论文部分内容阅读
周期性弹性复合结构(声子晶体)中传播的弹性波存在特殊的色散关系:弹性波只能在某段频率范围内无损耗的传播,该频率范围称为通带.一维声子晶体的色散问题可以看作分层介质中弹性波的传播问题,利用二维弹性理论予以分析.为了研究非局部效应对声子晶体带隙特性的影响,将Eringen的二维非局部弹性理论引入到Hamilton体系下,利用精细积分与扩展的Wittrick-Williams算法可获取任意频率范围内的本征解.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别.并进一步指出了该套算法的适用性和优势所在.
The elastic waves propagating in periodic elastic composite structures (phononic crystals) have a special dispersion relationship: the elastic waves can only propagate without loss in a certain frequency range, which is called the passband. The one-dimensional phononic crystals The dispersion problem can be regarded as the propagation problem of elastic waves in stratified media, and the two-dimensional elastic theory is used to analyze the problem.In order to study the effect of nonlocal effects on the bandgap characteristics of phononic crystals, Eringen’s two-dimensional nonlocal elastic theory is introduced into Hamilton System, the eigensolution in any frequency range can be obtained by using the precise integration and the extended Wittrick-Williams algorithm.The differences between the nonlocal theory and the traditional local theory are analyzed and compared by numerical calculation of different examples Further pointed out the suitability and advantage of this set of algorithms.