Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

Abstract

The numerical simulation of beams and plates with embedded acoustic black holes (ABHs) is computationally demanding because of the very thin thickness attained at the ABH central area. Semi-analytical approaches relying on the Rayleigh-Ritz method with wavelet or Gaussian basis functions have thus revealed as an accurate and fast alternative to determine the ABH vibration field in parametric studies. To date however, the vast majority of works on ABHs have only dealt with ABH indentations on straight beams and flat plates. It would be also worth exploring the feasibility of ABHs to control the vibrations of curved shells, typically found in aerospace and naval structures. In this work, we address this issue and extend the Gaussian expansion method (GEM) to characterize annular ABHs embedded on cylindrical shells. First, we show how the GEM can be modified to make Gaussian shape functions satisfy periodic boundary conditions in the circumferential direction of the cylinder. The GEM is then used to determine the vibration field of the ABH cylindrical shell and gets validated by comparison with finite element simulations. A thorough analysis of the performance of the annular ABH follows, which stresses the differences with the behavior of ABHs on flat surfaces. In particular, we show the influence that waves propagating in the circumferential direction have on the operational frequency range of the ABH. The effects of the viscoelastic layer and the inclusion of longitudinal stiffeners to strengthen the cylinder rigidity are also analyzed by means of the proposed GEM approach. This work broadens previous semi-analytical methods to start investigating the ABH effect on curved structures.

Progress and applications of acoustic black holes

“…通过在小波函数的基础上展开梁的横向位移场, 将运动方程转化为一组 线性方程组, 求解该方程组可以模拟结构的自由和受迫响应, 这种半解析模型在具有矩形横截面的经典欧拉-伯 努利声学黑洞梁 [8] 、 具有圆形横截面的经典欧拉-伯努利声学黑洞梁 [9] 和具有铝芯和钢上/下层的夹层梁 [10] 的情况下 得到了很好的验证. 之后的研究表明, 由于瑞利-里兹法中使用高斯基函数 [11] 比小波分解更加适合描述声学黑洞 区域的位移场, 因此高斯展开法也可用于求解声学黑洞梁 [11] 、板 [12] 以及壳 [13] 的动力响应. 此外, 几何声学 [14] 被用 于无限声学黑洞板, 传递矩阵法被用于声学黑洞梁 [15] 和管道声学黑洞终端 [16] .…”

Stress-strain state interactive visualization of the parametrically-defined thin-shell structures with the use of AR and VR technologies

“…The input parameters of a catenoid shell are linear dimensions a, a1, b and parameter c. The parametric form of a catenoid shell is as follows: (11) The basis for such a shell takes the following form: The appearance of the middle surface of a catenoid shell is given in Fig. 8.…”

“…The middle surface of a shell is the locus of points equidistant from the two surfaces that form this shell. Although such software packages as ANSYS and LIRA-SAPR enable graphic visualization of deformations, there is no standard technique or algorithm of visualization of deformed shells for variational analysis methods which are widely used in shell modeling [10][11][12]. In the meantime, the use of variational methods such as the Ritz method can significantly improve the accuracy of the analysis and reduce its time [2].…”

Annular acoustic black holes to reduce sound radiation from cylindrical shells

“…That resulted in typical phenomena of periodic systems, like the formation of frequency bandgaps reported for infinite periodic ABH beams in [27]. Another design has been recently proposed in [28][29][30] consisting of an annular ABH which aims at reducing vibrations on cylindrical shells. A FEM investigation was carried out in [28,29] to check its performance when submitted to simply supported periodic boundary conditions, and a semi-analytical approach was suggested in [30] to carry out detailed parametric analyses of the annular ABH cylinder vibration field.…”