A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries

Abstract

The dynamic behavior of cylindrical shells with arbitrary boundaries is studied in this paper. Love's shell theory and Hamilton's principle are employed to derive the motion equations for cylindrical shells. A semi-analytical methodology, which incorporates Durbin's inverse Laplace transform, differential quadrature method and Fourier series expansion technique, is proposed to investigate this phenomenon. The use of the differential quadrature method provides a solution in terms of the axial direction whereas the use of Durbin's numerical inversion method generates a solution in the time domain. Comparison of calculated frequency parameters to that derived from the literature illustrates the effectiveness of the method. Specifically, convergence tests indicate that the present approach has a rapid convergence, the time-history response and the Navier's solution are in great agreement. Comparisons between time-history responses derived by two shell theories show that the results fit well with each other when the thickness-radius ratios are small enough. An analysis of the influences of boundaries on the time-history response of cylindrical shells indicates that the peak displacement is closely related to the degrees of freedom of boundaries. The influences of the length-radius ratios and the thickness-radius ratios on the peak displacement are further investigated.

An Experimental and Modeling Study on Vibro-Acoustic Response of Double-Walled Steel Cylindrical Shells

“…Some analytical methods have been presented for the vibration responses of steel shells, which include Wave analysis method (Li 2009;Gan et al 2009), Fourier spectral element method (Jin et al 2017;Su et al 2016) and Transfer matrix method (Irie et al1984;Wang et al 2015). These analytical methods are employed frequently to analyze the dynamic behaviour of single cylindrical shells such as cylindrical shells (Liang et al 2019;, elliptic cylindrical shells , ring-stiffened cylindrical shells (Jafari et al 2006;), but analytical solutions are always limited to considering the existence of the fluid load and ringstiffeners. There are some semi-analytical methods are also put forward to solve the structure-acoustic problems and investigate other kinds of shell structures like conical-cylindrical shells (Wang et al 2016b); Qu et al 2013;Chen et al 2015) and cylinder-plate combination (Ma et al 2017;Tso and Hansen 1995).…”