0885–3010/$25.00 © 2010 IEEE 469 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 57, . 2, FEBRUARY 2010 Abstract—A ﬁnite element analysis and a parametric opti- mization of single-axis acoustic levitators are presented. The ﬁnite element method is used to simulate a levitator consist- ing of a Langevin ultrasonic transducer with a plane radiating surface and a plane reﬂector. The transducer electrical imped- ance, the transducer face displacement, and the acoustic radia- tion potential that acts on small spheres are determined by the ﬁnite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a ﬁber-optic vibration sensor. The numeri- cal acoustic radiation potential is veriﬁed experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reﬂector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reﬂector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W. I. I A  levitation has been used in many research areas, such as measurement of liquid surface tension [1], trapping of heavy gases [2], formation of ice particles in stationary ultrasonic ﬁelds [3], [4], and analytical and bioanalytical chemistry [5]. Diﬀerent techniques have been proposed to levitate particles, including magnetic levita- tion [6], optical levitation [7], and electrostatic levitation [8], [9]. The main advantage of acoustic levitation over other levitation techniques is that it does not have any special restriction on the levitated particle, such as its electric or magnetic properties. Therefore, acoustic levita- tion is suitable to levitate aqueous droplets and nonmetal- lic substances. The simplest acoustic levitator is called single-axis acoustic levitator and consists of an ultrasonic transducer and a reﬂector. Many single-axis acoustic levitators use a Langevin-type transducer [10], [11] to generate a stand- ing wave between the transducer and the reﬂector. This type of transducer is formed by pairs of piezoelectric rings sandwiched between 2 loading masses and prestressed by a central bolt. The applications involving acoustic levitation require knowledge of the acoustic forces that act on the levitated object. One of the ﬁrst works dealing with the acoustic radiation force on spheres was presented by King [12]. In his work, King presented a theoretical study on the force that acts on a rigid sphere in a standing wave ﬁeld. Some decades later, Gor’kov [13] derived a method to calcu- late the acoustic radiation potential that acts on a small sphere in an arbitrary acoustic ﬁeld. Barmatz and Col- las [14] applied the method of Gor’kov for deriving the acoustic radiation potential on a sphere for rectangular, cylindrical, and spherical standing wave ﬁelds. Because the geometries used by Barmatz and Collas are simple, the acoustic radiation potential is given by an analyti- cal solution. More recently, Xie and Wei [15], [16] used the boundary element method and the Gor’kov expression to study the inﬂuence of the geometrical parameters on a single-axis levitator. With this study, they designed a levitator that is able to levitate small living animals [17] and heavy tungsten balls [18]. An interesting approach to simulate an acoustic levitator was presented by Kozuka et al. [19]. In their work, the Rayleigh integral was used with multiple reﬂected waves between the transducer and the reﬂector to determine the standing wave acoustic ﬁeld. The numerical models commonly used in the design of acoustic levitators require the previous knowledge of the displacement distribution on the transducer face. There- fore, the complete levitator analysis requires at least 2 steps. First, a numerical model is used to determine the transducer displacement amplitudes. Then, these displace- ments are used in another numerical model to determine the acoustic radiation potential that acts on the levitated object. Aiming at modeling the entire acoustic levitator, this work presents a ﬁnite element analysis of a single-axis acoustic levitator consisting of a piezoelectric transducer and a plane reﬂector. Due to the levitator circular geome- try, axisymmetric elements are used to reduce the compu- tational time. The proposed model is also used to design a curved reﬂector and a new transducer with a concave radiating surface that maximizes the acoustic force on the levitated object. The simulation of the acoustic levitator includes the ﬂuid-structure interaction between the trans- ducer and air and the coupling between the electrical and mechanical properties of the piezoelectric material. II. N M The single-axis acoustic levitator used in this work con- sists of a 19.9-kHz transducer and a plane stainless steel Finite Element Analysis and Optimization of a Single-Axis Acoustic Levitator Marco A. B. Andrade, Flávio Buiochi, and Julio C. Adamowski Manuscript received August 20, 2009; accepted October 23, 2009. This work was supported by the following Brazilian sponsor agencies: CNPq, CAPES, and Petrobras/ANP. The authors are with the Mechatronics Engineering Department, Es- cola Politécnica da Universidade de São Paulo, São Paulo, Brazil (e-mail: marcobrizzotti@gmail.com). Digital Object Identiﬁer 10.1109/TUFFC.2010.1427