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基于模态试验修正的几何非线性降阶模型及复合材料加筋壁板强声响应验证

A MODAL-TEST-UPDATED GEOMETRICALLY NONLINEAR REDUCED-ORDER MODEL FOR PREDICTION OF RESPONSES UNDER INTENSE ACOUSTIC LOADING OF A COMPOSITE STIFFENED PANEL 1)

  • 摘要: 准确高效地预测声致振动响应是飞行器薄壁结构抗声疲劳设计的重要基础. 针对强随机声载荷下薄壁结构的几何非线性以及名义有限元模型与试验件的动力学偏差, 提出一种基于模态试验修正的非线性降阶模型(nonlinear reduced-order model, NLROM)方法. 方法创新在于构建“低幅模态试验校准—修正后模型重新降阶—强声响应独立验证”的耦合流程: 第一, 基于模态坐标投影构建含二次、三次非线性刚度项的降阶动力学方程, 以低维形式描述弯曲—膜内耦合及模态间非线性作用; 第二, 提出一阶主导模态频率灵敏度参数校准策略, 利用安装状态下的低幅模态试验识别敏感等效参数, 并在参数修正后重新计算模态基底和非线性刚度系数, 使低幅试验信息进入强声响应预测.163 dB强声响应数据不参与参数识别, 仅用于独立验证. 平面薄板算例表明, 所构建NLROM能够复现全阶有限元模型的主要共振峰,A、B测点位移均方根响应(root mean square, RMS)相对误差分别为4.0%和0.73%, 计算效率提高约14.2倍. 复合材料加筋壁板163 dB试验中, 修正参数NLROM对6#测点加速度RMS和5#测点0°方向应变RMS的相对误差分别为12.6%和0.46%, 均优于初始参数模型及修正参数线性模型. 四模型对比表明, 模态参数修正主要改善主导频率和基础响应量级, 几何非线性描述进一步改善强声载荷下的响应能量预测. 该方法可在当前结构、50 ~ 600 Hz载荷频带和已验证响应幅值范围内兼顾预测精度与计算效率, 为实际薄壁结构强声响应快速评估提供参考.

     

    Abstract: Accurate and efficient prediction of acoustically induced vibration is essential for the acoustic fatigue-resistant design of aircraft thin-walled structures. To address geometric nonlinearity under intense random acoustic loading and discrepancies in dynamic characteristics between nominal finite element models and test structures, a nonlinear reduced-order modeling (NLROM) method calibrated using modal test data is proposed. The primary innovation lies in an integrated framework comprising low-amplitude modal-test calibration, renewed model reduction of the updated model, and independent validation under intense acoustic loading. First, reduced-order dynamic equations incorporating quadratic and cubic nonlinear stiffness terms are formulated through projection onto modal coordinates, enabling the bending–membrane coupling and nonlinear modal interactions to be represented in a low-dimensional form. Second, a parameter-calibration strategy based on the frequency sensitivity of the first dominant mode is proposed. Low-amplitude modal tests conducted under installed boundary conditions are employed to identify sensitive equivalent parameters. Following parameter updating, the modal basis and nonlinear stiffness coefficients are recalculated, thereby incorporating information from the low-amplitude tests into the prediction of responses under intense acoustic loading. The response data measured under 163 dB acoustic loading are not used for parameter identification and are reserved exclusively for independent validation. A flat-plate example demonstrates that the proposed NLROM reproduces the principal resonance peaks of the full-order finite element model. The relative errors in the displacement root mean square (RMS) values at measurement points A and B are 4.0% and 0.73%, respectively, while the computational efficiency is improved by approximately 14.2 times. In the 163 dB acoustic test of a composite stiffened panel, the updated-parameter NLROM yields relative errors of 12.6% for the acceleration RMS at measurement point 6 and 0.46% for the strain RMS in the 0° direction at measurement point 5, outperforming both the initial-parameter model and the updated-parameter linear model. Comparisons among the four models indicate that modal-parameter updating primarily improves the dominant frequencies and overall response levels, whereas the incorporation of geometric nonlinearity further improves the prediction of response energy under intense acoustic loading. Within the investigated structure, the loading frequency range of 50–600 Hz, and the validated response-amplitude range, the proposed method achieves a favorable balance between predictive accuracy and computational efficiency, providing a practical reference for the rapid assessment of intense acoustically induced responses in thin-walled structures.

     

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