct simulation of the contact mechanics within a structural dynamics analysis. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. This document discusses a road-map for developing such constitutive models.