含单排周期微裂纹平板结构中的弹性波传播

Wave Propagation in Thin Plates With an Array of Periodic Cracks

受损伤固体中含有的微裂纹或微孔洞往往具有周期性,对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题,它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年,Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题,并推出显式分析结果。本文基于弹性动力学理论,分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况,可采用具有退化核第一类Fredholm积分方程方法分析求解,在求解中给出相应的无量纲数,例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。

There is usually an array of periodic cracks in damaged solids. It is an important subject, which is related directly with the intensity and lifetime of the structure, to research on elastic wave in mechanic. Presently, it is focus on the plane problem of elastic dynamics to research on the reflection and transmission of elastic waves in damaged solids. The problem of transmission of plane waves in solids with arrays of double periodic cracks had been analytically developed, and leaded to an explicit result by Scarpetta and Sumbatyan in 1995. Based on the theory of elastic dynamics, using the governing equation of thin plates, the reflection and transmission of flexural wave in thin plates with an array of periodic cracks were studied. The analytic results, it can be used in vibration design and control in engineering, of reflection and transmission coefficients were obtained. The numerical results were graphically presented. To any array of cracks, the nondimensional number was given, such as nondimensional wave number, ratio of size, through the method of the first Frdholm integral equation with degraded kernel. The results will expect to be applied in the engineering control of vibration.