Distributed Modal Signals of Conical Shells Based on Flexoelectric Effect

2012 ◽  
Author(s):  
H. Li ◽  
S. D. Hu ◽  
H. S. Tzou
Keyword(s):  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Ritz Method ◽  
Strain Component ◽  
Conical Shells ◽  
Total Signal ◽  
Flexoelectric Effect ◽  
Bending Strain ◽  
Spatially Distributed ◽  
Strain Components

Flexoelectricity is known as the electromechanical coupling effect between the strain gradient and the polarization. It is the only contribution of polarization from inhomogeneous mechanical deformation in nonpiezoelectric materials. Conical shells are commonly used as injectors, sprays and rocket nozzles, etc, which are generally clamped at the minor end and free at the major end when mounted. In this study, a flexoelectric layer is laminated on conical shells with clamped-free boundary conditions (BCs) to monitor the natural modal signal distributions. The direct flexoelectric effect defined in a tri-orthogonal coordinate system is presented first, followed by the sensing mechanism of a generic flexoelectric sensor patch. The mode shape functions of conical shells obtained by using the Rayleigh-Ritz method are briefly reviewed. The spatially distributed microscopic sensing signal with respect to position coordinates is evaluated in detail to reveal the modal signal distributions. Due to the gradient effect, the bending strain component is the only contribution to the total sensing signal. The total signal consists of two components resulting from the two bending strain components: circumferential bending strains and longitudinal bending strains. Analytical results show that, the flexoelectric sensing signal induced by the circumferential bending strain is the dominant contribution to the total signal for lower order modes. The optimal location of flexoelectric sensors is discussed for selected vibration modes.

Electromechanical Coupling and Signal Distribution of a Circular Cylindrical Shell Coupled With Segmented Sensors

2008 ◽  
Author(s):  
Shih-Lin Huang ◽  
Chin-Chou Chu ◽  
Chien C. Chang ◽  
H. S. Tzou
Keyword(s):  
Cylindrical Shell ◽  
Large Scale ◽  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Circular Cylindrical Shell ◽  
Open Circuit ◽  
Signal Generation ◽  
Signal Distribution ◽  
Shear Design ◽  
Spatially Distributed

The direct piezoelectric effect has long been recognized as an effective electromechanical coupling effect applied to designs of various transducers. Conventional sensor design usually follows three design principles: 1) the tension/compression design, 2) the bending or flexible design and 3) the shear design. These are mostly point-type transducers monitoring responses of discrete locations and, thus, they are not suitable to dynamic spatial monitoring of large-scale distributed structures, such as shells and plates. Accordingly, distributed designs and configurations, such as the segmentation and shaping techniques, have been proposed and evaluated in the last two decades. This study is to evaluate electromechanical coupling and signal generations of a coupled piezoelectric/elastic circular shell structure. A generic open-circuit signal equation of electromechanical coupling and signal generation is presented first, followed by a simplification to signal generation of a circular cylindrical shell case. The total signal generation and its contributing components are analyzed in the modal domain. Spatially distributed modal signals of various shell modes are calculated and the spatial signal distribution illustrates distinct modal characteristics resulting from microscopic modal strain behaviors. Thus, the optimal sensor location(s) for specific shell modes can be identified from the modal signal distribution plots.

Analytical studies on Mode III fracture in flexoelectric solids

2021 ◽  
pp. 1-32
Author(s):  
Xinpeng Tian ◽  
Mengkang Xu ◽  
Haiyang Zhou ◽  
Qian Deng ◽  
Qun Li ◽  
...  
Keyword(s):  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Expansion Method ◽  
Gradient Field ◽  
J Integral ◽  
Mode Iii ◽  
Flexoelectric Effect ◽  
Local Strength ◽  
Out Of Plane ◽  
Plane Displacement

Abstract Due to the stress concentration near crack tips, strong flexoelectric effect would be observed there, which might lead to new applications of flexoelectricity in material science and devices. However, different from the flexoelectric effect in cantilever beams or truncated pyramids, at the crack tip, multiple components of strain gradients with nonuniform distribution contribute to the flexoelectric effect, which makes the problem extremely complex. In this paper, with the consideration of both direct and converse flexoelectricity, the electromechanical coupling effect around the tip of a Mode III crack is studied analytically. Based on the Williams' expansion method, the displacement field, polarization field, strain gradient field along with the actual physical stresses field are solved. A path independent J-integral for Mode III cracks in flexoelectric solids is presented. Our results indicate that the existence of flexoelectricity leads to a decrease of both the J-integral and the out-of-plane displacement in Mode III cracks, which means that the flexoelectric effect around the tip of Mode III cracks enhances the local strength of materials.

scholarly journals Dynamics Analysis on Piezoelectric Laminated Vibrator and Optimization of PZT Position

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Caiqi Hu ◽  
Xiaoqi Hu ◽  
Jing Ji ◽  
Jude Liu ◽  
Shengduo Li
Keyword(s):  
Electromechanical Coupling ◽  
Vibration Mode ◽  
Coupling Effect ◽  
Ritz Method ◽  
Admissible Function ◽  
Coefficient Matrix ◽  
Functional Variation ◽  
Linear Superposition ◽  
Piezoelectric Vibrator ◽  
Admissible Functions

Piezoelectric laminated structure is widely used as actuator’s drive part. The different position of PZT on a piezoelectric vibrator causes different incentive effects. Therefore, seeking an optimal PZT position is of great significance to improve actuator’s drive forces and electromechanical conversion efficiency. In this research, the optimization of PZT position was studied using the approximate solution of piezoelectric vibrator mode shape with mutation sections. The vibration mode function was expressed as a linear superposition of the admissible function according to Rayleigh Ritz method. Then solving of functional variation was converted into the solving of the coefficient matrix of the admissible function by Hamilton’s principle. Through analyzing the forms of admissible functions, the admissible functions that satisfied the boundary conditions of displacement were chosen. For a given vibrator, approximate function for natural frequency and vibration mode was calculated in given admissible functions. Calculated values and experimental results were compared. Results showed that the more items an admissible function sequence had the closer the calculated results were to the experimental values. The errors of calculations were analyzed based on the selection of admissible functions and electromechanical coupling effect. Optimization of PZT position was achieved by analyzing the mode forces of the piezoelectric laminated vibrator.

An hourglass-type electromagnetic isolator with negative resistance electromagnetic shunt circuit

2020 ◽  
Vol 64 (1-4) ◽  
pp. 549-556
Author(s):  
Yajun Luo ◽  
Linwei Ji ◽  
Yahong Zhang ◽  
Minglong Xu ◽  
Xinong Zhang
Keyword(s):  
Vibration Isolation ◽  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Negative Resistance ◽  
Isolation System ◽  
Amplitude Vibration ◽  
Vibration Responses ◽  
The Stability ◽  
Isolation Performance ◽  
Shunt Circuit

The present work proposed an hourglass-type electromagnetic isolator with negative resistance (NR) shunt circuit to achieve the effective suppression of the micro-amplitude vibration response in various advanced instruments and equipment. By innovatively design of combining the displacement amplifier and the NR electromagnetic shunt circuit, the current new type of vibration isolator not only can effectively solve the problem of micro-amplitude vibration control, but also has significant electromechanical coupling effect, to obtain excellent vibration isolation performance. The design of the isolator and motion relationship is presented firstly. The electromechanical coupling dynamic model of the isolator is also given. Moreover, the optimal design of the NR electromagnetic shunt circuit and the stability analysis of the vibration isolation system are carried out. Finally, the simulation results about the transfer function and vibration responses demonstrated that the isolator has a significant isolation performance.

scholarly journals Conservation Integrals in Nonhomogeneous Materials with Flexoelectricity

2021 ◽  
Vol 11 (2) ◽  
pp. 681
Author(s):  
Pengfei Yu ◽  
Weifeng Leng ◽  
Yaohong Suo
Keyword(s):  
Electromechanical Coupling ◽  
Energy Momentum Tensor ◽  
Great Influence ◽  
Operator Method ◽  
Electric Polarization ◽  
Momentum Tensor ◽  
Noether Theorem ◽  
Strain Gradients ◽  
Flexoelectric Effect ◽  
Nonhomogeneous Materials

The flexoelectricity, which is a new electromechanical coupling phenomenon between strain gradients and electric polarization, has a great influence on the fracture analysis of flexoelectric solids due to the large gradients near the cracks. On the other hand, although the flexoelectricity has been extensively investigated in recent decades, the study on flexoelectricity in nonhomogeneous materials is still rare, especially the fracture problems. Therefore, in this manuscript, the conservation integrals for nonhomogeneous flexoelectric materials are obtained to solve the fracture problem. Application of operators such as grad, div, and curl to electric Gibbs free energy and internal energy, the energy-momentum tensor, angular momentum tensor, and dilatation flux can also be derived. We examine the correctness of the conservation integrals by comparing with the previous work and discuss the operator method here and Noether theorem in the previous work. Finally, considering the flexoelectric effect, a nonhomogeneous beam problem with crack is solved to show the application of the conservation integrals.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

The Effect of Drain/Gate Bias on Electromechanical Coupling Effect in Accelerometer Based on MESFET

2011 ◽  
Vol 11 (2) ◽  
pp. 384-388 ◽  
Author(s):  
Chenyang Xue ◽  
Zhenxin Tan ◽  
Weili Shi ◽  
Jun Liu ◽  
Binzhen Zhang ◽  
...  
Keyword(s):  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Gate Bias

Sensing Signal and Energy Generation Analysis on a Flexoelectric Beam

2012 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Cantilever Beam ◽  
Coupling Effect ◽  
Mechanical Strain ◽  
Electric Energy ◽  
Energy Generation ◽  
Electric Polarization ◽  
Ambient Vibration ◽  
Electric Voltage ◽  
Flexoelectric Effect ◽  
Fourth Mode

Flexoelectricity is known as an electromechanical gradient coupling effect. The direct flexoelectric effect that can convert mechanical strain gradient into electric polarization (or electric field) plays an important role in charge generation in the situation when piezoelectricity is absent. This study focuses on the application of the direct flexoelectric effect based on a flexoelectric cantilever beam to investigate its effectiveness of sensing signal and energy generation. The dielectric cantilever beam is deposited with electrodes both on top and bottom surfaces to generate an electric voltage. The sensing mechanism of flexo-piezo-electric effect is analyzed and the expression of sensing signal is derived. Results show that the output sensing signal is only contributed by the flexoelectric effect while the piezoelectric effect is eliminated due to the symmetric bending strains through the beam thickness. The spatial distribution of sensing signal when the fully covered electrode is uniformly segmented to 10 patches is evaluated as an illustration, and the flexoelectric sensitivity of about 0.15V/mm for the first mode and 4V/mm for the fourth mode is achieved. The optimal sensing position is dependent of the electrode size and the vibration mode and in general, it locates where the difference between the slopes at two ends of the electrode patch reaches maximum. Based on the flexoelectric voltage, the energy generation power is also conducted when the flexoelectric cantilever beam is treated as distributed energy harvesters. As a result, the maximal power of RMS is about 1.5×10−8W/mm for the first mode and increases to about 0.6mW/mm for the fourth mode. It provides an alternative way to harvest electric energy from the ambient vibration without using piezoelectricity.

Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells

2004 ◽  
Vol 71 (4) ◽  
pp. 502-507 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Present Method ◽  
Shell Theory ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Shells Of Revolution ◽  
Conical Shells ◽  
Thin Shell Theory ◽  
Time Periodic

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

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