Topology optimization of piezocomposite resonator for maximizing excitation strength and synthesizing desired eigenmodes

A topology optimization method is proposed for the design of piezocomposite resonator with the aim of maximizing excitation strength and synthesizing desired eigenmodes. The objective function consists of maximizing the electromechanical coupling strength at the mode of interest. The topology layout of a structure with desired eigenmodes is obtained by adding the modal assurance criterion as additional constraint in the topology optimization model. Numerical examples are presented and the results illustrate that aside from maximizing the electromechanical coupling strength, the existing eigenmode of the piezocomposite resonator can be modified to be the desired one at the mode of interest.

[1]  Ulrich Schmid,et al.  Modal optimization and filtering in piezoelectric microplate resonators , 2010 .

[2]  R. Lerch,et al.  Simulation of piezoelectric devices by two- and three-dimensional finite elements , 1990, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[3]  Jianhua Zhou,et al.  Structural Topology Optimization Through Explicit Boundary Evolution , 2017 .

[4]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[5]  Zhan Kang,et al.  Dynamic topology optimization of piezoelectric structures with active control for reducing transient response , 2014 .

[6]  R. Fox,et al.  Rates of change of eigenvalues and eigenvectors. , 1968 .

[7]  Jian Zhang,et al.  A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model , 2016 .

[8]  David J. Ewins,et al.  Modal Testing: Theory, Practice, And Application , 2000 .

[9]  Glaucio H. Paulino,et al.  Tailoring vibration mode shapes using topology optimization and functionally graded material concepts , 2011 .

[10]  Eberhard Bänsch,et al.  Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation , 2009 .

[11]  Zhan Kang,et al.  Topology optimization-based distribution design of actuation voltage in static shape control of plates , 2008 .

[12]  Seonho Cho,et al.  Design sensitivity analysis and topology optimization of eigenvalue problems for piezoelectric resonators , 2006 .

[13]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[14]  Wing Kam Liu,et al.  A level set approach for optimal design of smart energy harvesters , 2010 .

[15]  Hae Chang Gea,et al.  Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization , 2011 .

[16]  In-Won Lee,et al.  An efficient algebraic method for the computation of natural frequency and mode shape sensitivities—Part I. Distinct natural frequencies , 1997 .

[17]  J. Zelenka.  Piezoelectric Resonators and their Applications , 1986 .

[18]  Siu Wing Or,et al.  Piezocomposite ultrasonic transducer for high-frequency wire-bonding of microelectronics devices , 2007 .

[19]  Noboru Kikuchi,et al.  Design of piezoelectric transducers using topology optimization , 1999 .

[20]  N. Kikuchi,et al.  Design of piezocomposite materials and piezoelectric transducers using topology optimization— Part III , 1999 .

[21]  Emílio Carlos Nelli Silva,et al.  Topology optimization of smart structures: design of piezoelectric plate and shell actuators , 2005 .

[22]  Ramana V. Grandhi,et al.  A survey of structural and multidisciplinary continuum topology optimization: post 2000 , 2014 .

[23]  Z. Kang,et al.  Integrated Optimization of Material Layout and Control Voltage for Piezoelectric Laminated Plates , 2008 .

[24]  Xu Guo,et al.  Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework , 2014 .

[25]  Jian Zhang,et al.  Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons , 2016 .

[26]  Kurt Maute,et al.  Design of Piezoelectric Energy Harvesting Systems: A Topology Optimization Approach Based on Multilayer Plates and Shells , 2009 .

[27]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[28]  Richard B. Nelson,et al.  Simplified calculation of eigenvector derivatives , 1976 .

[29]  H. Gea,et al.  Topology optimization of energy harvesting devices using piezoelectric materials , 2009 .

[30]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[31]  E.C.N. Silva,et al.  Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization , 2010 .

[32]  Ulrich Schmid,et al.  Design and characterization of AlN-based in-plane microplate resonators , 2013 .