Vibration measurement by the time-averaged electronic speckle pattern interferometry methods

UN-PUNet for phase unwrapping from a single uneven and noisy ESPI phase pattern

The wrapped phase patterns of objects with varying materials exhibit uneven gray values. Phase unwrapping is a tricky problem from a single wrapped phase pattern in electronic speckle pattern interferometry (ESPI) due to the gray unevenness and noise. In this paper, we propose a convolutional neural network (CNN) model named UN-PUNet for phase unwrapping from a single wrapped phase pattern with uneven grayscale and noise. UN-PUNet leverages the benefits of a dual-branch encoder structure, a multi-scale feature fusion structure, a convolutional block attention module, and skip connections. Additionally, we have created an abundant dataset for phase unwrapping with varying degrees of unevenness, fringe density, and noise levels. We also propose a mixed loss function MS_SSIM + L2. Employing the proposed dataset and loss function, we can successfully train the UN-PUNet, ultimately realizing effective and robust phase unwrapping from a single uneven and noisy wrapped phase pattern. We evaluate the performance of our method on both simulated and experimental ESPI wrapped phase patterns, comparing it with DLPU, VUR-Net, and PU-M-Net. The unwrapping performance is assessed quantitatively and qualitatively. Furthermore, we conduct ablation experiments to evaluate the impact of different loss functions and the attention module utilized in our method. The results demonstrate that our proposed method outperforms the compared methods, eliminating the need for pre-processing, post-processing procedures, and parameter fine-tuning. Moreover, our method effectively solves the phase unwrapping problem while preserving the structure and shape, eliminating speckle noise, and addressing uneven grayscale.

Noncontact vibration measurement using three spatial-frequency shifting coherent digital holography

A new digital coherent holographic system that works as a spatial-frequency shifter for measuring three-dimensional (3D) vibration of an object is proposed. The spatial-frequency shifter is constructed by a system of three mirrors inclined with different small angles to shift the object wave to three different frequencies in the spatial-frequency domain. By applying the Fourier transform method and appropriate filters to the hologram recorded by the camera of the system, a three-phase set of object waves corresponding to three shifted frequencies was obtained. From the relation between the phases and the relative position of the object, the position of each point on the surface of the object along the x, y, and z directions was extracted from each hologram. The same process was repeatedly applied to a series of holograms recorded by a fast camera, allowing the 3D vibration of the object to be precisely observed.

Three-Dimensional Digital Image Correlation Based on Speckle Pattern Projection for Non-Invasive Vibrational Analysis

Non-contact vibration measurements are relevant for non-invasively characterizing the mechanical behavior of structures. This paper presents a novel methodology for full-field vibrational analysis at high frequencies using the three-dimensional digital image correlation technique combined with the projection of a speckle pattern. The method includes stereo calibration and image processing routines for accurate three-dimensional data acquisition. Quantitative analysis allows the extraction of several deformation parameters, such as the cross-correlation coefficients, shape and intensity, as well as the out-of-plane displacement fields and mode shapes. The potential of the methodology is demonstrated on an Unmanned Aerial Vehicle wing made of composite material, followed by experimental validation with reference accelerometers. The results obtained with the projected three-dimensional digital image correlation show a percentage of error below 5% compared with the measures of accelerometers, achieving, therefore, high sensitivity to detect the dynamic modes in structures made of composite material.

Efficient ESPI method to identify vibration characteristics of transparent films

Electronic speckle pattern interferometry (ESPI) has been frequently used to study vibration characteristics of engineering structures. However, efficient ESPI methods for identifying the vibration characteristics of transparent membranes are rarely reported. A convenient approach to determine the resonant frequencies and the vibration modes of transparent films is proposed. A quasi-common-path ESPI (QCP-ESPI) is developed to detect out-of-plane deformation and visualize vibrational modes of a vibrating transparent diaphragm. An amplitude-modulation-based method is proposed for quick and accurate determining resonance of oscillating objects during frequency scanning. Experimental performances demonstrate the feasibility and efficiency of the QCP-ESPI and amplitude-modulation-based methods for determining the resonant frequency and vibration modes of transparent objects.

LDV-induced stroboscopic digital image correlation for high spatial resolution vibration measurement

Vibration measurement, particularly mode shape measurement, is an important aspect of structural dynamic analysis since it can validate finite element or analytical vibration models. Scanning laser Doppler vibrometry (LDV) and high-speed digital image correlation have become dominant methods for experimental mode shape measurement. However, these methods have high equipment costs and several disadvantages regarding spatial or temporal performance. This paper proposes a laser Doppler vibrometer induced stroboscopic digital image correction for non-contact mode shape and operational deflection shape measurement. Our results verify that single-point LDV and normal rate cameras can be used obtain high spatial resolution mode shape and operational deflection shape. Measurement frequency range is much higher than the camera capturing rate. We also show that the proposed approach coincides well with time-averaged electronic speckle pattern interferometry.

Measurement of micro-harmonic vibration from optical feedback interferometry using wavelet trend analysis

Self-mixed optical feedback interferometry based laser sensors show promising results in the measurement of the vibration frequency. To date several measurement methods have been developed to extract the vibration information from the self-mixed (SM) signal; however, the complexity and accuracy of the methods still need improvement. The presented work tries to fulfill the gap by realizing a novel method using maximal overlap discrete wavelet transformation (MODWT) and multi-resolution analysis (MRA). The proposed method can reconstruct the micro-harmonic (< 5 μ m ) vibration up to 1 kHz even under weak feedback conditions. The mean squared error and the maximum relative error of the proposed method for this range remained below 1.89 × 1 0 - 3 & 8.79%, respectively. Although, above 1 kHz, the proposed method turns out to be futile to reconstruct the vibration signal but still capable to measure vibration frequency up to 10 kHz with an accuracy of ± 0.0001. The method also found suitable to measure non-sinusoidal vibration frequency with reasonable accuracy even for the moderate feedback conditions. The authors envision that the proposed method will provide a compact, non-contact, and low-cost alternative for the vibration frequency measurement hence useful in early fault detection schemes and lung abnormality diagnosis.

Speckle denoising by variant nonlocal means methods

This study aims to demonstrate the performances of nonlocal means (NLM) and their variant denoising methods, mainly focusing on NLM-shaped adaptive patches and several NLM-reprojection schemes for speckle noise reduction in amplitude and phase images of the digital coherent imaging systems. In the digital coherent imaging systems such as digital speckle pattern interferometry, digital holographic interferometry, etc., the image quality is severely degraded by additive uncorrelated speckle noise, due to the coherent nature of the light source, and therefore limits the development of several applications of these imaging systems in many fields. NLM and its variant denoising methods are employed to denoise the intensity/phase images obtained from these imaging systems, and their effectiveness is evaluated by considering various parameters. The performance comparison of these methods with other existing speckle denoising methods is also presented. The performance of these methods for speckle noise reduction is quantified on the basis of two criteria matrices, namely, the peak-to-signal noise ratio and the image quality index. Based on these criteria matrices, it is observed that these denoising methods have the ability to improve the intensity and phase images favorably in comparison to other speckle denoising techniques, and these methods are more effective and feasible in speckle-noise reduction.

DIC/Moiré hybrid method based on regular patterns for deformation measurement

Digital Image Correlation (DIC) is a superior optical method to measure the surface deformation with a high accuracy. Currently, most researches on DIC are based on random patterns. In this paper, A DIC/Moiré hybrid method using regular patterns is proposed for deformation measurement. In this method, a Moiré fringe technique based on correlation coefficient is developed to provide accurate initial deformation estimation for DIC. Experimental results indicate a higher computational efficiency by the proposed method than the conventional DIC method. It is also found that the calculation accuracy increases using regular patterns. The advantage of obtaining accurate initial estimation by the DIC/Moiré hybrid method may enable potential application in deformation measurements.

Speckle noise reduction in digital speckle pattern interferometric fringes by nonlocal means and its related adaptive kernel-based methods

Digital speckle pattern interferometry (DSPI) is widely used in many scientific and industrial applications. Besides its several advantages, one of the basic problems encountered in DSPI is the undesired speckle noise existing in the fringe pattern. In this paper, we demonstrate the performance of nonlocal means (NLM) and its related adaptive kernel-based filtering methods for speckle noise reduction in DSPI fringes. The NLM filter and its related kernel-based filters such as NLM-average, NLM-local polynomial regression, and NLM-shape adaptive patches are implemented first on simulated DSPI fringes, and their performances are quantified on the basis of peak signal-to-noise ratio (PSNR), mean square error (MSE), and quality index (Q). Further, their effectiveness and abilities in reducing speckle noise are compared with other speckle denoising methods. These filtering methods are then employed on experimental DSPI fringes. The obtained results reveal that these filtering methods have the ability to improve the PSNR and Q of the DSPI fringes and provide better visual and quantitative results. It is also observed that the proposed filtering methods preserve the edge information of the DSPI fringes, which is evaluated on the basis of the edge preservation index of the resultant filtered images.

General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition

Filtering off speckle noise from a fringe image is one of the key tasks in electronic speckle pattern interferometry (ESPI). In general, ESPI fringe images can be divided into three categories: low-density fringe images, high-density fringe images, and variable-density fringe images. In this paper, we first present a general filtering method based on variational image decomposition that can filter speckle noise for ESPI fringe images with various densities. In our method, a variable-density ESPI fringe image is decomposed into low-density fringes, high-density fringes, and noise. A low-density fringe image is decomposed into low-density fringes and noise. A high-density fringe image is decomposed into high-density fringes and noise. We give some suitable function spaces to describe low-density fringes, high-density fringes, and noise, respectively. Then we construct several models and numerical algorithms for ESPI fringe images with various densities. And we investigate the performance of these models via our extensive experiments. Finally, we compare our proposed models with the windowed Fourier transform method and coherence enhancing diffusion partial differential equation filter. These two methods may be the most effective filtering methods at present. Furthermore, we use the proposed method to filter a collection of the experimentally obtained ESPI fringe images with poor quality. The experimental results demonstrate the performance of our proposed method.

Methods of phase reconstruction for time-averaging electronic speckle pattern interferometry

Electronic speckle pattern interferometry is useful for the qualitative depiction of the deformation profile of harmonically vibrating objects. However, extending the process to achieve quantitative results requires unwrapping the phase in the interferogram, which contains significant noise due to the speckle. Two methods to achieve accurate phase information from time-averaged speckle pattern interferograms are presented. The first is based on a direct inverse of the regions within corresponding phase intervals, and the second is based on optimization of four independent parameters. The optimization method requires less time than more commonly used algorithms and shows higher precision of the resulting surface displacement.

Time-averaged photon-counting digital holography

Time-averaged holography has been using photo-emulsions (early stage) and digital photo-sensitive arrays (later) to record holograms. We extend the recording possibilities by utilizing a photon-counting camera, and we further investigate the possibility of obtaining accurate hologram reconstructions in rather severe experimental conditions. To achieve this, we derived an expression for fringe function comprising the main parameters affecting the hologram recording. Influence of the main parameters, namely the exposure time and the number of averaged holograms, is analyzed by simulations and experiments. It is demonstrated that taking long exposure times can be avoided by averaging over many holograms with the exposure times much shorter than the vibration cycle. Conditions in which signal-to-noise ratio in reconstructed holograms can be substantially increased are provided.

Experimental investigation on butane diffusion flames under the influence of magnetic field by using digital speckle pattern interferometry

In this paper, the effect of magnetic fields on the temperature and temperature profile of a diffusion flame obtained from a butane torch burner are investigated experimentally by using digital speckle pattern interferometry (DSPI). Experiments were conducted on a diffusion flame generated by a butane torch burner in the absence of a magnetic field and in the presence of uniform and nonuniform magnetic fields. A single DSPI fringe pattern was used to extract phase by using a Riesz transform and monogenic signal. Temperature inside the flame was determined experimentally both in the absence and in the presence of magnetic fields. Experimental results reveal that the maximum temperature of the flame is increased under the influence of an upward-decreasing magnetic gradient and decreased under an upward-increasing magnetic gradient while a negligible effect on temperature in a uniform magnetic field was observed.

Interferometric dynamic measurement: techniques based on high-speed imaging or a single photodetector

In recent years, optical interferometry-based techniques have been widely used to perform noncontact measurement of dynamic deformation in different industrial areas. In these applications, various physical quantities need to be measured in any instant and the Nyquist sampling theorem has to be satisfied along the time axis on each measurement point. Two types of techniques were developed for such measurements: one is based on high-speed cameras and the other uses a single photodetector. The limitation of the measurement range along the time axis in camera-based technology is mainly due to the low capturing rate, while the photodetector-based technology can only do the measurement on a single point. In this paper, several aspects of these two technologies are discussed. For the camera-based interferometry, the discussion includes the introduction of the carrier, the processing of the recorded images, the phase extraction algorithms in various domains, and how to increase the temporal measurement range by using multiwavelength techniques. For the detector-based interferometry, the discussion mainly focuses on the single-point and multipoint laser Doppler vibrometers and their applications for measurement under extreme conditions. The results show the effort done by researchers for the improvement of the measurement capabilities using interferometry-based techniques to cover the requirements needed for the industrial applications.

Continual mechanical vibration trajectory tracking based on electro-optical heterodyne interferometry

Vibration is one of the confused problems in many fields. To give a comprehensive analysis of vibration, an electro-optical heterodyne interferometry with temporal intensity analysis method that can track the trajectory of the vibration dynamically has been built in this paper. The carrier frequency is introduced by the electrically controlled electro-optical frequency shifter. The trajectory is obtained by using temporal evolution of the light intensity in heterodyne interferometry. The instantaneous displacement of the vibration is extracted with spectral analysis technique. No target mirror and moving parts are required in our self-developed system. The principle and system configuration are described. The simulations and the preliminary experiments have been performed and the results show that this trajectory tracking system is high-efficiency, low-cost, jamproof, robust, precise and simple.

High-frequency resonant characteristics of triple-layered piezoceramic bimorphs determined using experimental measurements and theoretical analysis

This is an experimental, theoretical, and numerical investigation of vibration characteristics in high-frequency resonance, which are studied for parallel- and series-type piezoelectric bimorphs. In the experimental measurements, the full-field optical technique known as electronic speckle pattern interferometry (ESPI) is used to measure the transverse (out-of-plane) and planar (in-plane) resonant frequencies and corresponding mode shapes for piezoelectric bimorphs. In addition, in-plane resonant frequencies are obtained from impedance analysis and the response curves of the frequency spectra show different vibration characteristics of the piezoelectric bimorphs with different electrical connections. Piezoelectric bimorphs with normal connections have three-dimensional coupled vibration characteristics and the out-of-plane vibration dominates the motion. However, only in-plane vibration motions can be excited in the high-frequency range for abnormal connections, and the resonant characteristics are similar to the single-layered piezoelectric plate. The triple-layered piezoelectric bimorphs with abnormal connection are also analyzed using theoretical analysis. The resonant frequencies, mode shapes, and normalized displacements are calculated based on the analytical solution. The experimental results and the theoretical analysis are in good agreement with the numerical calculations using the finite element method. From the discussion of the results for the parallel- and series-type piezoelectric bimorphs with normal and abnormal connections, the vibration characteristics at high frequencies are completely analyzed in this study.

Mode-shape measurement of piezoelectric plate using temporal speckle pattern interferometry and temporal standard deviation

This study proposes an image processing method to improve the quality of interference fringes in mode-shape measurement using temporal speckle pattern interferometry. A vibrating piezoelectric plate at resonance was investigated, and the full-field optical information was saved as a sequence of images. According to derived statistical properties, an algorithm was developed to remove noise from both the background and disturbance, resulting in high-resolution images of excellent quality. In addition, the resonant frequency and mode shape obtained using the proposed algorithm demonstrate excellent agreement with theoretical results obtained by the finite element method.

Dynamic phase evaluation in sparse-sampled temporal speckle pattern sequence

The rapid progress of modern manufacturing technology has posed stringent requirements for inspecting techniques for vibration characterization and dynamic testing. Because of its simplicity, accuracy, and whole-field character, speckle interferometry has served as one of the major techniques for dynamic measurement, where normally a dense-sampled temporal speckle sequence is captured for phase retrieval using Fourier or wavelet transforms. In this Letter, a method is proposed for phase evaluation of sparse-sampled speckle patterns when the sampling rate is lower than two points per temporal cycle. Dynamic experiments using a high-speed camera demonstrated the effectiveness of the proposed method for complicated wrapped phase retrieval in electronic/digital speckle pattern interferometry.

Experimental and numerical investigations of vibration characteristics for parallel-type and series-type triple-layered piezoceramic bimorphs

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.

Time-average TV holography for vibration fringe analysis

Time-average TV holography is widely used method for vibration measurement. The method generates speckle correlation time-averaged J0 fringes that can be used for full-field qualitative visualization of mode shapes at resonant frequencies of an object under harmonic excitation. In order to map the amplitudes of vibration, quantitative evaluation of the time-averaged fringe pattern is desired. A quantitative evaluation procedure based on the phase-shifting technique used in two beam interferometry has also been adopted for this application with some modification. The existing procedure requires a large number of frames to be recorded for implementation. We propose a procedure that will reduce the number of frames required for the analysis. The TV holographic system used and the experimental results obtained with it on an edge-clamped, sinusoidally excited square aluminium plate sample are discussed.

The influence of electrode designs on the resonant vibrations for square piezoceramic plates

In this paper, the resonant vibrations of square piezoceramic plates with four different electrode designs are investigated. Two experimental techniques, the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and the impedance analysis, are used to access the influence of the electrode arrangement on the resonant characteristics of square piezoceramic plates. Both the out-of-plane and in-plane resonant frequencies and full-field mode shapes of piezoceramic plates with various electrode designs are obtained from the AF-ESPI method. The impedance analyzer is used to measure the resonant and antiresonant frequencies of piezoceramic plates. The dynamic electromechanical coupling coefficient (EMCC), which relates to the ability of conversion between mechanical and electrical energy, is determined from the measured values of resonant and antiresonant frequencies. Experimental results of the resonant vibration characteristics of the square piezoceramic plates are verified by numerical computations based on the finite-element method. Excellent agreement between the experimental and numerical results is found in resonant frequencies and corresponding mode shapes. It is found that the electrode design has important influence on the resonant characteristics of piezoceramic plates. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.

Theoretical, numerical, and experimental investigation on resonant vibrations of piezoceramic annular disks

In this study, vibration characteristics of thin piezoceramic annular disks with stress-free boundary conditions are investigated by theoretical analysis, numerical simulation, and experimental measurement. The nonaxisymmetric, out-of-plane (transverse), and axisymmetric in-plane (tangential and radial extensional) vibration modes are discussed in detail in terms of resonant frequencies, mode shapes, and electrical currents. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), as well as the electrical impedance measurement are used to validate the analytical results. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be determined by the impedance analysis; hence, only resonant frequencies of extensional vibration modes are presented from the impedance analyzer. The LDV system is used to measure the resonant frequencies of transverse vibrations. However, both the transverse and extensional vibration modes and resonant frequencies of piezoceramic annular disks are obtained by the AF-ESPI method, and the interferometric fringes are produced instantly by a video recording system. Numerical results obtained by finite-element calculations are compared with those from theoretical analysis and experimental measurements. It is shown that the theoretical predictions of resonant frequencies and the corresponding mode shapes agree well with the experimental results. Good agreement between the predicted and measured electrical impedance also is found. The dependence of resonant frequencies and dynamic electromechanical coupling coefficients on the inner-to-outer radius ratio also is analyzed and discussed in this study.

Some opportunities for vibration analysis with time averaging in digital Fresnel holography

Features offered by the combination of time averaging and digital Fresnel holography are investigated. In particular, we introduce the concept of the zero-crossing phase of Bessel fringes, which allows a highly contrasted determination of the dark fringes in the hologram. We discuss some particularities of the digital reconstruction and show how time-averaged digital holography can be used to study vibration drifts. Experiment results are presented in the case of a loudspeaker under a sinusoidal excitation; digital and analogical holography are also compared.

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.

Vibration characteristics of composite piezoceramic plates at resonant frequencies: experiments and numerical calculations

The experimental measurement of the resonant frequencies for the piezoceramic material is generally performed by impedance analysis. In this paper, we employ an optical interferometry method called the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) to investigate the vibration characteristics of piezoceramic/aluminum laminated plates. The AF-ESPI is a powerful tool for the full-field, noncontact, and real-time measurement method of surface displacement for vibrating bodies. As compared with the conventional film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes are obtained experimentally at the same time. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. Two different configurations of piezoceramic/aluminum laminated plates, which exhibit different vibration characteristics because of the polarization direction, are investigated in detail. From experimental results, we find that some of the out-of-plane vibration modes (Type A) with lower resonant frequencies cannot be measured by the impedance analysis; however, all of the vibration modes of piezoceramic/aluminum laminated plates can be obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. Excellent agreements of the resonant frequencies and mode shapes are obtained for both results.

Experimental and numerical investigations of resonant vibration characteristics for piezoceramic plates

Electronic speckle pattern interferometry (ESPI) is a full field, non-contact technique for measuring the surface displacement of a structure subjected to static loading or, especially, to dynamic vibration. In this article we employ an optical system called the amplitude-fluctuation ESPI with out-of-plane and in-plane measurements to investigate the vibration characteristics of piezoceramic plates. Two different configurations of piezoceramic plates, namely the rectangular and the circular plates, are discussed in detail. 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. Because the clear fringe patterns will be 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. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes is demonstrated. The resonant frequencies of the piezoceramic plates are also measured by the conventional impedance analysis. From experimental results, we find that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by the impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extensional) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. It is shown that the numerical calculations and the experimental results agree fairly well for both the resonant frequencies and the mode shapes.

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.