Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness

✍ Scribed by Mousa Khalifa Ahmed

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 849 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1493

✦ Synopsis

In recent years, structural engineers have been gradually concerned with the analysis of cylindrical shells, which have non-circular profiles and are found to be in many engineering applications, such as aerospace, mechanical, nuclear, petrochemical, modern passenger airplanes, civil, and marine structures. The frequencies and mode shapes of the vibration of thin elastic shells essentially depend on some determining functions such as the radius of the curvature of the neutral surface, the shell thickness, the shape of the shell edges, and so forth. In simple cases when these functions are constant, the vibration deflection displacements occupy the entire shell surface. If the determining functions vary from point to point of the neutral surface, then localization of the vibration modes lies near the weakest lines on the shell surface, which has less stiffness. The kinds of these problems are found to be difficult, because the radius of its curvature varies with the circumferential coordinate, closed-form or analytic solutions cannot be obtained, in general, for this class of shells, numerical or approximate techniques are necessary for their analysis. Vibration problems in structural dynamics have become more of problems in recent years because the use of high-strength material requires less material for load support structures, and components have become generally more slender and are vibrate-prone. The vibration response of shells of revolution has been studied by many researchers because the basic equations for this was established by Flügge [1], Love [2], and Rayleigh [3]. The best collection of documents can be found in Leissa [4] in which more than 500 publications were analyzed and discussed in both linear and non-linear vibration cases for circular cylindrical shells. Recently, other related references may be found in the well-known work of Markus [5], Zhang et al. [6], Li [7], and Pellicano [8]. Some of researchers have considerable interest in the study of vibration behavior of circular cylindrical shells with variable thickness such as [9-13] in which their investigations have been made into different forms of thickness, that is, axial, circumferential, and step-wise thickness variation. A few researchers have devoted their studies for vibration characteristics of non-uniform circular cylindrical shells with constant thickness such as [14][15][16][17] in which their investigations have been made into different forms of radius of curvature, that is, oval, elliptical, and three-lobed and four-lobed cross sections. In contrast, the vibration study of non-uniform cylindrical shells with variable thickness has received much less attention, but some of implementations are well documented by Suzuki and Leissa [18], Mitao et al. [19], and Khalifa [20] in which their treatments have been modeled