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However, up to now, there are few open articles found about the vibration of a single cylindrical shell considering the random problem about the bolted joints. reported nonlinear flexural vibration of cylindrical shell under random pressure, random point loads or thermal effects. Random excitation is another important source which cause the random vibration of the structure such as beam, plate and shell. Rodrigues studied the nonlinear response of cylindrical shells with geometric imperfections. developed a unified approach to solve vibration problem of composite cylindrical shells, and some specific problems were simulated. For example, taking random scatter in the material properties into account, Yadav et al. Material and geometric imperfection is an important source which cause the random shell vibration. The random problem of the cylindrical shell has been reported mainly about the material and geometric imperfection or random excitations. Therefore, the random vibration of the cylindrical shell has been also a hot topic for researchers. However, there are some inherent variations in the structure, especially in the geometric parameter and the restraint condition of the cylindrical shell. The structure of the cylindrical shell is usually utilized in a lot of mechanical systems such as aerospace, submarines, due to its relatively small weight and load carrying capacity. This research introduces random theory into the modeling of bolted joints and proposes a reference result to interpret the complexity of the modal characteristics of cylindrical shells with non-uniform parameters of bolt joints. And some special cases were presented to help understand the effect of random mistuning. And the statistical analysis on the natural frequencies was evaluated for different mistuned levels. Then, the effect of the random distribution and the random constraint stiffness of the bolts on the frequency and mode shape were studied.

First, the frequency and mode shape of the tuned system were investigated and compared with FEM. The Monte Carlo simulation and statistical theory were applied to the statistical analysis of mode characteristics of the system. The vibration equation of the bolted joined cylindrical shell was derived based on Sanders’ thin shell theory.

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The bolted joints considered here were simplified as a series of springs with random features. To investigate the influence of non-uniform parameters of bolt joint, including the stiffness and the distribution position, on frequency complexity characteristics of cylindrical shell through a statistical method is the main aim of this paper.

However, in the actual working conditions, due to the manufacturing error, installation error and uneven materials of bolts, there are always random errors between different bolts. A typical bolted connection model is considered as a tuned system. Bolt connection is one of the main fixing methods of cylindrical shell structures.

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