负泊松比蜂窝夹层板作为一种特殊的复合材料结构,目前对其动态行为尚缺乏认识.应用Reddy剪切板理论分析了对边简支负泊松比蜂窝夹层板的弯曲振动.将内凹六边形胞元的蜂窝芯层等效为一正交异性层,芯层的等效弹性参数由修正后的Gibson公式得出.由具体算例可知经典叠层板理论和一阶剪切板理论不适合用于蜂窝夹层板的振动分析.应用Reddy剪切板理论研究了蜂窝夹层板板厚比、芯层板厚及胞元角度对弯曲振动频率的影响,并绘出相应的曲线图.结果表明:对于对边简支负泊松比蜂窝夹层板,当板厚比小于某一值时,固有频率参数随板厚比的增加而增加;但当板厚比大于该值时,固有频率参数随板厚比的增加呈现复杂的变化形式.本文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考.
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