The Sound of Power: How Radial Vibrations Transmit 10x More Energy Through Metal
The Promise of Powering Through Metal
Imagine a submarine cruising miles beneath the ocean surface, its batteries running low. Today, recharging means surfacing or docking — risky in hostile waters, impractical in remote deployments. Now imagine a different scenario: a charging pad hovers near the hull, and power flows wirelessly through the metal skin itself, no holes, no seals breached, no vulnerability created.
This isn't science fiction. It's the goal of through-metal acoustic power transfer (TM-APT), an emerging technology that uses ultrasonic sound waves traveling through solid metal to deliver electrical energy. And a new study reveals something that could reshape how engineers design these systems: one particular resonance mode blows the other out of the water.
Radial mode — where the piezoelectric transducer expands and contracts like the surface of a drum — transfers nearly ten times more power than the more commonly studied thickness mode. In laboratory prototypes using aluminum plates, radial operation hit 667.5 watts. Thickness mode maxed out at 77.3 watts. (Mukhopadhyay et al., 2026)
That gap matters enormously. If acoustic wireless power is going to graduate from laboratory curiosity to viable technology for charging batteries inside sealed metal enclosures — in submarines, in hazardous industrial equipment, in implanted medical devices — engineers need to know which approach actually works at scale. This paper provides the most comprehensive experimental comparison to date, along with a practical tool for quickly evaluating which design choices will pay off.
How to Send Power Through Solid Metal
The basic physics has been understood for decades. Piezoelectric materials — the same quartz crystals that spark cigarette lighters and power watch batteries — deform when you apply voltage. Reverse that process: deform them mechanically, and they generate voltage. In acoustic power transfer, you exploit both effects simultaneously. Apply an alternating voltage to a transmitter piezoelectric element, and it vibrates at ultrasonic frequencies, sending pressure waves through whatever medium touches it. On the other side of that medium, a receiver piezo captures the vibrations and converts them back into electricity.
The problem is that real-world systems introduce complications that textbook physics ignores. When you bond a piezo to a metal plate with adhesive, you've changed everything. The mechanical properties shift. The resonance frequencies drift. Unwanted "spurious modes" — vibrations at oddball frequencies — siphon power away from where you want it. The quality factor, which describes how sharply a system resonates (think of the difference between a tuning fork and a loose spring), typically drops. What worked beautifully in simulation may perform poorly on your workbench.
"Conventional piezoelectric resonator models generally do not capture assembly-induced non-idealities," the researchers note. Standard approaches like the KLM and Mason formulations can predict thickness-mode behavior with reasonable accuracy, but radial mode is another matter — it depends strongly on adhesive properties, plate geometry, boundary conditions, and the inevitable variations that come from hand-assembling prototypes. (Mukhopadhyay et al., 2026)
To get past this uncertainty, the team took an explicitly experimental approach. Rather than relying on theoretical models, they built multiple realistic prototypes, measured their electrical characteristics directly, and used those measurements to calculate how much power could actually flow through.
Building Prototypes That Stand Up to Reality
The experimental setup centered on three metal plate assemblies, each designed to mimic a sealed metal enclosure with piezoelectric transducers bonded to opposite faces. Two used aluminum — one 12 inches in diameter with 0.125-inch thickness, the other 14 inches with quarter-inch thickness — and one used a 12-inch steel plate at 0.125-inch thickness. Piezoelectric discs, 38.8 millimeters in diameter and 2.54 millimeters thick, were attached at the center of each face using silver epoxy adhesive, with the assembly cured under vacuum for proper bonding.
The piezos themselves were PZT-APC 840, a "hard" piezoelectric material chosen specifically for high-power applications. Hard piezoelectrics sacrifice some sensitivity for durability: they have lower dielectric losses and higher mechanical quality factor, meaning they convert electrical energy to mechanical vibration (and back) with less waste heat. This matters when you're pushing hundreds of watts through a component the size of a hockey puck.
The researchers had to balance competing constraints. Applying higher voltage extracts more power, but push too hard and the piezo depolarizes — its internal crystal alignment breaks down, permanently degrading performance. The team selected a thickness of 2.54 millimeters specifically to allow operation up to roughly 900 volts AC while keeping the electric field stress within safe limits. They chose the largest off-the-shelf diameter available to maximize surface area for heat dissipation.
Metal plate dimensions were tuned to match the piezo's natural resonance. For thickness-mode operation, the plate thickness was calculated to create mechanical resonance at the same frequency as the piezo's self-resonance (approximately 789 kilohertz), ensuring efficient acoustic coupling between transmitter and receiver. For radial-mode operation, the relevant frequency is much lower — around 55 kilohertz — and plate diameter matters more than thickness. Here the researchers chose plates roughly ten times the piezo diameter to help suppress unwanted flexural vibrations while keeping the dominant radial mode clean.
The assembly process itself introduced variables. Surface preparation, adhesive application uniformity, cure time, and wire attachment all affect the final result. The team cleaned and roughened metal surfaces with sandpaper, applied epoxy in a 1:1 ratio covering exactly the piezo's footprint, and cured under vacuum for over six hours. But even with standardized procedures, small differences crept in. The Z-parameters (complex impedances) measured at the transmitter and receiver ports didn't always match, indicating asymmetric bonding or connection variations between the two sides of each prototype. This underscores why experimental characterization matters: theoretical models assume perfect symmetry, but real assemblies never deliver it.
Cross-section of a plate showing ideal propagation of acoustic waves in thickness mode, creating nodes and antinodes. The wave travels through the metal barrier, with the piezo discs bonded to either face serving as transmitter and receiver.
The Two Modes: Thickness vs. Radial
Acoustic resonators can vibrate in different patterns, and these patterns have profound implications for power transfer capability. Thickness mode — the more intuitive one — involves compression and expansion along the axis perpendicular to the piezo disc faces. Think of pressing down repeatedly on a spring. Radial mode involves expansion and contraction in the plane of the disc, like the surface of a drumhead moving up and down. Both modes can carry energy, but they interact very differently with bonded metal structures.
The team characterized both modes using a vector network analyzer (VNA), which measures how radio-frequency energy flows through a two-port network. By sweeping frequency and recording S-parameters (scattering parameters), they could extract the full impedance characteristics of each prototype and construct an equivalent circuit model for power transfer analysis.
The results were striking. In thickness mode, bonding the piezos to metal caused roughly a 10% shift in resonance frequency and a substantial reduction in quality factor — the resonant peak became broader and flatter, meaning less energy storage and more damping. Spurious modes also appeared. But in radial mode, the quality factor change was negligible. Instead, the main effect was introducing multiple significant spurious modes and significantly reducing the separation between resonance and anti-resonance frequencies. (Mukhopadhyay et al., 2026)
The practical consequences differ. Thickness mode's reduced Q-factor means the system can't store as much energy at resonance, but the spurious modes, while present, don't dominate. Radial mode maintains sharp resonance but spreads power across multiple frequency peaks, making optimal frequency selection more critical. The reduced resonance-anti-resonance separation in radial mode also makes frequency control more challenging — you're working in a narrower band where getting the operating point right matters enormously.
Comparison of impedance characteristics showing how bonding a standalone piezo to a metal assembly shifts the resonance frequency, reduces Q-factor, and generates spurious modes. This fundamental behavior drives the design choices that follow.
The Power Numbers
The researchers developed an optimization framework to find the maximum achievable power under practical constraints. They swept the load impedance and calculated transferred power at each frequency, always respecting two hard limits: depolarization voltage (preventing damage to the piezo crystals) and thermal constraints (keeping the piezo below 100°C with power loss under 45 watts). The result was an optimal operating frequency, load impedance, and transmitter voltage for each prototype in each mode.
The numbers tell a clear story. In thickness mode, the three prototypes achieved maximum powers of 67.8 watts (12-inch aluminum), 77.3 watts (14-inch aluminum), and 31.4 watts (12-inch steel). The optimal frequencies fell between resonance and anti-resonance for the aluminum plates, but shifted above anti-resonance for the steel plate. Required compensation was capacitive in most cases. The 14-inch aluminum plate won, delivering about 77 watts.
In radial mode, the same prototypes hit 667.5 watts, 226.7 watts, and 215.5 watts respectively — roughly ten times the thickness-mode values. Optimal frequencies fell below the resonance frequency in all cases, requiring inductive compensation. The 12-inch aluminum plate dominated with 667.5 watts, while the other two configurations clustered around 220 watts. (Mukhopadhyay et al., 2026)
Maximum Achievable Power: Thickness vs Radial Mode
Comparison of maximum power transfer in watts for each prototype and mode, showing radial mode's 10x advantage.
| Label | Value |
|---|---|
| Thickness Mode | 67.8 |
| Radial Mode | 667.5 |
Maximum achievable power comparison between thickness and radial modes across the three prototype configurations. Radial mode dramatically outperforms thickness mode, with the 12-inch aluminum plate achieving nearly 668 watts compared to its 68-watt thickness-mode maximum.
The higher radial-mode power comes at a price. Achieving it requires operating the transmitter piezos at up to 520 volts — close to the depolarization limit — and using much higher load impedances (up to 464 ohms versus under 90 ohms for thickness mode). The compensation networks also become more complex, with radial mode requiring inductors in the hundreds of microhenries versus capacitors for thickness mode. These aren't dealbreakers, but they represent different design challenges.
The researchers also note a critical practical concern: using conductive adhesive electrically connects both piezos through the metal plate, which compromises the galvanic isolation between transmitter and receiver. This can introduce circulating currents, especially in thickness mode, that falsely reduce apparent efficiency. They recommend monitoring for common-mode current flow and employing common-mode chokes if necessary.
A Shortcut for Design Engineers
Building prototypes, measuring their characteristics, and running full power transfer calculations is time-consuming. Design engineers need faster ways to evaluate whether a proposed configuration is worth pursuing. So the team proposed a figure of merit (FOM) that captures power transfer capability using just a few key parameters from basic impedance measurements.
The FOM combines two factors. The first is the geometric mean of the quality factors measured at the resonance peaks of the transmitter and receiver ports. High Q means the system stores energy efficiently and loses it slowly — good for power transfer. The second factor is the ratio of transfer impedance (how well the input voltage couples to the output) to the geometric mean of the driving-point impedances. This captures both coupling strength and how the assembly loads the source and output. (Mukhopadhyay et al., 2026)
Formally, the FOM is:
where $Q_{r1}$ and $Q_{r2}$ are the quality factors at resonance for the two ports, $Z_{12}$ is the transfer impedance, and $Z_{11}$ and $Z_{22}$ are the input and output impedances respectively. The researchers showed that this formula, derived intuitively from maximum power transfer principles, correctly ranks the three prototypes by power transfer capability and identifies frequency peaks that correspond closely to the optimal operating frequencies from detailed analysis.
For the aluminum plate prototypes, the FOM correctly predicted that the 12-inch configuration would outperform the 14-inch configuration in both modes. It also correctly identified radial mode as superior across the board. More importantly, it did this using only the -3 dB bandwidth measurements and impedance magnitudes — quantities any engineer with a basic VNA can extract in minutes, without running full power transfer optimization.
The FOM doesn't replace detailed analysis — it filters. Engineers can use it to quickly screen multiple design options and identify the most promising candidates, then invest the time for comprehensive evaluation only on those configurations. This could dramatically accelerate the design cycle for TM-APT systems.
Optimal Operating Frequency by Mode and Prototype
Comparison of optimal operating frequencies in kilohertz, showing thickness mode operates in hundreds of kHz while radial mode operates around 55-65 kHz.
| Label | Value |
|---|---|
| Thickness | 873.5 |
| Thickness (14" Al) | 902.4 |
| Thickness (Steel) | 926 |
| Radial | 63.65 |
| Radial (14" Al) | 57.16 |
| Radial (Steel) | 65.15 |
Optimal operating frequency comparison between thickness and radial modes. Thickness mode operates in the hundreds of kilohertz range, while radial mode operates around 55-65 kilohertz. The frequency choice has significant implications for power electronics design and component selection.
What the Data Reveals About Materials and Geometry
Looking across the three prototypes, several patterns emerge that could guide future design. Aluminum outperformed steel in both modes. In thickness mode, the aluminum plates delivered roughly double the power of the steel plate (68-77 watts versus 31 watts). In radial mode, the advantage was even more dramatic: 12-inch aluminum hit 668 watts while the other configurations topped out around 220 watts. This suggests that acoustic impedance matching — how well sound waves transfer between materials — may play a significant role, even though the wavelength calculations suggested similar behavior.
Plate diameter mattered more in radial mode than thickness mode. The larger 14-inch aluminum plate actually underperformed the smaller 12-inch plate in radial mode (227 watts versus 668 watts), while in thickness mode the relationship was reversed (77 watts versus 68 watts). This makes intuitive sense: radial mode depends on vibrations in the plane of the plate, which are more sensitive to boundary conditions and plate dimensions, while thickness mode depends on through-thickness vibrations that are less affected by lateral dimensions.
The results also highlight the importance of prototype repeatability. Even with standardized assembly procedures, the team observed asymmetries between the two sides of each prototype. The quality factor measured at the transmitter port sometimes differed from that at the receiver port, reflecting variations in adhesive thickness or wire attachment. This isn't a flaw — it's a reality the methodology embraces. The two-port network model accommodates these asymmetries naturally, using the geometric mean of the two port impedances in the FOM rather than assuming perfect symmetry.
The Limitations Realistically
The researchers are careful to acknowledge what their approach doesn't capture. All power predictions are based on small-signal VNA characterization, where excitation voltages are fractions of a volt. Real systems may operate at hundreds of volts, and piezoelectric materials exhibit nonlinear behavior at high drive levels. Resonance frequencies can shift, quality factors can change, and temperature-dependent property variations become significant when dissipating tens of watts in a small volume.
Voltage-dependent nonlinearities in piezoelectrics are well documented in the literature. At high drive levels, the effective stiffness of the material changes, which shifts resonance frequencies. Heat buildup softens materials and reduces Q. The adhesive layer may exhibit different properties under mechanical stress than it does at rest. The team recommends large-signal characterization as the next step — exciting the piezos with high-amplitude sinusoids and re-extracting impedance parameters — while noting this requires precautions against overvoltage damage to the receivers.
Mechanical boundary conditions also affected measurements. Simply placing the prototype on a rigid surface versus a soft foam support changed the measured quality factor. This introduces ambiguity: are you characterizing the assembly's intrinsic capability, or its capability under specific mounting conditions? The researchers recommend consistent mechanical fixtures and documenting boundary conditions carefully when comparing results.
The power predictions assume ideal lossless power electronics. Real inverters, rectifiers, and compensation networks have losses that will reduce delivered power. The optimal load impedances identified (ranging from 58 ohms to 464 ohms) and compensation requirements (capacitors to hundreds-of-microhenry inductors) will need to be implemented with real components. How much loss these introduce depends on frequency, component selection, and circuit topology — questions beyond this paper's scope.
Why This Matters for Real-World Applications
Through-metal acoustic power transfer sits at an interesting intersection of capability and challenge. The applications that motivate it — sealed metal enclosures in harsh or sensitive environments — are genuinely important. Submarines and underwater vehicles need periodic charging. Industrial equipment operating in explosive atmospheres (oil platforms, chemical plants) cannot have electrical feedthroughs that might spark. Medical implants in metal cases need recharging without breaking the sterile barrier. Aerospace systems need power delivered through bulkheads without penetration.
Wireless power transfer through metal barriers is not a new problem, but existing solutions have limitations. Electromagnetic induction — the technology in wireless phone chargers — doesn't work through metal; the conductive barrier shorts out the magnetic field. Capacitive coupling (wireless power through electric fields) has very short range and only works through thin barriers. Acoustic transfer through metal is one of the few options that scales to practical power levels while handling substantial barrier thickness.
Previous work has demonstrated kilowatts of power transfer through metal using single piezoelectric elements, but those systems assumed idealized resonators. Moving to through-metal configurations with separate transmitter and receiver elements introduces the assembly effects this paper characterizes. Understanding those effects quantitatively is essential for designing systems that actually deliver their theoretical performance.
The radial-versus-thickness comparison is particularly valuable because these modes have different practical implications beyond raw power numbers. Thickness mode operates at higher frequencies (hundreds of kilohertz), which enables smaller passive components in the power electronics but also generates more switching losses and electromagnetic interference. Radial mode at lower frequencies (tens of kilohertz) is more compatible with conventional power electronics but may excite structural vibrations at problematic frequencies.
The figure of merit is arguably the paper's most practical contribution. Engineers developing TM-APT systems face a vast design space: different piezo materials, adhesive types, plate geometries, bonding processes, and operating modes. Experimental characterization is slow and labor-intensive. A quick metric that captures power transfer potential from basic measurements lets engineers iterate faster and identify promising configurations without building and testing every option.
What's Next
This work points toward several obvious extensions. Large-signal characterization would validate whether the small-signal predictions hold up under real operating conditions. The team specifically mentions nonlinear effects from piezoelectric materials, adhesive layers, and temperature-dependent property variations as areas requiring further study.
Thermal management deserves deeper investigation. The 100°C limit the researchers imposed is conservative — many piezoelectric materials can operate hotter — but heat removal from the bonded piezo through the metal barrier is genuinely challenging. Better understanding of heat paths, thermal interface materials, and active cooling could relax this constraint and enable higher power transfer.
Fabrication process development could reduce the assembly variability the team observed. Automated bonding with controlled adhesive thickness, consistent curing profiles, and robust electrical connections would make prototype performance more predictable. This is a materials and manufacturing engineering challenge, but it directly impacts whether experimental results translate to production systems.
Extending the approach to non-circular geometries matters for practical deployments. Metal enclosures aren't always round, and rectangular or irregular shapes introduce different vibrational modes and boundary conditions. The spurious mode complexity observed with square plates in prior work suggests these geometries require careful characterization.
Finally, demonstration at scale — building and testing a complete system delivering hundreds of watts through a metal barrier with realistic power electronics — would prove whether the theoretical performance actually materializes in practice. This paper provides the characterization framework and design guidance; translating that into a working system is the next step.
The researchers have given the field something valuable: not just data, but a methodology. Their experimental approach, two-port network analysis framework, and FOM for rapid screening constitute a toolkit that other engineers can use and extend. That's how technologies mature from promising demonstrations to practical systems — one careful characterization at a time.