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Semi-numerical methods hold significant value due to their efficiency in time-consuming calculations. Accordingly, this article proposes an effective strategy to derive the vibration parameters of cylindrical shells (CSs) with cutout utilizing a semi-analytical approach entitled differential transform method (DTM). To achieve this, the governing equations of motion are first introduced based on Sander's theory of shells. These equations give rise to a coupled system of linear ordinary differential equations, which pose a challenge in solving the eigenvalue problem. It should be emphasized that the classical version of the differential transform method could not be directly applied to solve the eigenvalue problem related to the above-mentioned coupled differential equation. An innovative technique is employed and discussed in the paper to remedy these difficulties, which could be widely used in similar problems. As a result, the natural frequencies and mode shapes of some CSs with cutouts, various internal angles, and diverse material characteristics are attained. The outcomes undergo validation through the hybrid finite element method, and the proposed method's accuracy is rigorously proved. In conclusion, the proposed DTM provides an efficient solution to the eigenvalue problem of coupled differential equations and offers a valuable tool for obtaining accurate vibration parameters of CSs. [ABSTRACT FROM AUTHOR]

AbstractThis article aims to analyze the free vibration of closed and open horizontal circular cylindrical shells based on the concept of state-space transformation in conjunction with the differential transform method (DTM). The governing equations of the cylinders were developed based upon Sanders’ thin shell theory. Then, the set of coupled governing differential equations transformed into nine first-order differential equations. Afterwards, the well-established semi-analytical scheme so-called DTM was employed to solve the differential equations. The numerical investigation of the present method was also comprehensively carried out by analyzing some closed and open cylindrical shells with different boundary and compatibility conditions. To ensure the correctness of the results, the outcomes were compared with experimental and other numerical results, especially with the well-known finite element method. Furthermore, some plots of two-dimensional and three-dimensional mode shapes for the first and second axial modes are depicted. [ABSTRACT FROM AUTHOR]

In the free vibration analysis of beams, the inclusion of an intermediate sliding connection with an attached mass-spring system has not been yet treated. The present paper studies the free vibrations of uniform Euler-Bernoulli beams with an intermediate sliding connection and joined by a mass-spring system. Two different types of beams are considered. The Type 1 is attached with a single-degree-of-freedom mass-spring system and the Type 2 is attached with a two-degree-of-freedom mass-spring system. The ends of both beams are elastically restrained against rotation and translation. First, the eigenvalue problems including differential equations and boundary conditions are introduced. Then, the frequency equation of beam could be found. The roots of this frequency equation, i.e., frequency parameters, for several cases along with mode shapes are presented. Some special cases for the sake of verification are thoroughly investigated. [ABSTRACT FROM AUTHOR]