Liang Weige, Liu Tao, Li Chi, Wang Qingshan
College of Weapons Engineering, Naval University of Engineering, Wuhan 430033, China.
Light Alloy Research Institute, Central South University, Changsha 410083, China.
Materials (Basel). 2023 Apr 24;16(9):3345. doi: 10.3390/ma16093345.
In this paper, we present a novel and unified model for studying the vibration of cylindrical shells based on the three-dimensional (3D) elastic theory and the Carrera Unified Formulation. Our approach represents a significant advancement in the field, as it enables us to accurately predict the vibrational behavior of cylindrical shells under arbitrary boundary conditions. To accomplish this, we expand the axial, circumferential, and radial displacements of the shell using Chebyshev polynomials and Taylor series, thereby reducing the dimensionality of the expansion and ensuring the precision and rigor of our results. In addition, we introduce three groups of artificial boundary surface springs to simulate the general end boundary conditions of the cylindrical shell and coupling springs to strongly couple the two surfaces of the cylindrical shell = 0 and = 2π to ensure continuity of displacements on these faces. Using the energy function of the entire cylindrical shell model, we obtain the characteristic equation of the system by finding the partial derivatives of the unknown coefficients of displacement in the energy function. By solving this equation, we can directly obtain the vibration characteristics of the cylindrical shell. We demonstrate the convergence, accuracy, and reliability of our approach by comparing our computational results with existing results in the literature and finite element results. Finally, we present simulation results of the frequency features of cylindrical shells with various geometrical and boundary parameters in the form of tables and figures. Overall, we believe that our novel approach has the potential to greatly enhance our understanding of cylindrical shells and pave the way for further advancements in the field of structural engineering. Our comprehensive model and simulation results contribute to the ongoing efforts to develop efficient and reliable techniques for analyzing the vibrational behavior of cylindrical shells.
在本文中，我们基于三维（3D）弹性理论和卡雷拉统一公式，提出了一种用于研究圆柱壳振动的新颖统一模型。我们的方法代表了该领域的重大进展，因为它使我们能够准确预测圆柱壳在任意边界条件下的振动行为。为实现这一目标，我们使用切比雪夫多项式和泰勒级数展开壳的轴向、周向和径向位移，从而降低展开的维度并确保结果的精度和严谨性。此外，我们引入三组人工边界表面弹簧来模拟圆柱壳的一般端部边界条件，并引入耦合弹簧来强耦合圆柱壳(= 0)和(= 2π)的两个表面，以确保这些面上位移的连续性。利用整个圆柱壳模型的能量函数，通过求能量函数中位移未知系数的偏导数，得到系统的特征方程。通过求解该方程，我们可以直接获得圆柱壳的振动特性。我们将计算结果与文献中的现有结果以及有限元结果进行比较，证明了我们方法的收敛性、准确性和可靠性。最后，我们以表格和图形的形式给出了具有各种几何和边界参数的圆柱壳频率特性的模拟结果。总体而言，我们认为我们的新方法有可能极大地增进我们对圆柱壳的理解，并为结构工程领域的进一步发展铺平道路。我们的综合模型和模拟结果有助于持续努力开发用于分析圆柱壳振动行为的高效可靠技术。
