Sensor Electromechanics and Distributed Signal Analysis of Piezo(Electric)-Elastic Spherical Shells Based on the Bending Approximation

2001 ◽  
Author(s):  
H. S. Tzou ◽  
P. Smithmaitrie
Keyword(s):  
Piezoelectric Sensor ◽  
Free Edge ◽  
Open Circuit ◽  
Mode Shapes ◽  
Shells Of Revolution ◽  
Spherical Shells ◽  
Distributed Sensor ◽  
Hemispherical Shell ◽  
Spatially Distributed ◽  
Strain Components

Abstract Spatially distributed modal voltages and sensing signal generations of a distributed piezoelectric sensor layer laminated on spherical shells of revolution are investigated in this study. The generic sensing signal equation is derived based on the direct piezoelectric effect, the Gauss theory, the open-circuit assumption, the Maxwell equation, and also the generic double-curvature thin shell theory. Due to difficulties in analytical solution procedures, assumed mode shape functions based on the bending approximation theory are used in the modal signal expressions and analyses. Spatially distributed electromechanical characteristics resulting from various meridional and circumferential membrane/bending strain components are evaluated and major signal sources are identified. Analytical results suggest that the spatially distributed modal voltages clearly illustrate the distinct modal behavior, similar to mode shapes. The major signal source of a free-edge hemispherical shell is the circumferential bending component. Accordingly, circumferential layout of distributed sensor strips would provide effective monitoring and diagnosis of free hemispheric shells.

On Vibrations of Elastic Spherical Shells

1962 ◽  
Vol 29 (1) ◽  
pp. 65-72 ◽  
Author(s):  
P. M. Naghdi ◽  
A. Kalnins
Keyword(s):  
Middle Surface ◽  
Free Edge ◽  
Free Vibrations ◽  
Numerical Results ◽  
Mode Shapes ◽  
Normal Displacement ◽  
Spherical Shells ◽  
Hemispherical Shell ◽  
Basic Equations ◽  
Circumferential Wave

This investigation is concerned with axisymmetric as well as asymmetric vibrations of thin elastic spherical shells. First, with the limitation to torsionless axisymmetric motion, the basic equations for spherical shells of the classical bending theory of Love’s first approximation are reduced to a system of two coupled differential equations in normal displacement of the middle surface and a stress function; this system of equations is applied to free vibrations of a hemispherical shell with a free edge and numerical results are obtained for the lowest natural frequency as a function of the thickness of the shell. The remainder of the paper is, in the main, devoted to a study of asymmetric vibrations of a hemispherical shell with a free edge according to the extensional theory. Numerical results for natural frequencies (of the four lowest circumferential wave numbers) and mode shapes are given and the results are compared with the prediction of Rayleigh’s inextensional theory.

Modal Voltages and Distributed Signal Analysis of Conical Shells of Revolution

2001 ◽  
Author(s):  
H. S. Tzou ◽  
W. K. Chai ◽  
D. W. Wang
Keyword(s):  
Conical Shell ◽  
Signal Analysis ◽  
Turbine Blades ◽  
Piezoelectric Sensor ◽  
High Signal ◽  
Shells Of Revolution ◽  
Conical Shells ◽  
Double Curvature ◽  
Shell Models ◽  
Spatially Distributed

Abstract Conical shells and components are widely used as nozzles, injectors, rocket fairings, turbine blades, etc. Dynamic and vibration characteristics of conical shells have been investigated over the years. In this paper, electromechanics and distributed sensing phenomena of a generic double-curvature shell and a conical shell are discussed, and governing sensing signal-displacement equations are derived. Spatially distributed modal voltages and signal generations of conical shells laminated with distributed piezoelectric sensor layers or neurons are investigated based on the Donnel-Mushtari-Valsov theory. Distributed modal voltages and their various signal components of conical shell models reveal that the dominating signal component among the four contributing signal components is the circumferential membrane component. This dominance is even more significant for lower shell modes and/or deep shells. In general, high strain regions result in high signal magnitudes. Accordingly, the spatially distributed signal patterns — the modal voltages — clearly represent the modal dynamic and strain characteristics of conical shells.

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.

Some Results on Axisymmetric Vibration of Spherical Shells of Variable Thickness

1990 ◽  
Vol 112 (4) ◽  
pp. 432-437 ◽  
Author(s):  
A. V. Singh ◽  
S. Mirza
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Spherical Shells ◽  
Varying Thickness ◽  
Wide Range

Natural frequencies and mode shapes are presented for the free axisymmetric vibration of spherical shells with linearly varying thickness along the meridian. Clamped and hinged edges corresponding to opening angles 30, 45, 60 and 90 deg have been considered in this technical brief to cover a wide range from shallow to deep spherical shells. Variations in thickness are seen to have very pronounced effects on the frequencies and mode shapes.

Spatially distributed sensor array calibration for photoacoustic imaging

2021 ◽  
Author(s):  
Yuting Jiang ◽  
Yunhao Zhu ◽  
Xiang Ma ◽  
Hongchen Zhan ◽  
Chenglei Peng ◽  
...  
Keyword(s):  
Sensor Array ◽  
Photoacoustic Imaging ◽  
Distributed Sensor ◽  
Spatially Distributed ◽  
Array Calibration

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.

Dynamic Buckling of Shallow Spherical Shells

1973 ◽  
Vol 40 (2) ◽  
pp. 411-416 ◽  
Author(s):  
R. E. Ball ◽  
J. A. Burt
Keyword(s):  
Computer Program ◽  
Dynamic Analysis ◽  
Digital Computer ◽  
Large Range ◽  
Dynamic Buckling ◽  
Geometrically Nonlinear ◽  
Shells Of Revolution ◽  
Spherical Shells ◽  
Static And Dynamic Analysis ◽  
Nonlinear Static

The dynamic behavior of clamped shallow spherical shells subjected to axisymmetric and nearly axisymmetric step-pressure loads is examined using a digital computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution. A criterion for dynamic buckling under the nearly axisymmetric load is proposed and critical buckling pressures are determined for a large range of shell sizes.

scholarly journals A New Analytical Method for Spherical Thin Shells’ Axisymmetric Vibrations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mariame Nassit ◽  
Abderrahmane El Harif ◽  
Hassan Berbia ◽  
Mourad Taha Janan
Keyword(s):  
Analytical Method ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Current Method ◽  
Free Edge ◽  
Free Vibrations ◽  
Thin Shells ◽  
Element Calculation ◽  
Spherical Shells ◽  
Clamped Edge

In order to improve the spherical thin shells’ vibrations analysis, we introduce a new analytical method. In this method, we take into consideration the terms of the inertial couples in the stress couples’ differential equations of motion. These inertial couples are omitted in the theories provided by Naghdi–Kalnins and Kunieda. The results show that the current method can solve the axisymmetric vibrations’ equations of elastic thin spherical shells. In this paper, we focus on verifying the current method, particularly for free vibrations with free edge and clamped edge boundary conditions. To check the validity and accuracy of the current analytical method, the natural frequencies determined by this method are compared with those available in the literature and those obtained by a finite element calculation.

Two degree of freedom vibration based electromagnetic energy harvester for bridge health monitoring system

2020 ◽  
pp. 1045389X2095945
Author(s):  
Muhammad Masood Ahmad ◽  
Farid Ullah Khan
Keyword(s):  
Cantilever Beam ◽  
Energy Harvester ◽  
Low Frequency ◽  
Open Circuit ◽  
Electromagnetic Energy ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Fixed End ◽  
Two Degree Of Freedom ◽  
Maximum Voltage

This paper presents an electromagnetic energy harvester to extract low frequency and low acceleration vibration energy available in a bridge environment. The developed harvester is a multi-mode oscillator with dual electromagnetic transduction mechanisms. The harvester consists of two cantilever beams. The first cantilever beam is split into two equal pieces along its length and the second beam placed in between them coming back to the fixed end and attached at outer end to the first beam. This way instead of a long conventional cantilever beam a compact harvester is fabricated. Two magnets as proof masses are attached to each free end of the beam making it a two degree of freedom system (2-DOF). The magnets are positioned to oscillate inside hand wound coils during operation. An analytical model was developed and COMSOL multiphysics was used to simulate the mode shapes of the harvester. The mathematical model was simulated for open circuit voltage in MATLAB and showed closely matching results with the experimental values. The harvester is characterized in lab for its performance under sinusoidal vibrations at low frequency (3 Hz–15 Hz) and low acceleration (0.01–0.09 g) levels. The 2-DOF harvester has two resonant frequencies of 4.4 Hz and 5.5 Hz and a volume of 333 cm3. It produces maximum voltage of 0.6 V at first resonance on coil-1 and maximum voltage of 1.2 V on coil-2 at second resonance at 0.09 g. At acceleration of 0.09 g the harvester produced 2.51 mW at first resonant frequency and 10.7 mW at second resonance. Moreover, the AC output voltage of the harvester is rectified to DC voltage by a three-stage Cockcroft-Walton multiplier type circuit. The DC power output at 0.05 g was 0.939 mW at first resonance and 0.956 mW at second resonance while maximum voltages of 5.4 V on coil-1 and 4 V on coil-2 were produced.

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