波浪与柔性压电膜结构相互作用的简化模型分析

Simplified analysis of interactions between water waves and flexible piezoelectric membrane structure

摘要

压电材料可以用来捕获海洋波浪能，将波能直接转化为电能。将压电膜与柔性膜相结合构成潜式防波堤结构，可以作为一种新型的波能转换装置，同时具有波能发电和消波的双重功能。本研究推导了柔性压电膜结构的无量纲运动方程，并基于势流理论利用数值波浪水槽模拟研究了波浪与柔性压电膜结构的相互作用。给出了柔性压电膜结构附加质量的预测方法，并讨论了影响柔性压电膜结构运动响应的主要控制参数。波浪作用下柔性压电膜结构的运动响应满足非线性振动微分方程，非线性项由无量纲膜结构弹性模量E^*控制。获得了柔性压电膜结构的共振周期，并给出柔性压电膜结构的无量纲附加质量的计算拟合公式；当无量纲初始张力T^*₀取值在1.31×10^-5～6.33×10^-4时，给出了柔性压电膜线性与非线性响应临界控制参数E^*的范围。

Abstract

Piezoelectric materials can be used to capture ocean wave energy，converting it directly into electricity. The combination of piezoelectric membrane and flexible membrane to form a submerged breakwater structure can be used as a new type of wave energy conversion device，which has the dual functions of wave energy generation and wave dissipation. In this paper，the dimensionless motion equation of the piezoelectric flexible membrane system was derived，and the interaction between the wave and the flexible piezoelectric membrane structure was studied by the numerical wave flume based on the potential flow theory. A method for predicting the additional mass of the flexible piezoelectric membrane was presented，and the main control parameters which affect the motion response of the flexible piezoelectric membrane were discussed. The response of the flexible piezoelectric membrane under wave action satisfied the nonlinear vibration differential equation，and the nonlinear term was controlled by the dimensionless elastic modulus E ^* of the membrane. The resonant period of the flexible piezoelectric membrane was obtained，and the fitting formula of the dimensionless additional mass of the flexible piezoelectric membrane was given. When the dimensionless initial tension T^* ₀ ranges from 1.31×10^-5～6.33×10^-4，the critical control parameter E^* is given. The results can provide theoretical basis for the design and engineering application of flexible piezoelectric membrane structures.

关键词

柔性压电膜 / 共振周期 / 附加质量 / 消波效果 / 波浪能

Key words

flexible piezoelectric membrane / resonance period / added mass / wave energy dissipation / wave energy

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基金资助

国家自然科学基金资助项目(12072306)

福建省自然科学基金资助项目(2023J011442)