Topology Optimized Design of Functionally Graded Piezoelectric Resonators with Specified Resonance Frequencies

2009 ◽  
Vol 631-632 ◽  
pp. 305-310
Author(s):  
Wilfredo Montealegre Rubio ◽  
Emílio Carlos Nelli Silva ◽  
Glaucio H. Paulino
Keyword(s):  
Finite Element ◽  
Resonance Frequency ◽  
Functionally Graded ◽  
Single Frequency ◽  
Continuum Approximation ◽  
Continuous Change ◽  
Piezoelectric Resonators ◽  
Resonance Frequencies ◽  
Functionally Graded Piezoelectric ◽  
Piston Mode

This work explores the design of piezoelectric resonators based on functionally graded material (FGM) concept. The goal is to design single-frequency Functionally Graded Piezoelectric Resonators (FGPR) subjected to the following requirements: (i) an assurance of the specified resonance frequency, and (ii) for most acoustic wave generation applications, the FGPR is required to oscillate in the piston mode. Several approaches can be used to achieve these goals; however, a novel approach is to design the piezoelectric transducer by using Topology Optimization Method. Accordingly, in this work, the optimal material gradation of an FGPR is found, which maximizes a specified and single resonance frequency subjected to a volume constraint. To track the desirable piston mode, a mode-tracking method utilizing the modal assurance criterion (MAC) is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element (GFE) concept, where these material properties are interpolated inside the finite element using interpolation functions. The optimization algorithm is constructed based on sequential linear programming (SLP), and the concept of the Continuum Approximation of Material Distribution (CAMD) is considered. The software is implemented in MATLAB language. In addition, to illustrate the method, a two-dimensional FGPR is designed with plane strain assumption. Performance of designed FGPR is compared with non-FGPR performance.

Finite Element Analysis and Experimental Studies on the Thickness Resonance of Piezocomposite Transducers

1996 ◽  
Vol 18 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Wenkang Qi ◽  
Wenwu Cao
Keyword(s):  
Finite Element ◽  
Resonance Frequency ◽  
Electromechanical Coupling ◽  
Effective Medium Theory ◽  
Experimental Studies ◽  
Effective Medium ◽  
Electromechanical Coupling Coefficient ◽  
Element Analysis ◽  
Medium Theory ◽  
Resonance Frequencies

Finite element method (FEA) has been used to calculate the thickness resonance frequency and electromechanical coupling coefficient kt for 2–2 piezocomposite transducers. The results are compared with that of the effective medium theory and also verified by experiments. It is shown that the predicted resonance frequencies from the effective medium theory and the unit cell modeling using FEA deviate from the experimental observations for composite systems with a ceramic aspect ratio (width/length) more than 0.4. For such systems, full size FEA modeling is required which can provide accurate predictions of the resonance frequency and thickness coupling constant kt.

Static Analysis of a Functionally Graded Piezoelectric Beam Using Finite Element Method

2010 ◽  
Author(s):  
Iman Eshraghi ◽  
Aghil Yousefi-Koma
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Static Analysis ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Functionally Graded ◽  
Bending Behavior ◽  
Functionally Graded Piezoelectric ◽  
Element Method

In this study static analysis of functionally graded piezoelectric material (FGPM) beams is performed using finite element modeling. First order shear deformation beam theory (Timoshenko beam theory) with the assumption of linear strain-displacement relations is used for modeling of displacement and strain fields in the beam. Theoretical formulations are derived employing Hamilton’s principle using linear constitutive relations of piezoelectric materials and including the effect of transverse shear deformation. Finite element method with one dimensional linear continuum isoparametric element, three displacement mechanical degrees of freedom, and one electric potential degree of freedom assigned to each node is then used to investigate the bending behavior of FGPM beam actuator under thermo-electro-mechanical loads. Consequently, a parametric study of the bending behavior of an FGPM beam is performed. The effects of slenderness ratio and fraction of volume of constituent materials, on the thermo-electro-mechanical characteristics are studied. It is shown that under electrical loading the beam represents the so-called non-intermediate behavior.

On Wave Diffraction of a Two-Dimensional Moonpool in a Two-Layer Fluid in Finite Water Depth

2018 ◽  
Author(s):  
Xingyu Song ◽  
Xin Xu ◽  
Xinshu Zhang ◽  
Yunxiang You
Keyword(s):  
Free Surface ◽  
Resonance Frequency ◽  
Internal Wave ◽  
Wave Mode ◽  
Resonance Frequencies ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Free Surface Wave ◽  
Piston Mode ◽  
Wave Elevations

This paper studies the wave diffraction of a two-dimensional moonpool in a two-layer fluid in finite water depth by using a domain decomposition scheme and an eigenfunction matching method. The formulae of the wave exciting forces, the free surface and internal wave elevations at zero-frequency are derived. Numerical convergence has been assessed by repeating the computations for increasing values of the truncation orders. The present model has been validated by comparing a limiting case with a single-layer fluid case and the comparisons are in general satisfactory. Although the wave exciting forces and free surface wave elevations around resonance frequency are overestimated, the piston mode resonance frequency is well predicted. Two typical configurations with different moonpool widths are selected for computations in both free surface and internal wave modes. It is found that, the wave exciting forces, free surface and internal wave elevations in internal wave mode are much smaller than those in free surface wave mode. In addition, the wave exciting forces in internal wave mode attenuate to zero quickly as incident wave frequency increases. For moonpool with small width, only piston mode resonance can be observed. The piston mode resonance frequencies identified in free surface and internal wave modes are the same. The characteristics of piston mode resonance can also be observed in the horizontal and vertical wave exciting forces. Around the piston mode resonance frequency, the wave exciting forces reach their local maximums. It is revealed that, as moonpool width increases, the piston mode resonance frequency decreases. Meanwhile, it shows that more asymmetric and symmetric sloshing mode resonances appear alternately and occur at higher frequencies than the piston mode resonance. Moreover, the predicted sloshing mode resonance frequencies are compared with those estimated by a simple approximate formula.

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