The improvement of ultrasonic phased array detection technology is a major concern of engineering community. Orthotropic piezoelectric fiber composite (OPFC) can be constructed to multielement linear array which may be applied conveniently to actuators and sensors. The phased array transducers can generate special directional strong actuator power and high sensitivity for its orthotropic performance. Focusing beam of the linear phased array transducer is obtained simply only by adjusting a parabolic time delay. In this work, the distributed point source method (DPSM) is used to model the ultrasonic field. DPSM is a newly developed mesh-free numerical technique that has been developed for solving a variety of engineering problems. This work gives the basic theory of this method and solves the problems from the application of new OPFC phased array transducer. Compared with traditional transducer, the interaction effect of two OPFC linear phased array transducers is also modeled in the same medium, which shows that the pressure beam produced by the new transducer is narrower or more collimated than that produced by the conventional transducer at different angles. DPSM can be used to analyze and optimally design the OPFC linear phased array transducer.

The ultrasonic phased array detection technology which was proposed by Crawford of America Conoco Company originated in the 1960s [

The group of Luo [

In this paper, new OPFC phased array transducers are semianalytically modeled by the distributed point source method (DPSM). The DPSM is used to model ultrasonic transducers for computing pressure and velocity fields generated by the new transducers. The group of Placko [

Based on a spatial distribution of point source, DPSM modeling can be used to compute the pressure field generated by an ultrasonic transducer which is placed in homogeneous or nonhomogeneous fluid media. A traditional transducer composed of many point sources which oscillate at the same time. Equation (

Geometric model of DPSM.

After adding the contributions of

Because the transducer surface vibrates with a nonzero velocity in

Vector

Finally, the square matrix

In the above equations

Then, the pressure

If the observation points are identical to the transducer surface points, matrix

When two transducers are placed in the same fluid, the pressure field can be modeled by superimposing two simpler parts, as shown in Figure

The interaction effects of two transducers by superimposing two parts.

The DPSM theory presented above is used to model ultrasonic field generated in a homogeneous fluid (water) by OPFC ultrasonic phased array transducer. The near field length and the divergence angle can be calculated in the method. Compared with the closed form analytical values, we can validate the accuracy of DPSM. The near field length

Coordinate coefficient of rectangle source acoustic field of OPFC element.

Figure

Spatial sources distribution.

Figure

Acoustic pressure along

Acoustic pressure variation in

Focusing beam is accomplished by combining a spherical timing relationship to produce a beam, which is focused at a given range and propagates at a specific angle. The focusing delays can be calculated by the following traditional formula [

Geometry of linear OPFC phased array for focal point

Consider Taylor expression,

Substituting (

So,

The delay of the

OPFC phased array transducer is composed of many elements arranged in a certain pattern that emit acoustic energy at different times. The elements can be pulsed in certain sequence to control the beam angle depending on the time delay.

OPFC phased array transducer can easily steer an ultrasonic beam in different directions without rotating or moving. But the traditional transducers are rotated to obtain the desired steering direction. Figure

(a) A steering angle of a phased array transducer. (b) A conventional transducer rotated at an angle.

Figure ^{2} and the number of point sources is 80. Each OPFC element is discredited into five point sources distributed along the

Acoustic pressure field generated by an OPFC phased array transducer for steering angles (a) 0°, (b) 15°, (c) 30°, and (d) 45°.

Acoustic pressure field generated by a traditional transducer for steering angles (a) 0°, (b) 15°, (c) 30°, and (d) 45°.

Figure

Comparison of the pressure by phased array and traditional transducer along the axis.

The interaction effect between two OPFC phased array transducers placed in the same medium is studied. Two transducers faces are placed parallel to each other and the central axes are collinear. The acoustic field generated by the one end as well as the scattered fields by the other end transducers is calculated. The surrounding medium is water. Figures

Acoustic pressure in the

Acoustic pressure in the

The fabrication principle of OPFC linear phased array is demonstrated for the special orthotropic performance. An OPFC linear phased array transducer with dynamic focusing is modeled by using DPSM. DPSM technology was utilized to compare the behavior of focusing in different angles of OPFC linear phased array and traditional transducer. Two linear phased array transducers placed face to face in the same medium are also modeled to study modeled to study the interaction effect. This demonstrated the importance of focusing in the near fields, while the directivity for focusing is very well defined. The OPFC linear phased array transducer can produce stronger and better collimated beams to detect the damages.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank the support of “863 Project” (2009AA03Z107), Natural Science Foundation of China (11272138), Jiangsu University Foundation (14JDG022), Doctor Point Foundation Project (20123227130002), and their colleagues for their contribution to the work.