Fluid-structure-electrical Modeling of Droplet Impact on Piezoelectric Beams Using Modified SPH Method

doi:10.3901/JME.260312

Abstract

Abstract: To accurately predict the complex fluid-structure interactions (FSI) of droplet impact on piezoelectric beams and the electromechanical coupling behaviors, a three-dimensional numerical model is developed based on the smoothed particle hydrodynamics (SPH) method and Mindlin-Reissner theory. This model integrates a weakly compressible SPH (WC-SPH) model for simulating the droplet and a total Lagrangian SPH (TL-SPH) shell model for simulating the thin-shell (beam) structure. The WC-SPH and TL-SPH models are coupled via a fluid-solid conatact algorithm to establish an efficient 3D numerical framework. By considering the piezoelectric constitutive relations and employing the shell mid-surface to describe the three-dimensional deformation of the structure, this model can accurately reproduce key droplet dynamics observed in impact experiments, such as spreading, rebound, and splashing. It can also predict the deformation and output voltage of the piezoelectric beam, achieving excellent agreement with experimental results, thereby comprehensively validating the effectiveness and accuracy of the SPH model. The influence of impact parameters and key structural parameters on the harvester performance is systematically analyzed. The research results serve as an effective tool for performance analysis and optimal design of piezoelectric droplet energy harvesting systems.

Key words: smoothed particle hydrodynamics, fluid-Structure Interaction, droplet impact, piezoelectric effect, energy harvesting

CLC Number:

TH113.1

HAO Guannan, LI Zhinan, ZHANG Hongxin, YU Ran, ZHANG Shuai. Fluid-structure-electrical Modeling of Droplet Impact on Piezoelectric Beams Using Modified SPH Method[J]. Journal of Mechanical Engineering, 2026, 62(13): 207-219.

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URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260312

http://www.cjmenet.com.cn/EN/Y2026/V62/I13/207

References

[1] CHEN Shuangyin，XIONG Chengwang，LIU Jianhua，et al. Energy collection from water flow based on single-electrode triboelectric nanogenerators[J]. Journal of Marine Science and Application，2025，24(2)： 415-427.
[2] WANG Tianrun，GUO Zinan，JIN Hao，et al. A coral-inspired and fully self-powered wave monitoring system based on hybridized triboelectric-electromagnetic nanogenerator[J]. Sensors and Actuators A：Physical，2025，387：116451.
[3] 单小彪，隋广东，田海港，等. 潜水式尾流激振压电俘能器的输出性能研究[J]. 机械工程学报，2022，58(20)：101-110. SHAN Xiaobiao，SUI Guangdong，TIAN Haigang，et al. Output characteristics investigation of submersible wake-excited piezoelectric energy harvester[J]. Journal of Mechanical Engineering，2022，58(20)：101-110.
[4] TANG Jingyao，LI Yiheng，YU Yirong，et al. Recent progress in flexible piezoelectric tactile sensors：materials，structures，fabrication，and application[J]. Sensors，2025，25(3)：964.
[5] 郝冠男. 水滴冲击压电俘能结构力电耦合响应机制研究[D]. 青岛：中国石油大学(华东)，2022. HAO Guannan. Electromechanical coupling response mechanism of piezoelectric energy harvesting structures under water droplet impact[D]. Qingdao：China University of Petroleum (East China)，2022.
[6] DONG Xiangwei，LI Zengliang，MAO Zirui，et al. Smoothed particle hydrodynamics simulation of liquid drop impinging hypoelastic surfaces[J]. International Journal of Computational Methods，2020，17(05)：1940001.
[7] ZHANG Haixiang，ZHANG Xiwen，YI Xian，et al. Effect of wettability on droplet impact：spreading and splashing[J]. Experimental Thermal and Fluid Science，2021，124：110369.
[8] WEISENSEE P B，MA J，SHIN Y H，et al. Droplet impact on vibrating superhydrophobic surfaces[J]. Physical Review Fluids，2017，2(10)：103601.
[9] MORALES F A P，SERFATY R，VEDOVOTTO J M，et al. Fluid–structure interaction with a finite element–immersed boundary approach for compressible flows[J]. Ocean Engineering，2023，290：115755.
[10] CHEN Feiguo，GE Wei. A review of smoothed particle hydrodynamics family methods for multiphase flow[J]. Chinese Journal of Theoretical and Applied Mechanics，2021，53(9)：2357-2373.
[11] BAGHERI M，MOHAMMADI M，RIAZI M. A review of smoothed particle hydrodynamics[J]. Computational Particle Mechanics，2024，11(3)：1163-1219.
[12] LONG Ting，HUANG Can，HU Dean，et al. Coupling edge-based smoothed finite element method with smoothed particle hydrodynamics for fluid structure interaction problems[J]. Ocean Engineering，2021，225：108772.
[13] CHEN Cheng，SHI Wenkui，SHEN Yanming，et al. A multi-resolution SPH-FEM method for fluid–structure interactions[J]. Computer Methods in Applied Mechanics and Engineering，2022，401：115659.
[14] HUO Ye，ZHONG Yuguang，XIN Minyan，et al. Modeling and simulation of droplet impact on an elastic beam based on FEM-SPH and SPH-SPH FSI methods[J]. Ocean Engineering，2024，310：118730.
[15] YU Ran，HAO Guannan，YANG Weijia，et al. An unresolved SPH-DEM model for simulation of ductile and brittle surface erosion by abrasive water-jet (AWJ) impact[J]. Scientific Reports，2024，14(1)：26115.
[16] SALEHIZADEH A，SHAFIEI A. A coupled ISPH-TLSPH method for simulating fluid-elastic structure interaction problems[J]. Journal of Marine Science and Application，2022，21(1)：15-36.
[17] HAO Guannan，DONG Xiangwei，LI Zengliang. Numerical investigation of water droplet impact on horizontal beams[J]. International Journal of Modern Physics C，2020，31(08)：2050118.
[18] ZHANG Aman，SUN Pengnan，MING Furen，et al. Smoothed particle hydrodynamics and its applications in fluid-structure interactions[J]. Journal of Hydrodynamics，Ser. B，2017，29(2)：187-216.
[19] 王志超，李大鸣，胡永文. 一种SPH应力修正算法及自由表面流中的应用[J]. 计算力学学报，2017，34：101-105. WANG Zhichao，LI Daming，HU Yongwen. A SPH stress correction algorithm and its application in free surface flow[J]. Chinese Journal of Computational Mechanics，2017，34：101-105.
[20] XIONG Yuege，WANG Xiaokun，XU Yanrui，et al. Dual-mechanism surface tension model for SPH-based simulation[J]. The Visual Computer，2024，40(7)：4765-4776.
[21] AKINCI N，AKINCI G，TESCHNER M. Versatile surface tension and adhesion for SPH fluids[J]. ACM Transactions on Graphics，2013，32(6)：1-8.
[22] TADDEI L，LEBAAL N，ROTH S. Axis-symmetrical Riemann problem solved with standard SPH method. Development of a polar formulation with artificial viscosity[J]. Computers & Mathematics with Applications，2017，74(12)：3161-3174.
[23] MONAGHAN J J. Smoothed particle hydrodynamics[J]. Reports on Progress in Physics，2005，68(8)： 1703-1759.