Analysis of the Resonant Characteristics of a Tonpilz Transducer with a Fixed Tail Mass by the Equivalent Circuit Approach

Abstract

In this paper, the resonant characteristic of a Tonpilz transducer with a fixed tail mass has been studied by means of an equivalent circuit approach. An equivalent circuit has been designed to describe the characteristic of a Tonpilz transducer that has an additional resonance because of its fixed tail mass. The transmitting voltage response of the transducer calculated by the designed circuit has been compared with that by the FEA (finite element analysis) to confirm the validity of the circuit. This equivalent circuit approach produces identical results with the FEA, in which the variation of resonant frequencies and TVR has been clearly figured out in relation to the stiffness of the mounting fixture and the mass of the tail mass. The suggested equivalent circuit can be utilized to figure out the characteristics of the Tonpilz transducer more efficiently than FEA that requires much calculation time and revision of the models in accordance with the variation of design variables.

Modeling and Design of a Rear-Mounted Underwater Projector Using Equivalent Circuits

“…Figure 2 shows the created two-dimensional (2-D) axis-symmetric model of the transducer and water medium. The basic model has a dimension similar to that used in our preliminary works [ 13 , 14 ]. For simplicity, a tie-rod was removed and only two piezoceramic disks with opposite poling directions were stacked in the model.…”

“…The superscripts D and E denote constant electric displacement and constant electric field, respectively. These considerations regarding component dimensions, circuit branch, and associated parameters represent the most important difference from our previous model [ 14 ], although a similar rear-mounting concept was applied in the previous EC model [ 13 ]. While our previous work introduced a lumped circuit model of the rear-mounted Tonpilz design, taking some errors caused by the simplification to lumped elements [ 14 ], this distributed model ensures a more accurate presentation of the transducer components.…”

“…In a previous study, we introduced the concept of a fixed tail mass Tonpilz design to mitigate this design problem ( Figure 1 ) [ 13 ]. In this design, an elastomer suspension supports a tail mass.…”

“…Due to the spring constant of a suspension, an additional resonance vibration mode exists in addition to the longitudinal resonance mode of a Tonpilz. This rear-mounted Tonpilz projector generated an elastic fixture-induced whole-body oscillation mode below the longitudinal resonance frequency, which allowed dual-band operation of the transducer [ 14 ]. Although the low-frequency mode showed a noticeable lack of transmitting sensitivity (less than −20 dB compared to the longitudinal mode), our preliminary studies, however, showed the feasibility of utilizing such low-frequency resonance for a separate transmission mode.…”