Amplitude-fluctuation Electronic Speckle Pattern Interferometry Research Articles

Solid-liquid coupling of in-phase and out-of-phase vibrations for two piezoelectric disks

Theoretical analysis is used to solve the solid–liquid coupled vibration characteristics for two piezoelectric disks in a limited space and verified with experimental measurements. Based on the Navier–Stoke equation and equilibrium of motion, the Rayleigh-Ritz and energy methods were developed to analyze the solid–liquid coupled system. Following an entire systematic procedure, two piezoelectric disks immersed in hydrostatic compressible fluids were analyzed using the piezoelectric constitutive equation to perform the in-phase and out-of-phase vibration. The full-field, non-contact, optical technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), was applied to experimentally measure the vibration properties in a solid–liquid coupling system, including the mode shapes and resonant frequencies. The experimental results are presented in good agreement with the theoretical solutions and finite element calculations. Under the solid–liquid coupled system, the distributions of pressure fields and velocity vectors of fluids were also determined in the correspondent vibrating modes. Finally, it is interesting to show the tendency to close the same resonant frequency both on the in-phase and out-of-phase vibrations when the fluid depth increases. The research outcomes can provide a guide in the design of hydrostatic components.

Theoretical, numerical and experimental investigation into vibration characteristics for composite structures of an annular membrane internally connected with a piezoceramic disk

Abstract This work analyzed the vibration characteristics of an annular membrane internally connected with a piezoceramic disk theoretically, numerically and experimentally. The general solution for the free vibration of an annular membrane under uniform tension was derived. Then, the displacement solutions for the piston modes and coupled modes of an annular membrane internally connected with a piezoceramic disk were derived. Two plate theories, Kirchhoff and Mindlin plate theories, were used to simulate the piezoceramic disk. The theoretical results are compared with the numerical results obtained from two finite element software packages: ABAQUS and COMSOL. The amplitude-fluctuation electronic speckle pattern interferometry was used to measure the resonant frequencies and associated mode shapes of five different type specimens with different sizes. Good agreements of dynamic characteristics determined by theoretical analysis, experimental measurements, and numerical calculation are presented for the annular membrane internally connected with piezoceramic disk structures.

Identification of defects in composite laminates by comparison of mode shapes from electronic speckle pattern interferometry

A novel technique for identifying defects in carbon fibre reinforced plates has been developed. Firstly, modal analysis by impact excitation was performed to obtain the first five resonant frequencies for three defect-free and three defective specimens with in-plane fibre waviness. Then amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) was used to obtain the mode shapes at these frequencies. The contours of the nodal regions visible in the mode shapes were extracted using a specially-developed algorithm employing density-based spatial clustering of applications with noise (DBSCAN). Fourier descriptors, that are invariant to rotations, translations, and scaling, were used to decompose the contours to reduce data dimensionality and make comparisons. The differences in contours between the two sets of specimens showed that the 4th and 5th mode shapes can be used for identifying the presence of the waviness defects. This technique for nodal region comparison was found to greatly simplify the comparison of fringe patterns for the purpose of damage assessment and could potentially be used as part of validation procedures.

Vibration characteristics of pipe based on panoramic amplitude-fluctuation electronic speckle pattern interferometry

The vibration characteristics of inner circular pipe surfaces were determined using the panoramic amplitude-fluctuation electronic speckle pattern interferemetry. A conical mirror was used to collect the inner surface information based on the reflection imaging principle. The planar image was converted into a spatial panoramic view after coordinate transformation, followed by 360° panoramic vibration information reconstruction. The modal measurement was carried out by the proposed method and compared with a numerical simulation and acoustic tests. The results demonstrated the accuracy and feasibility of the proposed method. To understand the influence of defects on vibration characteristics, prefabricated cracks with different lengths along axial and annular directions were introduced. The experimental results demonstrated that annular cracks had little effect on the mode shape. In contrast, the original repetition frequency characteristics were heavily influenced by the axial crack. Furthermore, the vibration modes exhibited veering and the natural frequency decreased significantly owing to the defect.

Panoramic amplitude-fluctuation electronic speckle pattern interferometry system for inner vibration measurement

We propose a panoramic vibration measurement system for the inner cylindrical surface of an object based on amplitude fluctuation electronic speckle pattern interferometry and developed according to the Michelson interference configuration. A conical mirror, aligned to the axis of the inner cylindrical surface, is illuminated to transform a single camera view into a panoramic view. After transposing the observation coordinate system, a complete inner 360-deg vibration pattern can be reconstructed. The principle of transformation from a Cartesian-coordinate system to a cylindrical-coordinate system is introduced in detail. The panoramic vibration of the inner circular tube is determined, and the first six modes are analyzed. The comparison and error analysis of the proposed system with the ANSYS simulation results prove the accuracy and feasibility of the system.

Analytical solution for the vibration characteristics of a partially immersed plate with experimental investigation on wet mode shapes

The objective of this paper was to investigate the relationship between dry mode shapes and the distortions associated with wet mode shapes base on theoretical analysis. The superposition method was used to construct the theoretical results of vibration behavior for cantilever plates. Flow field pressure was derived using an equation governing the behavior of incompressible fluids in a finite container. Analytic solutions for vibrations in a cantilever plate in air served as the fundamental function of the thin plate partially immersed in the liquid. We then used fluid pressure, and the deflection of the thin plate for the construction of frequency response functions for the analysis of vibration characteristics in the fluid-plate coupling system. Two powerful experimental measuring methods referred to as amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and the fiber Bragg grating (FBG) sensor were used to measure the resonant frequencies and wet mode shapes. A detailed investigation on the distortion phenomena of cantilever plate with different levels of submergence is presented. Effects of a solid wall on the vibrating plate are also discussed by the experimental measurement and theoretical analysis. Comparison of the results from theoretical analysis, finite element method, and experimental measurements confirmed the accuracy of our theoretical analysis. Our methodology provided an intuitive method to discuss the distortion phenomena of partially submerged plates based on the relationship between dry and wet mode shapes.

Theoretical analysis by Mindlin theory and experimental measurements of the piezoceramic circular bimorphs in resonance

This paper investigates the free vibration characteristics for piezoceramic bimorphs in series connections by using theoretical analysis, numerical calculation, and experimental measurement. Series- and parallel-type piezoceramic bimorphs under fully-clamped boundary conditions are analyzed in this study. The theoretical solutions are derived base on the Mindlin's plate theory to explore the coupled out-of-plane (transverse) and in-plane (planar) resonant vibration characteristics; the numerical calculations based upon finite-element method are also performed and agree very well with the theoretical results for resonant frequency and corresponding mode shape. Two optical techniques, amplitude- fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), and an impedance analysis are used to validate the theoretical and numerical results. It is shown that there is no difference between theoretical and numerical results regarding vibration characteristics of series- and parallel-type piezoceramic bimorphs. However, the experimental findings obtained by impedance analysis reveal that the boundary condition plays an important role for the excited vibration modes of parallel-type piezoceramic bimorphs. The imperfect clamped-circumference simulation in experimental procedure will result in some unexpected vibration modes arising, which can be distinguished between out-of-plane and in-plane modes by AF-ESPI measurement.

Efficient excitation of transverse vibrational modes using improved configurations of PFCs connected to an isotropic plate

In this work, we investigate efficient excitations of transverse (out-of-plane) vibrations of isotropic rectangular plates using piezoelectric fiber composites (PFCs) by experimental measurement. Four PFCs are separately bonded on a rectangular plate with four configured electrode connections to excite transverse vibration of the plate. The proposed configurations of the PFCs, including placements and electrode connections, are inspired by efficient transverse excitations of piezoelectric rectangular plates, whose mode shapes can be divided into four groups and whose electromechanical coupling efficiency can be largely improved by designs of partial electrodes. To visually demonstrate the excitation efficiency, an amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) measurement technique is set up to obtain full-field transverse mode shapes. Other than AF-ESPI, a laser Doppler vibrometer (LDV) displacement sensing system is employed to investigate the excitation performances of the PFCs according to resonant frequencies with emphasis on the influences of the measured nodal lines of the plate. The experimental results presented in this study indicate that the excitation efficiency of the transverse vibrations in flexible structures can be improved by bonding distributed PFCs with configured electrode connections. In addition, we show that the vibrations of isotropic rectangular plates can be related to those of piezoelectric rectangular plates, from the experimental modal excitation point of view.

Experimental and theoretical investigations on sensing and dynamic characteristics of PVDF thin film

Abstract This research investigates both the steady-state and transient dynamic characteristics of polyvinylidene fluoride (PVDF), which is one of the most commonly used piezoelectric polymers. In steady-state vibration, the visible resonant mode fringe patterns are obtained using the amplitude-fluctuation electronic speckle pattern interferometry experiment, and the point-wise displacement data are measured by laser Doppler vibrometer–dynamic signal analysis. Finite element analysis is also performed, and the numerical results are compared with the experimental ones for the steady-state vibration. In a transient dynamic experiment, the history of dynamic impact generated by a steel ball is measured by the PVDF, and the experimental results are compared with the theoretical results obtained by the Hertz contact law. The comprehensive information about steady-state and transient dynamic properties of PVDF membranes obtained in this study is expected to contribute to the further development of the PVDF piezoelectric element.

Resonant Frequency Reduction of Piezoelectric Voltage Energy Harvester by Elastic Boundary Condition

ABSTRACTMost vibration-based energy harvesters, including piezoelectric harvester system, perform efficiently at only its resonant frequency as linear resonators, usually at very high frequency which are out of the range of frequency of interest. In real life applications, these linear resonators are impractical since real ambient vibrations are simply having varying lower frequencies. Hence, design a tuneable vibration energy harvester at a lower and useful frequency range of interest are essential in allowing promising energy output to meet intended power input at a more practical approach. In this paper, the piezoelectric voltage energy harvester (PVEH) was designed with a flexible fixture with the aim to reduce its first fundamental natural frequency. Two thickness of elastic fixtures were applied to generate power on PVEH. Three experimental techniques were used to measure the vibration characteristics of PVEH. First, the full-field optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) measured simultaneously the resonant frequencies and mode shapes. This is followed by the pointwise measurement system, laser Doppler vibrometer (LDV) in which the resonant frequencies were measured by dynamic signal swept-sine analysis. The resonant frequencies and anti-resonant frequencies were also obtained by impedance analysis. The results obtained from experimental measurements were compared with finite element numerical calculation. It is found that the boundary conditions under the elastic fixtures can effectively reduce the resonant frequency of the PVEH with a reasonable voltage output. The fundamental natural frequency of PVEH with the thickness of 0.58-mm elastic fixture is reduced to 37 Hz maintaining at 7.1 volts (1.2 mW), in comparison with the natural frequency on cantilevered PVEH at 78 Hz that produces 7.7 volts (6.5 mW).

Experimental and Numerical Investigation of Resonance Characteristics of Novel Pumping Element Driven by Two Piezoelectric Bimorphs

This paper describes the vibration characteristics of a dual-bimorph piezoelectric pumping element under fluid–structure coupling. Unlike the single bimorph used in most previous studies, the proposed device comprises two piezoelectric bimorphs within an acrylic housing. Amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) was used to examine the visible displacement fringes in order to elucidate the anti-phase as well as in-phase motions associated with vibration. Analysis was also conducted using impedance analysis and laser Doppler vibrometer (LDV) based on the measurement of point-wise displacement. The experimental results of resonant frequencies and the corresponding mode shapes are in good agreement with those obtained using finite element analysis. The gain of flow rate obtained by the anti-phase motion of the dual-bimorph pumping element is larger than both those obtained by in-phase motion and the single bimorph pumping element. This work greatly enhances our understanding of the vibration characteristics of piezoelectric pumping elements with two bimorphs, and provides a valuable reference for the further development of bionic pump designs.

Experimental and Numerical Investigation on Vibration of Sandwich Plates with Honeycomb Cores Based on Radial Basis Function

The vibration characteristic of the sandwich plate with a honeycomb core was investigated by experimental measurements and numerical calculation based on radial basis function (RBF). RBF method was used not only in the meshless approach but also in the post-processing of the experimental data. During the experiment, amplitude-fluctuation electronic speckle pattern interferometry was applied to access the resonant frequencies and the corresponding vibration mode shapes simultaneously. Then RBF method was used to improve the quality of patterns and reconstruct the out-of-plane vibration amplitude after fringe analysis. As for numerical calculation, the modal parameters were numerically predicted using the first-order shear deformation theory. The computation approach was based on collocation with multi-quadric radial basis function. To understand the influence of the thickness of face sheet on dynamic behaviors, three types of specimens with different thickness were tested and analyzed. Of particular interest was that the vibration modes show veering due to the thickness increment. Furthermore, the numerical predicted results were compared with the experimental measurements for the first five modes. They are in good agreement with each other for resonant frequencies, mode shapes and relative out-of-plane amplitudes.

Theoretical analysis based on fundamental functions of thin plate and experimental measurement for vibration characteristics of a plate coupled with liquid

This study combined theoretical, experimental, and numerical analysis to investigate the vibration characteristics of a thin rectangular plate positioned horizontally at the bottom of a rectangular container filled with liquid. Flow field pressure was derived using an equation governing the behavior of incompressible fluids. Analytic solutions to vibrations in a thin plate in air served as the fundamental function of the thin plate coupled with liquid. We then used liquid pressure, and the out-of-plane deflection of the thin plate for the construction of frequency response functions for the analysis of vibration characteristics in the liquid-plate coupling system. Two experimental methods were employed to measure the vibration characteristics of the thin plate immersed in water. The first involved using sensors of polyvinylidene difluoride (PVDF) to measure transient signals of fluid-plate system subjected an impact at the thin plate. These were then converted to the frequency domain in order to obtain the resonant frequencies of the fluid-plate coupling system. The second method was amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), which was used to measure the dynamic characteristics of the thin plate in the flow field. This method was paired with the image processing techniques, temporal speckle pattern interferometry (TSPI) and temporal standard deviation (TSTD), to obtain clear mode shapes of the thin plate and resonant frequencies. Comparison of the results from theoretical analysis, finite element method, and experimental measurements confirmed the accuracy of our theoretical analysis, which was superior to the conventional approach based on beam mode shape functions. The experimental methods proposed in this study can be used to measure the resonant frequencies of underwater thin plates, and clear mode shapes can be obtained using AF-ESPI. Our results indicate that the resonant frequencies of thin plates underwater are lower than those in air. To a limited extent, increasing the depth of water enhanced the reduction of resonant frequencies.

Investigations of the transverse vibration characteristics of piezoceramic circular plates with V-notches

This article pertains to experimental validation of the study presented in a previous paper by the same authors , in which the transverse vibration characteristics of piezoceramic circular plates with V-notches were investigated theoretically using Ritz’s method incorporating defined equivalent constants. For experimental measurement, two optical methods – amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometry (LDV) – were employed to conceptualize the analytical results. The AF-ESPI method demonstrates the advantages of combining high fringe sensitivity and noise reduction, which are achieved using the time-averaged and subtraction electronic speckle pattern interferometry methods, respectively. Both vibration mode shapes and resonant frequencies of V-notched piezoceramic plates were obtained using the AF-ESPI method; in addition, the resonant frequencies were also determined quickly using the LDV method. By varying the corner angles and notch–depth ratios, various types of piezoceramic plate (V-notched, sectorial, semicircular, segmented, and sharp-notched) were used for experimental measurements. Numerical calculations were performed using the finite element method, and the results were compared with the experimental measurements and theoretical predictions. It was shown that the resonant frequencies and mode shapes obtained using the two experimental methods agreed fairly closely with the theoretical and numerical results.

Vibrational mode and sound radiation of electrostatic speakers using circular and annular diaphragms

This study modeled two diaphragms comprising a pair of indium tin oxide (ITO) transparent plates sandwiching a vibrating diaphragm to create circular (30mm radius) and annular (30mm outer and 3mm inner radius) push–pull electrostatic speakers. We then measured the displacement amplitudes and mode shapes produced by the devices. Vibration characteristics were used to predict sound pressure levels (SPLs) using the lumped parameter method (LPM) and distributed parameter method (DPM). The two measurement results obtained using a laser system were compared to the SPLs obtained using traditional acoustic measurement (AM) from 20Hz to 20kHz in order to verify our predictions. When using LPM and DPM, the SPL prediction results in the first three symmetric modes were in good agreement with the AM results. Under the assumption of linear operations, the DPM and amplitude-fluctuation electronic speckle pattern interferometry (ESPI) techniques proved effective in determining the visualization of mode shape (0,1)–(0,3). The use of ITO plates is a practical technique for the prediction of SPL, as well as measurement of mode shapes. The four evaluation methods, i.e. LPM, DPM, ESPI and AM, present a high degree of consistency with regard to vibrational mode and sound radiation characteristics.

Vibration measurement based on electronic speckle pattern interferometry and radial basis function

A method incorporating amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) with radial basis function (RBF) was proposed to investigate vibration characteristics of structures. The vibration patterns were obtained by AF-ESPI. A novel pre-filtering RBF method was presented to improve the quality of patterns. The out-of-plane vibration amplitude was rebuilt after fringe analysis. Ideal pre-filtering widow sizes for the presented RBF were given based on numerical experiments. For validation, an aluminum circular plate with fixed boundary was determined and compared with FEM, confirming the effectiveness of the proposed method. Finally, vibration characteristics of sandwich panels with honeycomb core were measured. The influence of presence of a pre-notch at different location was also investigated.

Free vibration investigations for the cantilever-symmetric and skew-symmetric trapezoidal plates with cracks

Using the advantages of non-contact and full-field measurements, the optical technique called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) with out-of-plane setup is employed to investigate the free vibration of cantilever-symmetric and skew-symmetric trapezoidal plates with cracks. Three different types of crack locations will be discussed in detail in this study, one is along the middle chord line and the others are along the clamped edge. Prior to the study of cracked trapezoidal plates, a cantilever rectangular plate is used to carry out the AF-ESPI measurement, and then the experimental results are checked by theoretical and numerical calculations. Numerical calculations based on the finite element method are performed and compared with the experimental results, in which good agreement is obtained for resonant frequencies and mode shapes. Finally, the influences of crack length and location on the vibration behavior of the cracked trapezoidal plates are studied in terms of the dimensionless frequency parameter vs. the crack length ratio. With the aid of mode shape observation, the variation in resonant frequencies is specified; furthermore, it is found that the crack existence does not affect the resonant frequencies for some vibration modes.

Investigations on vibration characteristics of two-layered piezoceramic disks

This paper investigates the transverse and planar vibration characteristics of two-layered piezoceramic disks for traction-free boundary conditions by theoretical analysis, finite element numerical calculation, and experimental measurements. Amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer (LDV), and impedance analysis were used to perform measurements and verify the theoretical solutions for extensional, tangential, and transverse vibrations. The poling direction of piezoelectric elements determines whether they are denoted as either of series- or parallel-type. This study observed that the resonant frequencies and mode shapes of the series- and parallel-type piezoceramic disks present different dynamic characteristics in resonance. Planar and transverse vibrations are coupled in series-type piezoceramic disks and uncoupled in those of parallel-type. Good agreements of dynamic characteristics determined by theoretical analysis, experimental measurements, and numerical calculation are presented for series- and parallel-type piezoceramic disks.

Electromechanical coupling efficiency of transverse vibration in piezoelectric plates according to electrode configuration

This study proposes a method of configuring electrodes for piezoelectric plates to improve the electromechanical coupling efficiency of transverse (out-of-plane) vibration. Two optical techniques were employed to investigate the transverse vibration. We first used a non-contact, full-field measurement technique called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) to determine resonant frequencies and mode shapes in real time. Second, a point-wise measurement device called a laser Doppler vibrometer was used to obtain the spectrum for out-of-plane frequencies. Four electrode configurations with completely free boundary conditions were used to study the electromechanical coupling efficiency of piezoelectric plates. We conclude that the design of the electrodes clearly influences the electromechanical coupling efficiency of piezoelectric plates. The experimental results related to resonant frequency and mode shape were verified using the finite element method (FEM). The numerical calculations are in good agreement with experimental results. Furthermore, according to FEM results, the distribution of electric potential gradient is similar to the mode shape measured by AF-ESPI, making it applicable to the configuration of electrodes in optimizing the excitation of piezoelectric plates. This study proposes the determination of the electromechanical coupling factor to predict the efficiency of transverse vibration in piezoelectric plates.

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.