Nonlinear Fluid-Structure Dynamics in Biomedical Energy Harvesting Systems: A Multi-Physics Framework for Self Powered Medical Implants and Wearable Health Monitors

Abstract

This paper presents a comprehensive multi-physics analytical framework for understanding the nonlinear dynamics of fluid-structure interactions in biomedical energy harvesting systems, addressing critical limitations in traditional power sources for implantable medical devices. By integrating classical sloshing eigenvalue theory with fluid-structure interaction dynamics, we develop a coupled Hamiltonian model that captures the complex energy exchange between external mechanical excitation (from physiological movements such as respiration, cardiac motion, or locomotion), structural vibration of a cantilever beam with tip-mounted mass, and internal liquid sloshing within a prismatic cavity. The analysis reveals that phase-adjustable liquid motion can significantly enhance energy harvesting efficiency by modifying the effective system damping through resonance tuning, with the phase difference between structural oscillation and liquid sloshing governing the transition between energy dissipation (out-of-phase, Δφ ≈ π) and motion amplification (in-phase, Δφ ≈ 0). Drawing on recent advances in spectral geometry, we establish asymptotic expansions for the sloshing eigenvalue counting functions, decomposing the spectrum into discrete edge wave components localized near corners and continuous surface wave modes spanning the free surface. This decomposition demonstrates how corner geometry - particularly angles α=β=π/4 in V-shaped cavities - fundamentally shapes the spectral landscape and determines the availability of low-frequency resonant modes for biomechanical energy coupling. The nonlinear dynamical analysis identifies Hopf bifurcations at critical excitation velocities, followed by period doubling cascades leading to chaos, with the Feigenbaum constant δ ≈ 4.67 confirming universal scaling behavior. Using multi-scale perturbation methods, we characterize the slow-fast dynamics governing amplitude modulation and energy transfer across time scales relevant to physiological rhythms. Parametric optimization reveals that liquid volume fractions of 40-50% in V-shaped cavities achieve optimal frequency matching between sloshing modes (ωslosh =√(g/le )) and structural natural frequencies, enabling broadband operation across excitation frequencies of 0.5-10 Hz with power densities of 1-2 mW/m2 - sufficient for powering distributed biomedical sensor networks and low-power implantable devices. Computational verification using finite element methods confirms theoretical spectral predictions with deviations below 5%, while bifurcation analysis and phase dependent damping correlations (R2>0.92) validate the dynamical framework. This work bridges classical hydrodynamics - from Ursell's edge waves to modern spectral theory - with contemporary biomedical engineering applications, providing design guidelines for cavity geometry, liquid filling, and passive phase control that enhance operational bandwidth by 50-112% compared to liquid-free systems, offering a foundation for next-generation adaptive biomedical energy harvesters capable of operating in real-world physiological environments.

Keywords: Nonlinear Sloshing Dynamics; Biomedical Energy Harvesting; Fluid-Structure Interaction; Implantable Device Power; Wearable Health Monitoring; Self-Powered Medical Sensors

Citation

Abdollahzadeh Jamalabadi MY. Nonlinear Fluid-Structure Dynamics in Biomedical Energy Harvesting Systems: A Multi-Physics Framework for Self-Powered Medical Implants and Wearable Health Monitors. WebLog J Med Sci. wjms.2026.i2803. https://doi.org/10.5281/zenodo.23299478