A MEMS square Chladni plate resonator

Laser Doppler vibrometry (LDV) is a well known technique to measure the motions, vibrations and mode shapes of structures and machine components. Photodetector-based LDV can only offer a point-wise measurement. However, it is possible to scan the laser beam to build up a vibrometric image. These scanning laser Doppler vibrometers (SLDV) assume that the measurement conditions remain invariant while multiple and identical, sequential measurements are performed. This assumption makes SLDVs impractical to do measurement on transient events. In this paper, we introduce a new method of generating multiple laser beams with different frequency shifts. The laser beams are projected on different points, and the reflected beams interfere with a common reference beam. The cross-talk among object beams can be bypassed with a proper selection of frequency shifts. A simultaneous vibration measurement on multiple points is realized using a single photodetector. Based on the proposed spatial-encoding technology, a self-synchronized prototype of fiber-based multipoint laser Doppler vibrometer at 1550nm wavelength is developed. An addition red pilot laser is used for aiming purpose. It has the flexibility to measure the vibration of different points on various surfaces. The prototype is used to measure the vibration of different points on a cantilever beam and a plate. The measured results match well with simulation results using finite element method (FEM).

This paper presents the effect of temperature on the natural frequency of (1,1) mode shape of a Resonant MEMS IR bolometer pixel in the range of 295-340 K. The detector pixel has a square plate geometry having side length of 1400μm and thickness of 35μm. The resonating plate is supported at its geometric center, enabling more robust pixels with fill factor greater than 90% and less complicated fabrication process. The sensor is fabricated using a Silicon-On-Glass (SOG) process. For the first time in the literature, the closed form equation to calculate the natural frequency of the fundamental mode shape of a MEMS square plate as a function of temperature change is derived for the single crystal silicon as the structural material. FEM simulations and experiments are conducted to verify the analytical model. For the electromechanical response characterization of the pixel structure, frequency response and system level temperature tests are conducted. Fundamental natural frequency shift is also tested during the frequency response tests for the same temperature range and the scale factor of the fabricated sensor is measured to be 1.90Hz/K for mode shape (1,1).

This paper presents a method to measure responses for a sinusoidally excited structure using a continuously scanning Laser Doppler Vibrometer (LDV). The LDV output signal is an amplitude-modulated vibration, whereby the excitation signal will be modulated by the response of the excited structure. Using an applicable demodulation the mode shape defined along a scan line can be derived by the envelope of the modulated vibration. By using an adaptable digital low-pass filter and parallel measuring of responses and mirror drive signal in the time domain the mode shape can be directly derived from the measured response. So the demodulation is a fast method to identify the mode shape from the measured response, because of its completion in the time domain. For that purpose the method is capable for using the responses online for normal mode tuning. Furthermore it is necessary for normal mode testing to measure complex responses to make an affirmation about the separation of real mode shapes. The method will match these requirements.

The effectiveness of wavelet transform in detecting delamination damages in multilayered composite beams and plates is studied here. The damaged composite beams and plates are modeled in finite element software ABAQUS and the first few mode shapes are obtained. The mode shapes of the damaged structures are then wavelet transformed. It is observed that the distribution of wavelet coefficients can identify the damage location of beams and plates by showing higher values of wavelet coefficients at the position of damage. The effectiveness of the method is studied for different boundary conditions, damage location and size for single as well as multiple delaminations in composite beams and plates. It is observed that both discrete wavelet transform (DWT) and continuous wavelet transform (CWT) can detect the presence and location of the damaged region from the mode shapes of the structures. DWT may be used to approximately evaluate the size of the delamination area, whereas, CWT is efficient to detect smaller delamination areas in composites.

In this paper, we report optical and mechanical properties of low temperature plasma enhanced chemical vapor-deposited (PECVD) amorphous hydrogenated silicon carbide (a-SiC:H) thin films. Initial screening of this process using hydrogen-dilution was performed with a two-level, three-parameter design of experiments (DOE) with eight samples. In this process regime, it was determined that the main parameters affecting silicon carbide (SiC) deposition were the RF power and the hydrogen flow rate. Based on the DOE results, a further set of four samples was prepared to modulate deposition rate and stoichiometry. Material characterization of these samples using Fourier transform infrared spectroscopy (FTIR), X-ray photolectron spectroscopy (XPS), surface profilometry and ellipsometry is presented. Further, to determine the mechanical properties, cantilevers were fabricated and characterized using scanning electron microscopy (SEM) and laser Doppler vibrometry (LDV). Based on the resonant frequency measurement and film density, the Young's modulus for the films was determined.

Application of modal analysis to the watermelon through finite element modeling for use in ripeness assessment

The mode shapes of beam-type structures, such as aircraft wings and wind turbine blades, involve a high degree of coupling between bending and torsional deformations. In the case of wind turbine blades, different types of deformation are typically easily recognized by visual observation. However, this visual approach is sometimes challenging for high-order mode shapes, which involve complex coupling of both bending and torsional deformations. This work proposes a novel mode shape recognition algorithm, called the finite cross-section method (FCSM), for application to highly coupled beam-type structures not only to identify the deformation components of complex beam mode shapes but also more importantly to quantify their respective relative contribution. In the application case study for the FCSM, the entire structure is discretized into multiple cross sections. The flap-wise, edge-wise, and torsional deformation components of the entire structure are determined at the cross-section level. The deformation components of the entire structure and their respective contribution are obtained from assembling all cross sections. To validate the mode shape recognition performance, FCSM is applied to and demonstrated on four test cases: (1) numerical mode shapes of a simple cantilever beam, (2) numerical mode shapes from a straight wind turbine blade, (3) numerical mode shapes of a swept wind turbine blade, and (4) experimental mode shapes from a high spatial resolution 3D scanning laser Doppler vibrometer (SLDV) modal test. Both numerical and experimental studies demonstrate that FCSM can successfully recognize the quantitative contribution of flap-wise, edge-wise, and torsional deformation.

The dynamic characteristics of parallel-type and series-type piezoelectric bimorphs are analyzed in this study. The transverse (out-of-plane) and planar (in-plane) vibrations for piezoceramic bimorphs in normal and abnormal connections are investigated experimentally by 2 noncontact optical techniques and impedance analyzer. Electronic speckle pattern interferometry (ESPI) is the major experimental technique for measuring the resonant frequency and corresponding vibration mode shape. Out-of-plane and in-plane vibrations of piezoelectric bimorphs at resonance are obtained by a self-arranged ESPI optical setup. The laser Doppler vibrometer (LDV) is a point-wise measurement technique for out-of-plane displacement and is used to determine the out-of-plane resonant frequencies. The impedance analyzer is used to measure the resonant frequencies for in-plane motions. It is noted from the experimental results that the out-of-plane modes are the dominant motion for the normal connection and only symmetric vibration mode shapes can be excited. The in-plane motions are large enough to be measured using the ESPI method for normal connections. The in-plane resonant modes are observed for parallel-type piezoelectric bimorph in parallel connections; however, the in-plane mode shapes are similar to the out-of-plane mode shapes for the series-type piezoelectric bimorph in series connection. Hence, the particle motions of the piezoelectric bimorph at resonance are essentially 3-D for the normal connection. It is interesting to note that both symmetric and asymmetric out-of-plane vibration mode shapes can be excited with large applied voltage but no in-plane motion is observed for the abnormal connection. In addition to experimental methods, numerical computations based on the finite element method are used to verify the experimental results. Good agreements of the resonant frequencies and mode shapes are obtained for experimental and numerical results.

3D scanning laser Doppler vibrometry (LDV) systems continue to gain popularity for use in experimental modal analysis as the systems become more widespread. LDV is, by its nature, limited to measurements with line-of-sight visibility. This work presents an application of 3D scanning LDV to a test article with un-instrumented internal features that were not accessible to the lasers. The internal features, while not directly measurable, were known to contribute strongly to the modal characteristics of the test article. Initially, a traditional roving hammer test was conducted and modal parameters were extracted. The limited degrees of freedom inherent to this test method proved to be inadequate to correctly identify key mode shapes. It was found that by increasing the measurement point density and including all three translational degrees of freedom at each point, the key modal characteristics of the full system were able to be inferred from purely external measurements. These characteristics were essential in updating the mechanical behavior and material properties of the corresponding finite element model. The response measurements required for system identification were only practically achievable using the 3D LDV system. Comparisons of key experimental results to those of the calibrated analytical model are demonstrated.

As a result of the increase in use of composites in the Aircraft Industry, use a better knowledge and behavioral prediction is desired. This can be done through computational models and/or physical testing. Numerous FEA programs are used to aid in the design process and to predict the performance and behavior of composite structures. There are also many non destructive methods of investigation (NDI) which are used in both quality control and behavioral observations. A composite flight structure common to many airplanes is a radome, which can be defined as a structural enclosure used to protect an antenna from the environment which includes the aerodynamic loading and weather. FEA model validation is performed by comparison to vibration testing as well as internal pressure testing. Shearography allows us to measure the surface deformation of an object when under a stress. Shearography was completed to determine any possible defects caused in manufacturing (or transporting) the radome. De-lamination will possibly cause unpredicted response in the vibration or pressure tests. Areas of different construction as well as defects will deflect non-uniformly. There were no flaws detected in the composite radome tested. Laser Doppler Vibrometry (LDV) is a non-contact vibration measurement that is used to determine the natural frequencies and mode shapes of the Composite Radome Structure. The vibration testing was completed using a few different boundary conditions which include approximately free-free BC's and fixed BC's. The testing has corresponded accurately in comparison to the FEA model however; it is suspected that there is some slight error caused by the fixed fixture for vibration testing.

Piezoelectric plates can provide low-frequency transverse vibrational displacements and high-frequency planar vibrational displacements, which are usually uncoupled. However, piezoelectric shells can induce three-dimensional coupled vibrational displacements over a large frequency range. In this study, three-dimensional coupled vibrational characteristics of piezoelectric shells with free boundary conditions are investigated using three different experimental methods and finite element numerical modeling. For the experimental measurements, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to obtain resonant frequencies and radial, lateral, and angular mode shapes. This optical technique utilizes a real-time, full-field, non-contact optical system that measures both the natural frequency and corresponding vibration mode shape simultaneously. The second experimental technique used, laser Doppler vibrometry (LDV), is a pointwise displacement measurement method that determines the resonant frequencies of the piezoelectric shell. An impedance analyzer is also used to determine the resonant frequencies of the piezoelectric shell. The experimental results of the resonant frequencies and mode shapes for the piezoelectric shell are verified with a numerical finite element model. Excellent agreement between the experimental and numerical results is found for the three-dimensional coupled vibrational characteristics of the piezoelectric shell. It is noted in this study that there is no coupled phenomenon at low frequencies over which radial modes dominate. However, three-dimensional coupled vibrational modes do occur at high resonant frequencies over which lateral or angular modes dominate.

The excitation of two low-mode number, flexible cylinders in uniform-flow is investigated to determine effects of structural mode shape on vortex-induced vibrations. Experiments are performed in a re-circulating flow channel and in a small flow visualization tank using object tracking and digital particle image velocimetry (DPIV) to measure the excitation of the cylinder, to estimate forces acting on the structure, and to observe the wake of the structure under the observed body motions. Previous research has focused on understanding the effect of in-line to cross-flow natural frequency ratio on the excitation of the structure in an attempt to model the excitation of multiple structural modes on long, flexible bodies. The current research investigates the impact of structural mode shape on this relationship by holding the in-line to cross-flow natural frequency constant and attempting to excite a specific structural mode shape. It is found that the combination of an odd mode shape excited in the cross-flow direction with an even mode shape in the in-line direction results in an incompatible synchronization condition, where the dominant forcing frequency in-line may experience a frequency equal to the cross-flow forcing frequency, a condition only observed in rigid cylinder experiments when the natural frequency ratio is less than one. This is consistent with the first mode being excited in both in-line and cross-flow directions, however this leads to an asymmetric wake. The wake is observed using DPIV on a rigid cylinder with forced motions equivalent to the flexible body. A case of mode switching is also observed where the even in-line mode exhibits an excitation at twice the cross-flow frequency; however the spatial mode shape in-line appears similar to the first structural mode shape. It is hypothesized that this situation is possible due to variation in the effective added mass along the length of the cylinder.

The wave front corrector is one of the three key elements in adaptive optics, along with the wave front sensor and the control computer. Low cost, compact deformable mirrors are increasingly available. We have tested the AOptix bimorph deformable mirror, originally developed for ultra-high bandwidth laser communication systems, to determine its suitability for vision science applications, where cornea and lens introduce optical aberrations. Measurements of the dynamic response of the mirror to a step input were obtained using a commercial Laser Doppler Vibrometer (LDV). A computer-controlled Twyman-Green interferometer was constructed to allow the surface height of the deformable mirror to be measured using Phase-Shifting Interferometry as a function of various control voltages. A simple open-loop control method was used to compute the control voltages required to generate aberration mode shapes described by the Zernike polynomials. Using this method, the ability of the deformable mirror to generate each mode shape was characterized by measuring the maximum amplitude and RMS error of each Zernike mode shape up to the fifth radial order. The maximum deformation amplitude was found to diminish with the square of the radial order of the Zernike mode, with a measured deformation of 8 microns and 1.5 microns achieved at the second-order and fifth-order Zernike modes, respectively. This deformation amplitude appears to be sufficient to allow the mirror to correct for aberrations up to the fifth order in the human eye.

Most research on computer vision (CV)-based vibration measurement is limited to the determination of discrete or coarse mode shapes of the structure. The continuous edge of the structure in images has rich optical features, and thus, by identifying and tracking the movement of the structure’s edge, it is possible to determine high-resolution full-field mode shapes of the structure without a preset target. The present study proposes a CV-based method of full-field mode shape identification using the subpixel edge detection and tracking techniques. Firstly, the Canny operator is applied on each frame of the structure vibration video to extract the pixel-level edges, and the improved Zernike orthogonal moment (ZOM) subpixel edge detection technique is adopted to relocate the precise structure edges. Then, all the detected edge points are tracked to obtain the full-field dense displacement time history that is subsequently used to determine the structure frequencies and compute full-field mode shapes by combining the covariance driven stochastic subspace identification (SSI-COV) with the hierarchical cluster analysis. Finally, the proposed method is verified on the aluminum cantilever beam in the laboratory and the Humen Bridge in the field. The results show that the proposed method is able to detect more precise structure edges and identify the full-field displacement and mode shapes of structures without the need for installing artificial targets on the structure in advance, which provides valuable information for the structural condition assessment, especially for structures with small-amplitude vibrations.

This paper proposes an approach to extract the mode shapes of beam-like structures from the dynamic response of a moving mass. When a mass passes through a beam containing several artificially installed humps, its vertical acceleration can be recorded. After applying fast Fourier transformation to the dynamic response, one can extract the mode shapes of the beam. The surface roughness was neglected compared to the humps and its adverse effect on the extraction was reduced. The passing mass performs as both “exciter” and “massage receiver”; therefore, this method requires only one single accelerometer, making it more convenient and time saving in practice. Moreover, to estimate the possible error in extracting mode shapes, a wavenumber domain filtering technique is used to reconstruct the general profiles of mode shapes. Experimental validation of this approach in laboratory scale was conducted. The experimental results show that the proposed method performs well in extracting lower order mode shapes. It should also be noted that the passing mass can not have a very high velocity (e.g. 80 mm/s), otherwise the mass may jump and separate from the beam, and the proposed method may fail to identify mode shapes.