ACOUSTIC WAVE PROPAGATION IN HIGH SCALE IMPEDANCE MISMATCH MEDIUMS

A finite element analysis of acoustic propagation in a multilayered medium is presented in this paper. A circular transmitter (diameter 14 mm, thickness 3 mm) and a rectangular receiver (20×10×0.5 mm) are set to detect the variations in the propagation pattern. A complex medium (70×40×60 mm) composed of skin, fat, muscle, bone and liquid is designed in a simulated environment. A scale of frequencies (10 kHz to 2 MHz) is applied to trace the impact on the propagation pattern as well. It is found from the analysis that fat and liquid layers affect the acoustic propagation the most (-69 dB), which results in a significant drop in the received sound pressure level at the receiving end. Again, other than skin and fat layers, low frequencies (less than 1 MHz) are more beneficial in terms of sound pressure level. However, higher frequencies contribute to lower displacements at the receiving end, which will cause less power potential as well. ABSTRAK: Analisis elemen terhingga bagi penyebaran akustik dalam medium berlapis dibentangkan dalam kajian ini. Pemancar bulat (diameter 14 mm, ketebalan 3 mm) dan penerima segi empat tepat (20 × 10 × 0.5 mm) diatur bagi mengesan perubahan pola penyebaran. Medium kompleks (70 × 40 × 60 mm) yang terdiri daripada kulit, lemak, otot, tulang dan cecair direka dalam persekitaran simulasi. Skala frekuensi (10 kHz hingga 2 MHz) digunakan bagi mengesan corak penyebaran. Dapatan kajian menunjukkan bahawa lapisan lemak dan cecair mempengaruhi penyebaran akustik (-69 dB), yang mengakibatkan penurunan mendadak tahap penerimaan tekanan bunyi di hujung penerima. Selain lapisan kulit dan lemak, frekuensi rendah (kurang dari 1 MHz) adalah lebih berguna dari segi tahap tekanan suara. Walau bagaimanapun, frekuensi lebih tinggi menyebabkan kurang anjakan di hujung penerima, sekaligus mengurangkan potensi daya tenaga.


INTRODUCTION
Wireless power transfer (WPT) has drawn significant industrial attention in recent times. The initial intention of this scientific module was to provide mobility to handheld devices. Soon, it was realized that over kW range power can be transferred wirelessly by https://doi.org /10.31436/iiumej.v22i2.1563 WPT. To do so, inductive, capacitive, microwave, and acoustic coupling can be used. Among these, inductive WPT is widely practiced and commercially available with high efficiency and power (30 kW) [1][2][3]. It was recently reported that 5 to 7 meter separation distance between receiver and transmitter was achieved by inductive WPT [4,5]. Nevertheless, inductive WPT suffers from coupling misalignment and penetration losses [6]. Capacitive WPT is still in the developing stage. Unfortunately, the inverse property of capacitance to distance limits the separation (<1 mm) and efficiency of this WPT [7][8][9][10]. Microwave WPT can provide very high efficiency and wide propagation area as well, due to its high energy density penetration [11][12][13]. Again, optical WPT is capable of transmitting energy over a long range (>km), however, suffers from the requirement for a line of sight [14][15][16].
Acoustic energy transfer (AET), unlike the aforementioned WPTs, transfers power by propagating energy as sound or vibration waves [17]. The propagated energy is then collected by a receiver which converts the vibration energy to useful electrical energy. To do so, piezoelectric conversion termed as piezoelectricity is practiced so far. Recent interest in wireless powering of implantable devices added to the need to study acoustic propagation in a complex multilayered medium with high scale impedance mismatch, which closely characterizes the human body. Hence, in this paper, we have designed a multilayer medium that is composed of the same type of layers available in the human body. We have considered a wireless pacemaker system and hence, we have limited our study to the human chest only.
The scope of this paper includes a finite element analysis of the acoustic wave propagation in a multilayered medium. The medium is specific for very high impedance mismatched layers. As we are considering AET for implants, it is worthy to investigate the impact of the medium with different physical characteristics. Also, the effect of applying a wide range of frequencies (10 kHz to 2 MHz) is considered in the scope. Nevertheless, dynamic receivers or transmitters are not considered in this study, rather we have considered the fixed locations for the transmitter and receiver.

MODELLING IN FINITE ELEMENT ANALYSIS
It is possible to analyze the acoustic propagation under a simulated environment using finite elements. Hence, the system is designed and analyzed with finite elements. As such, a transmitter-receiver coupling is designed for the finite element analysis. The transmitter is a simple circular transceiver with a zinc oxide (ZnO) layer and an aluminum (Al) layer. It is 14 mm in diameter and 3 mm in thickness (Al layer 1 mm and ZnO 2 mm). In contrast, the receiver is a simple ZnO rectangular block with a 20×10×0.5 mm 3 dimension. The reason to keep the transmitter in circular shape is to use the benefit of the directional acoustic beams. Also, a rectangular configuration is more beneficial as receiver [18]. The transmitter and receiver are depicted in Fig. 1.
The medium is designed to resemble human chest layers. It is a 70×40×60 mm 3 block with skin, fat, muscle, bone and liquid (water) layers. Hence, the medium reflects a very high scale impedance mismatch within the layers. An additional liquid block is added to compensate for the medium impedance. The medium details are given in Fig. 2 Figures 3,4, and 5 describe the propagation pattern and received sound pressure level by the rectangular receiver. From the figures, it is clear that fat and liquid layers contribute to decreasing the acoustic pressure field and sound pressure level. However, the irregular spatial acoustic beam formation is observed as well. The sound striking the receiving cantilever does so with a pressure value of approximately 111 dB to as high as 114 dB. A more focused presentation of the received sound pressure level is placed in Fig. 5. The electric potential generated in the receiver terminal has the range of -9.0320e-15 to -5.6501e-13 volt. The total displacement in the receiver is found to be 6.94e-9 mm. Again, the maximum stress on the receiver is 31.4 Pa.  The impacts of an applied frequency of 40 kHz is presented here. The results suggest that low-density mediums mostly impact the acoustic pressure fields. These result in weaker SPL to the next medium. However, if we increase the applied frequency, the reflections within the medium become more severe. In fact, at 2 MHz, the self-reflection becomes visible and mainly located between the two liquid layers. Figure 3 presents the SPL reflected by the receiver. It is clear from the figure that the reflected SPL can vary from 110 to -50 dB. Also, the reflections mainly occurred in the middle of the receiver even though it is placed at the bottom end of the medium. Figure 6 presents the SPL against the applied frequencies on the layer with the attached receiver. The applied frequency range is 10 kHz to 2 MHz. The SPL varied from as low as 68 dB to as high as 132 dB. The lowest SPL is found at 1.45 MHz (68 dB) whereas the highest SPL values are available close to 1.21 MHz (132 dB). Hence, it is clear from the figure that the SPL distribution is not benefitted by the frequency increment.     Table 2 describe the more specified SPL profile according to the layers of the medium. According to the design, there are six layers in total between the transmitter and the receiver. Layer 1 and layer 2 are of liquid material. In layer 1, min observed SPL is approximately 68 dB at 1.45 MHz, whereas, max SPL is 132 dB at 1.21 MHz. In layer 2, min SPL drops down to approximately 57 dB at 0.79 MHz, and max SPL to 126 dB at 0.55 MHz. The SPL drops even more in layer 3 to min approximately 52 dB at 1.    Figures 8 and 9 show the displacements that occurred in the receiver. Root mean square (RMS) of displacements is presented in Fig. 8 while the total displacements are shown in Fig. 9. Interestingly, increased frequencies have decreased the displacements in the receiver. As the wavelength becomes smaller, it is losing power as well. From the figure we can see, 0.065 nm total displacements are observed (RMS 0.047 nm) for 10 kHz applied frequency. In comparison, 0.04 nm (RMS 0.028 nm) for 30 kHz, and less than 0.01 nm (RMS 0.047 nm) for 20 kHz. The rest of the frequencies will cause less than 0.004 nm displacements.

ACOUSTIC PROFILE AND ANALYSIS
From the aforementioned results, it is noticeable that increasing frequencies is not going to be beneficial in the context of displacements that will directly impact the AET performance. For acoustic energy transfer, the transmitted energy will be collected by the receiver in the form of acoustic vibrations. Now, vibration will cause certain displacements in the receiver and the relationship is linear. Higher vibration will certainly cause higher displacements. In relation, higher displacements in piezoelectric layers will benefit with a higher electrical output which is the ultimate goal of a wireless power transfer system. Therefore, it is evident that for AET lower frequencies are preferable for implantable devices.

CONCLUSION
Finite element analysis of acoustic wave propagation in a very high scale impedance mismatch medium is presented in this paper. The analysis is mainly focused on acoustic energy transfer for implantable wireless devices as the medium contains a wide range of impedances. A circular transmitter and a rectangular receiver are paired to transfer acoustic waves in a multilayered medium that replicates the high scale impedance mismatch. A prescribed vibration is generated in the transmitter which is collected by the receiver to evaluate the impact of the multilayer configuration on the acoustic propagation. Sound pressure level (SPL) and receiver displacements are particularly focused to trace the effect of wide scale applied frequencies. It is found from the results that the SPL can be varied from as low as 68 dB (1.45 MHz) to as high as 132 dB (1.21 MHz). Hence, it is clear from the figure that the SPL distribution is not benefitted by the frequency increment. The electric potential generated in the receiver terminal has the range of -9.0320e-15 to -5.6501e-13 volts. The total displacement in the receiver is found to be 6.94e-9 mm. Again, the maximum stress on the receiver is 31.4 Pa. Therefore, as conclusion, the increased frequency can benefit the SPL while it decreases the displacements in the receiving end. As the displacement magnitude directly impacts the receiver performances, it is more beneficial to use less than MHz range frequencies for acoustic energy transfer applications.