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

Xu Liang, Xing Zha, Xue Jiang, Zeng Cao, Yuhong Wang, Jianxing Leng

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
LanguageEnglish
Pages145-155
Number of pages11
JournalOcean Engineering
Volume178
Early online date9 Mar 2019
DOIs
Publication statusPublished - 15 Apr 2019

Fingerprint

Dynamic analysis
Inverse transforms
Laplace transforms
Fourier series
Equations of motion

Keywords

  • time-history response
  • frequency parameter
  • differential quadrature method

Cite this

Liang, Xu ; Zha, Xing ; Jiang, Xue ; Cao, Zeng ; Wang, Yuhong ; Leng, Jianxing. / A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries. In: Ocean Engineering. 2019 ; Vol. 178. pp. 145-155.
@article{53d912cfd22a41d98ea46d40582a5e52,
title = "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.",
keywords = "time-history response, frequency parameter, differential quadrature method",
author = "Xu Liang and Xing Zha and Xue Jiang and Zeng Cao and Yuhong Wang and Jianxing Leng",
year = "2019",
month = "4",
day = "15",
doi = "10.1016/j.oceaneng.2019.02.074",
language = "English",
volume = "178",
pages = "145--155",
journal = "Ocean Engineering",
issn = "0029-8018",
publisher = "Elsevier",

}

A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries. / Liang, Xu; Zha, Xing; Jiang, Xue; Cao, Zeng; Wang, Yuhong; Leng, Jianxing.

In: Ocean Engineering, Vol. 178, 15.04.2019, p. 145-155.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries

AU - Liang, Xu

AU - Zha, Xing

AU - Jiang, Xue

AU - Cao, Zeng

AU - Wang, Yuhong

AU - Leng, Jianxing

PY - 2019/4/15

Y1 - 2019/4/15

N2 - 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.

AB - 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.

KW - time-history response

KW - frequency parameter

KW - differential quadrature method

U2 - 10.1016/j.oceaneng.2019.02.074

DO - 10.1016/j.oceaneng.2019.02.074

M3 - Article

VL - 178

SP - 145

EP - 155

JO - Ocean Engineering

T2 - Ocean Engineering

JF - Ocean Engineering

SN - 0029-8018

ER -