Sound radiation of complex mode shapes

要有效地抑制噪声污染，就必须对噪声源有准确的认识。如今，关于振动声学的基础知识已经有了深入和巩固。噪声源的主要特征是振动幅度、频谱含量和频率相关辐射能力。由于结构的动力响应是由模态振型决定的，因此对后者进行了详细的研究。相关研究主要基于结构阻尼均匀分布的假设和简化了底层微分方程的简单边界条件。然后相关的特征问题得到实正态模。这个假设对许多应用程序都是有效的，并且提供了足够准确的结果。然而，纤维增强塑料制成的高性能轻质结构的应用越来越多，同时也增加了声学要求，从而增加了声学阻尼措施。由于减重的原因，后者位于关键结构点，这违背了结构阻尼均匀分布的假设。因此，结构共振是由复杂形状的模态决定的，即正向波而不是驻波。边界条件也可能导致这些复杂的模态振型。复杂模态的存在提出了它们对声辐射影响的问题。本课题的基本假设是：非比例阻尼引起的复模态振型的复杂程度对重合频率以下的声辐射有显著影响。声辐射特性可以用复辐射系数来描述。本项目将系统地研究模态振型复杂度与声辐射之间的关系。

The effective suppression of noise pollution requires the precise knowledge of the noise generating sources. Nowadays a profound and consolidated basic knowledge on vibroacoustics exists. Sources of noise are mainly characterized by vibration amplitude, spectral content, and frequency dependent radiation capability. The latter was investigated in detail in terms of structural mode shapes because the dynamic response of structures is determined by mode shapes. The related research is mainly based on the assumption of homogenously distributed structural damping and simple boundary conditions which simplifies the underlying differential equations. Then the related eigenproblem yields real normal modes. This assumption is valid for many applications and delivers sufficiently accurate results. However, the increasing application of high performance light weight structures made from fiber reinforced plastics simultaneously increase the acoustic requirements and, in consequence measures for acoustic damping. The latter are located at critical structural points for weight-saving reasons which violates the assumption of homogenously distributed structural damping. Consequently the structural resonances are determined by modes of complex shapes, i.e. forward waves instead of standing waves. Boundary condition may cause these complex mode shapes as well. The existence of complex modes raises the question of their influence on sound radiation.The basic hypothesis of the project is that the grade of complexity of complex mode shapes caused by non-proportional damping has a significant influence on the sound radiation below the coincidence frequency. The sound radiation characteristics should by describable by a complex radiation coefficient. The project will systematically investigate the relation between the mode shape complexity and the sound radiation.