Distributed flexoelectric modal signals on circular cylindrical shells

2017 ◽  
Vol 232 (6) ◽  
pp. 952-961 ◽  
Author(s):  
Hua Li ◽  
Kaiming Hu ◽  
HS Tzou
Keyword(s):  
Strain Gradient ◽  
Cylindrical Shells ◽  
Mechanical Strain ◽  
Electric Polarization ◽  
Design Parameters ◽  
Flexoelectric Effect ◽  
Bending Strain ◽  
Longitudinal Bending ◽  
Circular Cylindrical Shells ◽  
Sensing Characteristics

Flexoelectricity exhibits both direct effect and converse effect. For direct flexoelectric effect, mechanical strain gradients induce a homogeneous electric polarization in dielectrics. Thus, the induced electric field between the electrodes can be measured. Compared with the piezoelectric sensors, the main advantage of the flexoelectric sensors is that they are not sensitive to the in-plane strains. This paper presents segmented flexoelectric sensors laminated on circular cylindrical shells, and investigates the electromechanical strain-gradient/signal-generation characteristics and distributed modal flexoelectric signals on the cylindrical shells. The dynamic equations of the proposed flexoelectric sensor are derived based on the direct flexoelectric effect and thin shell assumptions. The model of modal signal is derived to investigate the sensing characteristics. In case studies, the effects of design parameters, i.e. size and thickness of the sensors and geometry of the shells, are evaluated and compared. Numerical results indicate that the contribution of longitudinal bending strain gradient is dominant in the total signals of most evaluated modes, except that in modes 1 and 2, where the contribution of the circumferential bending strain gradient is slightly higher. The amplitudes of the modal signals decrease with the shell radius, but increase with the sensor thickness.

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.

Low Buckling Stresses of Axially Compressed Circular Cylindrical Shells of Finite Length

1965 ◽  
Vol 32 (3) ◽  
pp. 533-541 ◽  
Author(s):  
N. J. Hoff
Keyword(s):  
Normal Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Critical Value ◽  
Stress Resultant ◽  
End Conditions ◽  
Simple Support ◽  
Longitudinal Bending ◽  
Circular Cylindrical Shells ◽  
Axial Normal Stress

Exact solutions are derived of the classical differential equations defining the deformations of axially compressed thin-walled circular cylindrical shells. The end conditions along the circular edges are assumed as the vanishing (a) of the radial displacement; (b) of the longitudinal bending moment; (c) of the variation in the axial normal stress resultant; and (d) of the circumferential membrane shear stress resultant. Under these conditions of simple support the critical value of the uniformly distributed axial normal stress is one half the classical critical value.

Flexoelectric Energy Harvesting of Circular Rings

2013 ◽  
Author(s):  
X. F. Zhang ◽  
S. D. Hu ◽  
H. S. Tzou
Keyword(s):  
Energy Harvesting ◽  
Output Power ◽  
Strain Gradient ◽  
Electromechanical Coupling ◽  
Energy Harvester ◽  
Excitation Frequency ◽  
Design Parameters ◽  
Equivalent Resistance ◽  
Flexoelectric Effect ◽  
Piezoelectric Energy

Flexoelectricity, the electromechanical coupling of the polarization response and strain gradient, occurs in solid crystalline dielectrics of any symmetry or asymmetric crystals. Different from the piezoelectric energy harvester, an energy harvester based on the direct flexoelectric effect is designed in this study. The energy harvester consists of an elastic ring and a flexoelectric patch laminated on its outer surface. Due to the direct flexoelectric effect, the electric energy induced by the strain gradient of the flexoelectric patch is harvested to power the electric device when the ring is subjected to mechanical excitations. Electromechanical coupling equation of the flexoelectric energy harvesting system in close-loop circuit condition is derived. In this study, dynamic response, output power across the external resistor and energy harvesting results are evaluated when the ring is excited by a harmonic point loading. The output power is a function of the external excitation frequency, the external equivalent resistance, the flexoelectric patch’s thickness and other design parameters. Case studies of those parameters for the flexoelectric energy harvester are presented to optimize the output power. Results show that the optimal excitation frequency is equal to the natural frequency for each mode, and the optimal equivalent resistance is dependent of the equivalent capacitance of the flexoelectric patch and the excitation frequency. Since the output power of the flexoelectric energy harvester is similar to that of the piezoelectric energy harvester, comparison of the two harvesters is also discussed. With all the optimal conditions discussed, it can supply a design principle in the engineering applications.

Spatial Electrostrictive Actuation of Circular Cylindrical Tubes

2008 ◽  
Author(s):  
Shih-Lin Huang ◽  
Chin-Chou Chu ◽  
Chien C. Chang ◽  
Horn-Sen Tzou
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Input Voltage ◽  
Positive Control ◽  
Design Guidelines ◽  
Design Parameters ◽  
Control Force ◽  
Cylindrical Tubes ◽  
Piping Systems ◽  
Circular Cylindrical Shells

Circular cylindrical shells are common components in aerospace structures and many other engineering systems, e.g., rockets, tubes, piping systems, peristaltic pumps, storage tanks, etc. Electromechanical actuators laminated on the shell surfaces can certainly strengthen the shell when needed. Or, regulated inputs to the surface actuators can introduce prescribed surface waves to control the shell oscillation. This study is to evaluate spatial actuation characteristics of circular cylindrical shells using segmented electrostrictive actuators. Electrostrictive actuations induced by surface laminated electrostrictive actuators are defined first. Governing equations of a hybrid circular cylindrical shell/electrostrictive actuator system are formulated. The total electrostrictive actuation and its contributing circumferential membrane/bending and longitudinal bending components are evaluated with respect to shell modal characteristics, design parameters and control voltages. The actuator’s quadratic behavior only generate a positive control force or moment and thus an actuator patch can suppress (or amplify) the vibration in the positive (or negative) displacement. Accordingly, the quadratic electrostrictive actuation suggests that appropriate input voltage(s) need to be carefully applied to specific actuator(s) or regions in order to control, but not to amplify, the shell oscillations. Based on the spatially distributed modal actuation, generic design guidelines and optimal actuation locations are proposed.

scholarly journals Engineering of atomic-scale flexoelectricity at grain boundaries

2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Mei Wu ◽  
Xiaowei Zhang ◽  
Xiaomei Li ◽  
Ke Qu ◽  
Yuanwei Sun ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Strain Gradient ◽  
Electromechanical Coupling ◽  
Mechanical Strain ◽  
Atomic Scale ◽  
Strain Gradients ◽  
Flexoelectric Effect ◽  
Unit Cells ◽  
Large Elastic Deformation

AbstractFlexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the electrical polarization response to mechanical strain gradients that is not restricted by the symmetry of materials. However, large elastic deformation is usually difficult to achieve in most solids, and the strain gradient at minuscule is challenging to control. Here, we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~1.2 nm−1) within 3–4-unit cells, and thus obtain atomic-scale flexoelectric polarization of up to ~38 μC cm−2 at a 24° LaAlO3 grain boundary. Accompanied by the generation of the nanoscale flexoelectricity, the electronic structures of grain boundaries also become different. Hence, the flexoelectric effect at grain boundaries is essential to understand the electrical activities of oxide ceramics. We further demonstrate that for different materials, altering the misorientation angles of grain boundaries enables tunable strain gradients at the atomic scale. The engineering of grain boundaries thus provides a general and feasible pathway to achieve tunable flexoelectricity.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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