基于等效场空间预报噪声的高阶梯度光滑无网格方法研究

The control of noise radiated by vibrating structure in low and middle frequency ranges is a major challenge in the design and build of ships and warships all over the world. Accurately predicting the radiated acoustic field is the premise of noise control. However, it has not been well solved for accurate vibration noise predicting in the frequency range (around f≤500 Hz). Based on the coupling of meshfree weak-form method and Dirichlet to Neumann (DtN) boundary, this project is aiming to develop a new method of computing sound radiation in infinite domain for accurate prediction of the noise from the ship structure. In order to achieve research objective, main contents are as follows. Firstly, the coupled model of the meshfree weak-form method and the DtN boundary will be studied to establish mathematical formulation correctly. Secondly, the influence on numerical dispersion error from softening stiffness using high-order smoothing technique and partly smoothed form will be investigated. Thirdly, meshfree interpolation scheme will be optimized for reducing interpolation error. Finally, the numerical and experimental tests will be designed to verify the accuracy, stability and practicability of the method. The successful implementation of this project will generate an accurate and effective numerical method for sound radiation predicting, which can thoroughly improve the numerical accuracy of low and middle frequency acoustic problems and lay not only theoretical foundation but also provide technical support for noise control in ship designing and building.

控制结构振动辐射的中低频噪声是世界各国舰船设计与制造面临的重大难题，而准确预报出结构辐射的声场是进行噪声控制的前提，但是中低频段（约f≤500 Hz）准确的振动噪声预测还未得到很好地解决。本项目拟对弱式无网格法耦合Dirichlet to Neumann （DtN）边界进行研究，构建能够准确计算无限域结构声辐射的数值方法，为船舶结构中低频噪声的准确预报提供理论和算法依据。具体内容包括：研究建立计算无限域结构声辐射的弱式无网格耦合DtN边界的数学模型；在弱式无网格框架下，研究通过高阶梯度光滑算法软化数值模型刚度及采用局部梯度光滑来降低数值色散误差，通过优化无网格插值方案来减小数值插值误差；并通过数值和试验验证方法的准确性、稳定性及实用性。本项目的完成将构建一套准确有效的预报结构声辐射的数值方法，全面提高结构中低频段噪声预报的精度，为舰船进行噪声控制奠定理论和技术基础。

声场数值计算技术是舰船噪声研究的一个重要领域。本项目围绕自由场空间声场计算中的色散误差控制和浅海舰船地震波预报算法缺失的基础性关键问题，全面系统的开展了基于无网格预报声场的数值方法研究和基于波叠加计算舰船地震波的理论与算法研究，内容包括：1）自由场声辐射计算的弱式无网格模型的建立，以提高中、低频声场预报精度；2）水下声散射计算的光滑无网格模型的构建，抑制中频数值色散误差；3）波数积分叠加理论与算法研究，解决海水-弹性海底均质浅海环境中水下舰船地震波精确预报的需求。取得的主要成果有：建立了弱式无网格耦合Modified Dirichlet to Neumann（MDtN）边界声辐射计算模型，提出了计算水下结构声辐射的弱式改进的插值无单元伽辽金耦合MDtN边界条件方法和弱式径向基点插值耦合MDtN边界条件方法，实现了声场精确预报；构建了能适度软化数值模型声刚度的光滑无网格声散射计算模型，提出了计算水下目标声散射的点基局部光滑移动最小二乘插值方法和单元基光滑浓缩径向点插值方法，有效抑制了中频数值色散误差；采用修正的格林函数满足浅海边界条件，解析构建波叠加法中的等效源，提出混合波叠加理论与算法，解决了海水-弹性海底均质浅海环境中水下舰船地震波预报的需求。项目研究成果可为舰船声学设计、噪声控制和声学性能评估提供理论依据和技术支持。