饱和多孔介质板的吻合频率和临界频率分析

Coincidence frequency and critical frequency of thin plates made of saturated porous materials

板结构在隔声设计中应用广泛,而临界频率和吻合频率与板结构的声辐射和隔声性能有着密切的联系。从吻合效应产生的机理,形成吻合效应的条件出发,基于含液饱和多孔弹性薄板的振动控制方程,通过理论分析得到了饱和多孔薄板吻合频率和临界频率的计算公式。作为数值算例,对含液饱和多孔板的吻合频率和临界频率进行了参数分析。讨论了饱和多孔板的吻合频率随板厚、孔隙率、入射角和渗透系数的变化规律,并比较了不同孔隙率下饱和多孔板和弹性板的吻合频率随厚度和入射角的变化。结果表明,弹性板的吻合频率远远大于饱和多孔板的吻合频率,它们的吻合频率随厚度、入射角的增大而减小,随孔隙率的增大而增大,而渗透系数对吻合频率几乎没有影响。

Plate structures are widely used in acoustical insulation design,their critical frequency and coincidence frequencies are closely related to sound radiation and sound insulation performance of plate structures. From the mechanism of coincidence effect and conditions to cause coincidence effect,based on the vibration control equation of thin plates made of saturated porous materials,the calculation formulas for critical frequency and coincidence frequency of thin plates made of saturated porous materials were deduced through theoretical analysis. Using numerical examples,the parametric analysis for coincidence frequency and critical frequency of thin plates made of saturated porous materials were performed. The variation laws of coincidence frequency with changes of plate thickness,porosity,incident angle,and permeability coefficient were analyzed. The coincidence frequencies of thin plates made of saturated porous materials under different porosities were compared with those of elastic solid plate with changes of plate thickness and incident angle. Results showed that coincidence frequencies of single-phase elastic solid plates are much larger than those of thin plates made of saturated porous materials,their coincidence frequencies decrease with increase in plate thickness and incident angle,and increase with increase in porosity,while permeability coefficients almost have no effect on their coincidence frequencies.