Wilfredo Montealegre Rubio

Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures—FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.

Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems

This work explores the design of piezoelectric transducers based on functional material gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; however, this work focuses on finding the optimal material gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT optimal material gradation for maximizing specified resonance frequencies; (ii) to design piezoelectric resonators, thus, the optimal material gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the ‘modal assurance criterion’ is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear programming, and the concept of continuum approximation of material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.

Modeling of functionally graded piezoelectric ultrasonic transducers

The application of functionally graded material (FGM) concept to piezoelectric transducers allows the design of composite transducers without interfaces, due to the continuous change of property values. Thus, large improvements can be achieved, as reduction of stress concentration, increasing of bonding strength, and bandwidth. This work proposes to design and to model FGM piezoelectric transducers and to compare their performance with non-FGM ones. Analytical and finite element (FE) modeling of FGM piezoelectric transducers radiating a plane pressure wave in fluid medium are developed and their results are compared. The ANSYS software is used for the FE modeling. The analytical model is based on FGM-equivalent acoustic transmission-line model, which is implemented using MATLAB software. Two cases are considered: (i) the transducer emits a pressure wave in water and it is composed of a graded piezoceramic disk, and backing and matching layers made of homogeneous materials; (ii) the transducer has no backing and matching layer; in this case, no external load is simulated. Time and frequency pressure responses are obtained through a transient analysis. The material properties are graded along thickness direction. Linear and exponential gradation functions are implemented to illustrate the influence of gradation on the transducer pressure response, electrical impedance, and resonance frequencies.

Topology Optimized Design, Microfabrication and Characterization of Electro-Thermally Driven Microgripper

This article presents a systematic and logical study of the topology optimized design, microfabrication, and static/dynamic performance characterization of an electro-thermo-mechanical microgripper. The microgripper is designed using a topology optimization algorithm based on a spatial filtering technique and considering different penalization coefficients for different material properties during the optimization cycle. The microgripper design has a symmetric monolithic 2D structure which consists of a complex combination of rigid links integrating both the actuating and gripping mechanisms. The numerical simulation is performed by studying the effects of convective heat transfer, thermal boundary conditions at the fixed anchors, and microgripper performance considering temperature-dependent and independent material properties. The microgripper is fabricated from a 25 μm thick nickel foil using laser microfabrication technology and its static/dynamic performance is experimentally evaluated. The static and dynamic electro-mechanical characteristics are analyzed as step response functions with respect to tweezing/actuating displacements, applied current/power, and actual electric resistance. A microgripper prototype having overall dimensions of 1 mm (L) × 2.5mm (W) is able to deliver the maximum tweezing and actuating displacements of 25.5 μm and 33.2 μm along X and Y axes, respectively, under an applied power of 2.32 W. Experimental performance is compared with finite element modeling simulation results.

Toward design of Functionally Graded Piezoelectric Ultrasonic Motors using topology optimization

In this work, piezoelectric ultrasonic motors are designed based on the Functionally Graded Material (FGM) concept by using topology optimization. FGMs are composite advanced materials, which are made by changing gradually the properties with position inside material domain. The FGM concept applied to piezoelectric structures allows modifying their dynamic characteristics. In this work, Functionally Graded Piezoelectric Ultrasonic Motors (FGPUMs) are designed, aiming to find the optimal topology and gradation of the material properties along a specific direction to target desired eigenmode shapes. The design of FGPUMs is not an easy task to be accomplished by using trial and error methods; thus, the Topology Optimization Method (TOM) is applied to reach this goal. Here, FGPUMs are designed as standing-wave motors, by combining different vibration modes (different eigenmodes). The eigenmode control is achieved by maximizing the amplitude of vibration at certain user-defined points. The Modal Assurance Criterion is applied as mode shape-tracking method. To treat the material gradation, the Graded Finite Element is implemented. The optimization algorithm is implemented based on Sequential Linear Programming. To show the improvement and the advantage of using FGM and TOM for designing FGPUMs, a graded ultrasonic piezomotor, with material gradation along thickness direction, is considered.

Manufacturing of PZT-nickel functionally graded piezoelectric ceramics

A recent approach for designing and manufacturing piezoelectric ceramics consists of using the functionally graded materials (FGM) concept. In this work, nickel (Ni) is used to generate a new PZT-Ni graded ceramic and its dynamic behavior is experimentally explored. The PZT-Ni graded ceramic is manufactured by using the technique of Spark Plasma Sintering (SPS). The ceramic is graded from the top to the bottom surface (along 6 mm of thickness). Specifically, five layers of green powders are sintered: 100 wt% PZT-5A, 90 wt% PZT-5A and 10 wt% Ni, 80 wt% PZT-5A and 20 wt% Ni, 70 wt% PZT-5A and 30 wt% Ni, 60 wt% PZT-5A and 40 wt% Ni. Thus, Ni is used as a second phase, which is added to a PZT-5A matrix, changing its concentration. No manufacturing defects or cracks or exfoliated layers are observed. However, graphite diffusion is observed from the graphite die into the graded ceramic, which does not affect its performance; hence, the ceramic contains enough piezoelectric properties, which allows its polarization and dynamic characterization by determining the impedance curve of the PZT-Ni graded ceramic. The PZT-Ni graded ceramic vibrates at 1.04 MHz, 1.55 MHz and 2.07 MHz.A recent approach for designing and manufacturing piezoelectric ceramics consists of using the functionally graded materials (FGM) concept. In this work, nickel (Ni) is used to generate a new PZT-Ni graded ceramic and its dynamic behavior is experimentally explored. The PZT-Ni graded ceramic is manufactured by using the technique of Spark Plasma Sintering (SPS). The ceramic is graded from the top to the bottom surface (along 6 mm of thickness). Specifically, five layers of green powders are sintered: 100 wt% PZT-5A, 90 wt% PZT-5A and 10 wt% Ni, 80 wt% PZT-5A and 20 wt% Ni, 70 wt% PZT-5A and 30 wt% Ni, 60 wt% PZT-5A and 40 wt% Ni. Thus, Ni is used as a second phase, which is added to a PZT-5A matrix, changing its concentration. No manufacturing defects or cracks or exfoliated layers are observed. However, graphite diffusion is observed from the graphite die into the graded ceramic, which does not affect its performance; hence, the ceramic contains enough piezoelectric properties, which allows its polarizat...

Multimodal and unimodal Functionally Graded Piezoelectric Ultrasonic Transducers

Piezoelectric transducers are usually designed to have a multimodal or unimodal frequency response, which defines the kind of acoustic wave pulse generated (short pulse or continuous wave, respectively). Functionally Graded Materials (FGMs) are made by gradually changing the properties along a material domain. On the other hand, the Topology Optimization Method (TOM) is a generic and systematic optimization technique, which combines optimization algorithms with Finite Element Method to maximize a user-defined objective function. In this work, the main goal is to find the optimal material distribution of Functionally Graded Piezoelectric Ultrasonic Transducers (FGPUTs), including the following requirements: (i) an FGPUT with unimodal dynamic behavior in a desired frequency band; (ii) an FGPUT with multimodal dynamic behavior in a user-defined frequency band. For measuring the strength of a specific mode, the Electromechanical Coupling Coefficient (EMCC) is utilized. For tracking a desirable mode, the Modal Assurance Criterion is applied. The optimization algorithm is constructed based on Sequential Linear Programming. To illustrate the method, two FGPUTs are designed.

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

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.

Numerical and Analytical Design of Functionally Graded Piezoelectric Transducers

This paper presents analytical and finite element methods to model broadband transducers with a graded piezoelectric parameter. The application of FGM (Functionally Graded Materials) concept to piezoelectric transducer design allows the design of composite transducers without interface between materials (e.g. piezoelectric ceramic and backing material), due to the continuous change of property values. Thus, large improvements can be achieved in their performance characteristics, mainly generating short‐time waveform ultrasonic pulses. Nevertheless, recent research on functionally graded piezoelectric transducers shows lack of studies that compare numerical and analytical approaches used in their design. In this work analytical and numerical models of FGM piezoelectric transducers are developed to analyze the effects of piezoelectric material gradation, specifically, in ultrasonic applications. In addition, results using FGM piezoelectric transducers are compared with non‐FGM piezoelectric transducers. We ...