Abstract

In this study, viscoelastic damped dynamic behaviors of laminated composite shells (LCS) under different dynamic loads were investigated. In order to obtain better numerical stability, the truncated series method was used in the formation of equations governing the system. While deriving the equations governing the system, the z/R terms are usually neglected, whereas only 3 and higher order terms are truncated here. The method of truncated equations has been used for the first time as suggested here to obtain viscoelastic damped behavior of dynamically loaded LCS. The governing equation of composite shells was obtained with the help of Hamilton’s principle. Afterwards, time dependent partial differential equations were obtained by applying Navier solution method to these valid equations. These equations were transformed into Laplace space in order to solve time dependent partial differential equations. The transformation of the resulting calculations from Laplace domain into the time domain was conducted with the help of Modified Durbin algorithm. In addition, one of the goals of this research is to highlight the importance of including the (1+z/R) part in the equations to account for the curvature effect of the shells. The addition of these effects and truncated series method to the equations and the investigation of their effects are the originalities of the present study. The present work obtained values were compared with the results obtained with Newmark’s approach and ANSYS finite element methods. The numerical results showed that the proposed approach is a highly effective and efficient solution that can be easily applied to laminated viscoelastic shell problems.

摘要

在本研究中，研究了层合复合材料壳体（LCS）在不同动态载荷下的粘弹性阻尼动态行为。为了获得更好的数值稳定性，在建立系统控制方程时采用了截断级数法。在推导控制系统的方程时，z / R项通常被忽略，而这里仅截断 3 阶及更高阶项。此处建议的截断方程方法首次用于获得动态加载 LCS 的粘弹性阻尼行为。借助哈密顿原理，得到了复合材料壳的控制方程。然后，通过对这些有效方程应用纳维求解方法，得到了与时间相关的偏微分方程。这些方程被转换到拉普拉斯空间中，以便求解与时间相关的偏微分方程。借助改进的杜宾算法将结果计算从拉普拉斯域转换到时域。此外，这项研究的目标之一是强调包括 (1+ z/ R ) 方程中的部分用于考虑壳的曲率效应。将这些效应和截断级数法添加到方程中并研究它们的效应是本研究的独创性。将当前工作获得的值与使用 Newmark 方法和 ANSYS 有限元方法获得的结果进行了比较。数值结果表明，所提出的方法是一种高效且高效的解决方案，可以轻松应用于层合粘弹性壳问题。