Dynamic analysis is an essential factor in the design, fabrication and optimization of micro-systems. Micro-scanners are currently subjected to wide research work. In this paper, the dynamic behavior of a monolithic single-crystal silicon microstructure is investigated. The microstructure used is a double-paddle scanning mirror for laser applications. It consists of two similar plates (wings) connected to another plate (mirror) and is suspended by one torsion bar. The dynamic analysis is conducted numerically, using finite element analysis. The numerical modeling is described. The numerical results are validated experimentally by measuring the frequency response functions collected at some points on the scanner surface. The experimental modal analysis is performed using a laser Doppler vibrometer and an acoustic excitation device. The excitation device consists of a polyester resin mount with two conic-shaped ducts which give access to the back of the two wings from one side and to two mini loudspeakers on the other side. This excitation device was used and good agreement was found between the numerically predicted and the experimentally identified modal parameters. The non-intrusive excitation mechanism and the optical measurement techniques used in the experiments are discussed. A high quality factor is identified for the chosen operational mode shape.
The coupling loss factors are of critical importance when building and solving Statistical Energy Analysis (SEA) models. This paper proposes a methodology to numerically estimate these factors for frame-type structures. The estimated factors are compared with those obtained through analytical expressions for frame structures, where members are joined at right angles. The example used to verify the proposed technique consists of two infinite beams connected at a right angle modeled via the Spectral Element Method (SEM) using throw-off elements. It is shown that the obtained coupling loss factors compare very well with the analytical expressions that may be derived for this simple right-angle connection case. By using the SEM approach, the coupling loss factors can be obtained for arbitrary frame structure connections, thus facilitating the analysis via SEA
The total structural intensity in beams can be considered as composed of three types of waves: bending, longitudinal, and torsional. In passive and active control applications, it is useful to separate each of these components in order to evaluate their contribution to the total structural power flowing through the beam. In this paper, a twisted z-shaped beam is used in order to allow the three types of waves to propagate. The contributions of the structural intensity, due to these waves, are computed from measurements taken over the surface of the beam with a simple homodyne interferometric laser vibrometer. The optical sensor incorporates some polarizing optics, additional to a Michelson type interferometer, to generate two optical signals in quadrature, which are processed to display velocities and/or displacements. This optical processing scheme is used to remove the directional ambiguity from the velocity measurement and allows nearly all back-scattered light collected from the object to be detect. This paper investigates the performance of the laser vibrometer in the estimation of the different wave components. The results are validated by comparing the total structural intensity computed from the laser measurements, with the measured input power. Results computed from measurements using PVDF sensors are also shown, and compared with the non-intrusive laser measurements.
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