Amplitude-fluctuation Electronic Speckle Pattern Interferometry Research Articles

Experimental measurement and numerical analysis on resonant characteristics of piezoelectric disks with partial electrode designs

Three experimental techniques are used in this study to access the influence of the electrode arrangement on the resonant characteristics of piezoceramic disks. These methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, pointwise displacement, and electric impedance, respectively. In this study, one full electrode design and three nonsymmetrical partial electrode designs of piezoelectric disks are investigated. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time for out-of-plane and in-plane motions. The second experimental method is the impedance analysis, which is used to measure the resonant and antiresonant frequencies. In addition to these experimental methods, LDV-DSA is used to determine the resonant frequencies of the vibration mode with out-of-plane motion. From the experimental results, the dependence of electrode design on the vibration frequencies and mode shapes is addressed. Numerical computations based on the finite element method are presented, and the results are compared with the experimental measurements. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.

Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates.

Based on the electroelastic theory for piezoelectric plates, the vibration characteristics of piezoceramic disks with free-boundary conditions are investigated in this work by theoretical analysis, numerical simulation, and experimental measurement. The resonance of thin piezoceramic disks is classified into three types of vibration modes: transverse, tangential, and radial extensional modes. All of these modes are investigated in detail. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. Because the clear fringe patterns are shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Good quality of the interferometric fringe patterns for both the transverse and extensional vibration mode shapes are demonstrated. The resonant frequencies of the piezoceramic disk also are measured by the conventional impedance analysis. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be measured by the impedance analysis, and only the resonant frequencies of extensional vibration modes can be obtained. Numerical calculations based on the finite element method also are performed, and the results are compared with the theoretical analysis and experimental measurements. It is shown that the finite element method (FEM) calculations and the experimental results agree fairly well for the resonant frequencies and mode shapes. The resonant frequencies and mode shapes predicted by theoretical analysis and calculated by finite element method are in good agreement, and the difference of resonant frequencies for both results with the thickness-to-diameter (h/D) ratios, ranging from 0.01 to 0.1, are presented.

Vibration analysis of angle-ply laminated composite plates with an embedded piezoceramic layer.

An optical full-field technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is used in this study to investigate the force-induced transverse vibration of an angle-ply laminated composite embedded with a piezoceramic layer (piezolaminated plates). The piezolaminated plates are excited by applying time-harmonic voltages to the embedded piezoceramic layer. Because clear fringe patterns will appear only at resonant frequencies, both the resonant frequencies and mode shapes of the vibrating piezolaminated plates with five different fiber orientation angles are obtained by the proposed AF-ESPI method. A laser Doppler vibrometer (LDV) system that has the advantage of high resolution and broad dynamic range also is applied to measure the frequency response of piezolaminated plates. In addition to the two proposed optical techniques, numerical computations based on a commercial finite element package are presented for comparison with the experimental results. Three different numerical formulations are used to evaluate the vibration characteristics of piezolaminated plates. Good agreements of the measured data by the optical method and the numerical results predicted by the finite element method (FEM) demonstrate that the proposed methodology in this study is a powerful tool for the vibration analysis of piezolaminated plates.

Experimental whole-field interferometry for transverse vibration of plates

Most of the work on vibration analysis of plates published in the literature are analytical and numerical and very few experimental results are available. Existing modal analysis techniques such as accelerometers and laser Doppler vibrometers are pointwise measurement techniques and are used in conjunction with spectrum analyzers and modal analysis software to characterize the vibration behaviour. In this study, a whole-field technique called amplitude-fluctuation electronic speckle pattern interferometry optical system is employed to investigate the vibration behaviour of square isotropic plates with different boundary conditions. This method is very convenient to investigate vibration objects because no contact is required compared to classical modal analysis using accelerometers. High-quality interferometric fringes for mode shapes are produced instantly by a video recording system. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present method. Two different types of boundary conditions are investigated in this study, namely free–free–free–free (FFFF, 27 modes) and clamped–clamped–clamped–clamped (CCCC, 12 modes). The numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes.

Full-Field Three-Dimensional Volume Vibrations for Piezoceramic Materials in Resonance

Three-dimensional volume vibrations for piezoceramics, which couple the out-of-plane and in-plane vibrations, are investigated by using an optical interferometry method called the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI). The optical systems for AF-ESPI with out-of-plane and in-plane measurements are employed to analyze the volume vibration of piezoceramic material for a rectangular parallelepiped configuration. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time. Two out-of-plane and two in-plane measurements are needed to construct the complete information of vibration mode shape. However, by tilting the specimen with an angle, the coupled out-of-plane and in-plane motions can be obtained from only one out-of-plane setup and measurement. The dominant motion of the volume vibration can be identified from the mode shape by tilting the specimen. Finally, the impedance analysis and finite element method with three-dimensional model are also utilized, and the results are compared with the measurements by AF-ESPI. Excellent agreements of the resonant frequencies and mode shapes are obtained from both results. .

Vibration analysis of piezoelectric materials by optical methods

This study provides two noncontact and realtime optical measurement methods to assess the displacement, natural frequencies, and mode shapes of a vibrating piezoelectric material. The methods are carried out using amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), which are full-field and point-wise displacement measurement, respectively. Because the fringe patterns measured by AF-ESPI appear as a clear picture at the natural frequency, both natural frequencies and mode shapes of the vibrating material can be successfully obtained. In the LDV system, a swept-sine excitation signal from the function generator to the beam can result in a corresponding peak in frequency response curve at natural frequencies. From the frequency response curve, the natural frequencies are thus acquired. Measured results by both methods are seen to be in good agreement with theoretical predictions by the Galerkin method and finite element method.

Experimental Investigations on Dynamic Characteristics of a Multilayer Piezoelectric Stack Actuator

AbstractMultilayer piezoelectric stack actuators are widely used in many industrial applications and the investigation on the dynamic behavior of this element is needed. In this study, two optical interferometric techniques called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV) are used to experimentally investigate the vibration characteristics of a single-layer piezoelectric disc and a multilayer piezoelectric stack actuator. These two techniques are full-field measurement for AF-ESPI and point-wise displacement measurement for LDV. Because the clear fringe patterns obtained by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes of the piezoelectric disc and the multilayer piezoelectric stack actuator are obtained simultaneously by the AF-ESPI method. Interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. In addition to the proposed two optical techniques, numerical computations based on a commercially available finite element package are presented for comparison with the experimental results. Good agreement between the measured data by experimental methods and the numerical results predicted by FEM is found in resonant frequencies and mode shapes for the single-layer piezoelectric disc. However, some discrepancies are observed for the results obtained by AF-ESPI and impedance analysis for the multilayer piezoelectric stack actuator. A detailed discussion is made to address important issues of this problem.

Experimental full field investigations of resonant vibrations for piezoceramic plates by an optical interferometry method

The experimental measurement of resonant frequencies for piezoelectric material is generally performed by impedance analysis. In this paper we employ an optical interferometry method, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), to investigate the vibration characteristics of piezoceramic plates. This method demonstrates its advantages of combining noise reduction, like the subtraction method, and high fringe sensitivity, like the time-averaged method. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Based on the fact that clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding mode shapes are obtained experimentally at the same time. Excellent quality for the interferometric fringe patterns of the mode shapes is demonstrated. We find from experimental results that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extension) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, numberical finite element calculations are also performed, and the results are compared with the experimental measurements. Excellent agreement for the resonant frequencies and mode shapes are obtained from both results.

EXPERIMENTAL MEASUREMENTS BY AN OPTICAL METHOD OF RESONANT FREQUENCES AND MODE SHAPES FOR SQUARE PLATES WITH ROUNDED CORNERS AND CHAMFERS

Most of the work done on vibration of plates published in the literature includes analytical and numerical studies with few experimental results available. In this paper, an optical system called the amplitude-fluctuation electronic speckle pattern interferometry for the out-of-plane displacement measurement is employed to investigate the vibration behavior of plates with rounded corners and with chamfers. The boundary conditions are traction free along the circumference of the plate. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present method. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Good agreements are obtained for both results. It is interesting to note that the mode number sequences for some resonant modes are changed. The transition of mode shapes from the square plate to the circular plate is also discussed.

Experimental Investigation of Vibrating Laminated Composite Plates by Optical Interferometry Method

Most of the work done for the vibration of composite plates published in the literature are analytical and numerical studies with few experimental results available. In this study, an experimental amplitude-fluctuation electronic speckle pattern interferometry method for out-of-plane displacement measurement is employed to investigate the vibration behavior of square and rectangular composite plates with different stacking sequences. Both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present method. High-quality interferometric fringes for mode shapes are produced instantly by a video recording system. Four different types of geometric configurations and stacking sequences of 16-layer laminated composite plates are investigated in this study, namely, a [0] 16 square plate, a [0] 16 rectangular plate, a [0/45/90/-45] 2s square plate, and a [0/45/90/-45] 2s rectangular plate. The numerical calculations by the finite element method and Rayleigh-Ritz technique are performed, and the results are compared with the experimental measurements. Good agreement is obtained for both results of resonant frequencies and mode shapes.

Experimental and numerical analysis of vibrating cracked plates at resonant frequencies

Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless frequency parameter (λ 2) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the cracked plate will be safe.

The investigation of three-dimensional vibration for piezoelectric rectangular parallelepipeds using the AF-ESPI method.

Electronic speckle pattern interferometry (ESPI) is a powerful tool for the full-field measurement of a deformed body. In this paper, a three-dimensional vibrating block that couples the out-of-plane and in-plane motions is investigated using the amplitude-fluctuation ESPI (AF-ESPI). This method demonstrates the advantages of combining high processing speed, such as in the subtraction method, with high fringe sensitivity, such as in the time-averaged method. The optical system for AF-ESPI is then employed to analyze the volume vibration of piezoelectric material for a rectangular parallelepiped configuration. Based on the fact that fringe patterns measured by the AF-ESPI method appear as a clear picture only at the resonant frequency, both the natural frequencies and the out-of-plane and in-plane vibration mode shapes are successfully obtained in this study. Finally, the impedance analysis as well as the finite element method (FEM) with three-dimensional model are also conducted to compare with the result obtained by AF-ESPI. It is shown that the numerical calculation and the experimental result agree fairly well for both the resonant frequency and the mode shape in three-dimensional configurations.

Investigation of the size effect of composite patching repaired on edge-cracked plates

Experimental methods including amplitude fluctuation electronic speckle pattern interferometry (AF-ESPI) and modal testing are combined herein to investigate the patching efficiency of an edge-cracked aluminium alloy plate repaired using a composite patch. In order to optimise the patching geometry, the dimensions of composite patch were selectively extended along the planform dimensions ( x and y), respectively. By virtue of clear variations in mode shapes arising from different patches, preferred composite patches were determined for each mode.

Inverse Evaluation of Material Constants for Composite Plates by Optical Interferometry Method

Electronic speckle pattern interferometry (ESPI) is a powerful tool for the full field, noncontact, and real-time measurement method of surface displacements for deformed bodies. As compared with the conventional film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of ESPI are produced instantly by a video recording system. In this study, the amplitude fluctuation ESPI (AF-ESPI) optical system is used for measuring the resonant frequencies and mode shapes of vibrating composite plates. By making use of the resonant frequencies for free plates obtained experimentally, an inverse evaluation for the material constants is developed using the Rayleigh-Ritz technique and the Simplex method for function minimization. Finally, finite element calculation is used to construct the mode shapes from the obtained material constants by inverse evaluation, and the results are compared with the experimental observations. The experimental method based on optical AF-ESPI setup and the inverse algorithms proposed might become a reliable and self-consistent methodology for evaluating material constants of composite plates.

Experimental investigation of vibration of the shadow mask with different assembly conditions

In this paper, for different assembly conditions, the natural frequencies, mode shapes and amplitude fluctuation electronic speckle pattern interferometry (AF-ESPI) fringe patterns of the shadow mask were obtained and used to visualize the difference among the assembly conditions. Specimens of three groups including one original design, adding welds along the rims of the shadow mask in the direction of the horizontal axis and changing the thickness of the plate spring were investigated. From the AF-ESPI results, except the mode 3, the natural frequencies are increased by adding welding points along the rims in the direction of the horizontal axis. For the case of increasing the thickness of the plate spring, the natural frequencies of all modes are increased. Generally speaking, adding welds improve the vibration behavior for the third, fourth and fifth modes. The first and second modes, however, are predominated by the shadow mask. In addition, the vibration characteristics of the sixth mode is not improved by changing the assembly conditions.