Analysis of the free vibration of cantilever cylindrical thin elastic shells by the matrix progression method

Nonlinear vibrations of clamped-free circular cylindrical shells

“…[29][30][31]. However, till now, the only available research on nonlinear vibrations of clamped-free (cantilever) shells is the experimental study performed by Chiba [32,33] on large amplitude free vibrations of polyester shells.…”

Fundamental frequency of a cantilever composite cylindrical shell

“…Applications of the Rayleigh-Ritz method to the solution of the vibration problems for cylindrical cantilever shells are reported in the papers by Sharma and Johns [8], Sharma [9,10] and Warburton and Higgs [11]. Tottenham and Shimizu [12] investigated vibrations of cantilever cylindrical shells using a matrix progression method. An integral equation technique was used to determine the natural frequencies of vibration of the clamped-free shells in the article by Srinivasan and Sankaran [13].…”

The Dynamic Similitude Design of a Thin-Wall Cylindrical Shell with Sealing Teeth and Its Geometrically Distorted Model

“…where (A.2) (b) Therefore, the items of (13) can be rewritten as follows: Considering the derivation discussed above, T = ∏ =1Ũ is difficult to calculate directly. Reference [19] presented a method to calculate the transfer matrix.…”

“…where * = ∏ 5 0 =1Ũ 0 0 . Substituting (19) into the transfer matrix of the cylindrical shell, in which thickness ℎ is a variable and other parameters of the cylindrical shell are the same as those of the stiffened shell,…”

“…Therefore, an equivalent cylindrical shell is investigated to match the stiffened shell. Different equivalent thicknesses and average equivalent thicknesses are designed by employing a transfer matrix [19] and similitude theory.…”