Simultaneous measurement of dynamic displacement and strain in a single fiber using coarse wavelength-division multiplexing and fiber Bragg-grating filter-based sensing system.

Displacement and strain, two of the most important physical quantities in experimental solid mechanics, are seldomly measured simultaneously in a single experimental configuration. In order to provide and improve corresponding sensing techniques, an experimental setup system for simultaneous measurement of dynamic displacement and strain on a flexible cantilever beam using two fiber Bragg gratings (FBGs) in a single fiber is proposed. To realize high-speed multiplexing and demodulation, a configuration incorporating a coarse wavelength-division multiplexing (CWDM) technique and an FBG transmission filter is implemented. The cantilever beam is subjected to steel-ball impact from which the dynamic multipoint displacement/strain sensing performances of the CWDM and FBG filter-based sensing system are demonstrated. Experimental results in temporal and frequency domain are compared with those obtained by the finite element method (FEM) predictions based on identification of the impact-loading history. A noncontact Fotonic displacement sensor and a polyvinylidene-fluoride film (PVDF) strain sensor are also used for comparison. With transient and resonant frequency simulations conducted by the FEM, loading effects of the sensing system are examined. The results obtained in this study indicate that the proposed CWDM and FBG filter-based sensing system is capable of performing simultaneous multipoint displacement/strain measurements in a single fiber with large bandwidth, high sensitivity, and low intensity loss.

Rapid inspection method for measuring interior tilt and decenter in singlet lens.

The objective of this study was to present a high-speed, on-line means of measuring interior tilt and decentration in a singlet lens. We propose a noncontact method based on polarized optics, which provides inspection functions for the practical measurement of lenses. The proposed system was used to measure a tilted and decentered lens, and the results of which showed strong agreement with those obtained in theoretical predictions and CodeV simulations. The proposed method provides a wide field of inspection applicable to lenses with a diameter up to 70 mm. Measurement accuracy is of 0.14 deg/pixel in tilt, and 33 µm/pixel in decentration. Inspection time is only 0.78 s.

High-resolution electronic interferometry for the measurement of in-plane vibration.

This study proposes an algorithm based on the standard deviation in the temporal domain to remove influences from background noise and ambient disturbance and enhance the quality of images obtained using interferometric technology. From measurements of the first ten in-plane resonant frequencies and mode shapes of vibrating zirconate titanate (PZT) laminates, we investigated the resonant characteristics in both the U and V directions. The resulting interference fringes were used to quantify the vibration amplitude of PZT plates on a submicron scale. The resonant frequencies obtained using the proposed method are in excellent agreement with those obtained using the finite element method and an impedance analyzer.

Experimental investigation of the cross-sensitivity and size effects of polyvinylidene fluoride film sensors on modal testing.

Due to advantages such as light weight, flexibility, and low cost, polyvinylidene fluoride (PVDF) films have been widely used in engineering applications as sensors for detecting strain, pressure, or micro-force. However, it is known that PVDF strain sensors have strain cross-sensitivity in mutually orthogonal directions. Furthermore, the size of the PVDF film sensor would also affect the dynamic strain sensing performance. In this paper, to investigate the cross-sensitivity and size effects experimentally, we employ PVDF film sensors to perform dynamic measurements on a cantilever beam. Since the vibrations of the cantilever beam are excited by impacts of a steel ball, the induced highly repeatable transient responses contain a wide range of resonant frequencies and thus can be used to investigate both the size and cross-sensitivity effects of the PVDF film sensors in a dynamic sensing environment. Based on the experimental results of the identified resonant frequencies compared with results obtained from a strain gauge, finite element calculations, and theoretical predictions, suggestions for the use of the PVDF strain sensor in modal testing are given in this paper.

Investigation of the transient behavior of a cantilever beam using PVDF sensors.

In this paper, a PVDF film sensor was used to measure the transient responses of a cantilever beam subjected to an impact loading. The measurement capability of a PVDF sensor is affected by the area of the PVDF film sensor and the signal conditioner (charge amplifier). The influences of these effects on the experimental measurements were investigated. The transient responses for the dynamic strain of the beam were measured simultaneously by the PVDF sensor and a conventional strain gauge. The resonant frequencies of the beam were determined by applying the Fast Fourier Transform on transient results in the time domain of the PVDF sensor and the strain gauge. The experimentally measured resonant frequencies from the PVDF sensor and the strain gauge were compared with those predicted from theoretical and FEM numerical calculations. Based on the comparison of the results measured for these two sensors, the PVDF film sensor proved capable of measuring transient responses for dynamic strain, and its sensitivity is better than that of the strain gauge. Furthermore, almost all the resonant frequencies can be obtained from the results of transient responses for PVDF film.

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.

Performance analysis of a fiber Bragg grating filter-based strain/temperature sensing system based on a modified Gaussian function approximation method.

This paper analyzes the performance of a fiber Bragg grating (FBG) filter-based strain and/or temperature sensing system based on a modified Gaussian function (MGF) approximation method. Instead of using a conventional Gaussian function, we propose the MGF, which can capture the characteristics of the sidelobes of the reflected spectrum, to model the FBG sensor and filter. We experimentally demonstrate that, by considering the contributions of the sidelobes with the MGF approximation method, behaviors of the FBG filter-based FBG displacement and/or temperature sensing system can be predicted more accurately. The predicted behaviors include the saturation, the sensitivity, the sensing range, and the optimal initial Bragg wavelengths of the FBG sensing system.

Dynamic sensing performance of a point-wise fiber Bragg grating displacement measurement system integrated in an active structural control system.

In this work, a fiber Bragg grating (FBG) sensing system which can measure the transient response of out-of-plane point-wise displacement responses is set up on a smart cantilever beam and the feasibility of its use as a feedback sensor in an active structural control system is studied experimentally. An FBG filter is employed in the proposed fiber sensing system to dynamically demodulate the responses obtained by the FBG displacement sensor with high sensitivity. For comparison, a laser Doppler vibrometer (LDV) is utilized simultaneously to verify displacement detection ability of the FBG sensing system. An optical full-field measurement technique called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to provide full-field vibration mode shapes and resonant frequencies. To verify the dynamic demodulation performance of the FBG filter, a traditional FBG strain sensor calibrated with a strain gauge is first employed to measure the dynamic strain of impact-induced vibrations. Then, system identification of the smart cantilever beam is performed by FBG strain and displacement sensors. Finally, by employing a velocity feedback control algorithm, the feasibility of integrating the proposed FBG displacement sensing system in a collocated feedback system is investigated and excellent dynamic feedback performance is demonstrated. In conclusion, our experiments show that the FBG sensor is capable of performing dynamic displacement feedback and/or strain measurements with high sensitivity and resolution.

Improved-bonding linearly chirped fiber grating for a high-sensitivity surface-mounted strain sensor.

For a competitive sensor, both the sensitivity enhancement and calibration convenience are important. However, for surface-mounted fiber grating strain sensors, researchers in previous studies have seldom addressed these two capabilities simultaneously. Using the coupled-mode theory, we calculated the voltage signals from the filtered spectral-power interrogation system for a fiber Bragg grating with a glued grating or with a glue-free grating subject to different strain fields. Under a grating zone (the targeted surface), a one-dimensional linearly varied strain field, described by both the parameters of the average strain and the strain gradient, was considered. Finally, a simple and easy formula is provided (the improved-bonding linearly chirped fiber grating) to achieve both the sensitivity enhancement and calibration convenience at the same time for the strain sensor.

Pointwise fiber Bragg grating displacement sensor system for dynamic measurements.

A method for setting up a fiber Bragg grating (FBG) sensor which can measure the pointwise, out-of-plane or in-plane dynamic displacement is proposed. The proposed FBG sensor is reusable. A multiplexing demodulation system based on a single long-period fiber grating is used in this study. The experimental results of the steady-state motion for a multilayer piezoelectric actuator and the dynamic response of a cantilever beam subjected to impact loadings are presented. These results indicate that the proposed displacement sensor has the ability to measure the out-of-plane dynamic displacement with high sensitivity. Measurements for a piezoceramic plate excited by high frequency show that the proposed displacement sensor also has the ability to provide the in-plane dynamic displacement up to 20 kHz.

Dynamic in-plane resonant characteristics of piezoceramic and piezolaminated composite plates.

Piezolaminated composite plates have received considerable attention in various industrial applications due to their intelligent characteristics. In this investigation, two experimental measurement techniques are used to determine the in-plane resonant vibration of angle-ply laminated composites embedded with a piezoceramic layer (piezolaminated plates) for different stacking angles. The first method is a full-field optical technique, which is called the AF-ESPI (amplitude-fluctuation electronic speckle pattern interferometry). This is the major experimental method. The AF-ESPI method is used to determine the in-plane resonant frequency and corresponding mode shape of a single-layer piezoceramic plate and piezolaminated plates with five different stacking angles. The second experimental technique, the impedance analyzer, is employed to determine the in-plane resonant frequency. Finally, numerical computations based on the finite element analysis are presented for comparison of the two experimental results. Excellent agreement between the experimentally measured data and the numerically calculated results are found for in-plane resonant frequencies and mode shapes. This study indicates that the dynamic characteristics of inplane resonant vibrations for piezolaminated plates with different stacking angles are quite different.

Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs.

Three experimental techniques are used in this study to access the resonant characteristics of piezoceramic bimorphs in parallel and series connections. These experimental 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, point-wise displacement, and electric impedance, respectively. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time by the AF-ESPI method. LDV-DSA is used to determine the resonant frequencies of the vibration mode for out-of-plane motion. The impedance analysis is used to measure the resonant and antiresonant frequencies for in-plane motion. Although the out-of-plane mode is the dominant motion of piezoceramic bimorphs, it is found in this study that the amount of displacement for the in-plane motion in parallel connection is large enough to be measured by AF-ESPI and impedance. It is interesting to note that resonant frequencies of the specimen in parallel connection for the out-of-plane motion determined by LDV-DSA are the same as that for the in-plane motion obtained by impedance. Furthermore, both in-plane and out-of-plane mode shapes for the specimen in parallel connection are obtained in the same resonant frequency from the AF-ESPI method. It is concluded in this study that the particle motions of piezoceramic bimorphs for parallel connection in resonance are essentially three-dimensional. However, it is found that only out-of-plane vibration modes can be excited for the specimen in series connection. Numerical computations based on the finite-element method are presented, and the theoretical predicted results are compared with the experimental measurements. Good agreements between the experimental measured data and numerical calculated results are found for resonant frequencies and mode shapes of the piezoceramic bimorph.

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.

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.

Investigation of polyvinylidene fluoride (PVDF) films in identifying high-frequency vibration modes of flexible plates.

Compared with piezoelectric ceramics such as lead zirconate titanate (PZT) ceramics, the low density and high compliance of the PVDF films make them a more suitable choice in modal testing, especially for detecting high-frequency modes in flexible or inflatable structures. In this work, dynamic sensing performances of PVDF films for flexible structures in modal testing are examined, with considerations including the repeatability of the impact source, the accuracy of the sensing responses, and the influences of the nodal lines on the frequency spectra of the transient responses. Two flexible plates with different boundary conditions and thickness are considered. Experimental results, compared with FEM computations or theoretical predictions, demonstrate the excellent dynamic sensing performance of the PVDF film in modal testing applications, especially for identification of high-frequency modes on flexible structures.

Measurement of resonant mode of piezoelectric thin plate using speckle interferometry and frequency-sweeping function.

This study proposes a frequency-sweeping function of electronic speckle pattern interferometry, based on standard deviation in the temporal domain. The proposed method facilities the measurement of resonant vibration, and provides stable and clear interference fringes. This study investigated the third in-plane eigenmode of a thin piezoelectric plate, using the finite element method and an impedance analyzer to verify the dynamic response obtained using the proposed method. We analyzed the vibration amplitude of interference fringes to obtain quantitative results on the sub-micron scale. The close agreement between the experimental results demonstrates the effectiveness of using the frequency-sweeping function to obtain the resonant states and provides an accurate prediction of resonance. Furthermore, statistical analysis of interference fringes obtained using the subtractive, mean, and the standard deviation method is performed. The result shows that the standard deviation method provides higher quality and stability of fringe pattern.

Experimental measurements and finite element analysis of the coupled vibrational characteristics of piezoelectric shells.

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.