【摘 要】
：
When waves propagate in a certain structure,the dispersion equations are usually transcendental equations about wavenumber and frequency,which does not allo
【机 构】
：
StateKeyLaboratoryofMechanicsandControlofMechanicalStructures/CollegeofAerospaceEngineering,NanjingU
【出 处】
：
The 5th Asian Conference on Mechanics of Functional Material
论文部分内容阅读
When waves propagate in a certain structure,the dispersion equations are usually transcendental equations about wavenumber and frequency,which does not allow the existence of analytical solution.So far,it is still lack of a general method to calculate such a transcendental equation,especially in complex wavenumber domain.In this paper we will introduce an effective approach to deal with the problem.The presented approachadopts the so-called modulus convergence method.Briefly,the process of the method has two steps.First,the minimal modulus of the equations in a small region is found by comparing the moduli of the equations at different discrete points in the region.Second,the null points are distinguished from these points of minimal moduli according to the convergence of the moduli of the equations around null point.The mathematical derivation of the convergence of the moduli of the equations around null points is presented strictly when the transcendental equation is univariate.Similar process also applies tothe case when the equations are multivariate.For multivariate equations,the forms of scanning space are chosen according to the numbers of the variables and the dimensions of the solution space.The way to choose scanning space is discussed in detail.Finally,several examples are used to validate the proposed approach.As a result,the three-dimensional spatial dispersion curves about complex wavenumbers and real frequencies are correctly obtained.
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