Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh–Ritz method

A finite strip for the vibration analysis of rotating cylindrical shells

“…by applying Hamilton's principle. In the case of a rotating cylindrical shell, the latter approach is more convenient, as shown for example in [38]. Love's simplification [56] allows for the shell strain field to be separated into membrane strains and bending strains [24] ( 1) where ε i are the membrane strains, κ i denote the change in curvature due to the shell bending, and z is the distance of a shell layer from the reference mid-surface.…”

“…(11) (38) Substituting (12) and (17) into (38), one obtains after integration over the circumference ? (39) The kinetic energy (39) is also time invariant, as is the strain energy (28) for the same reason of rotating fixed mode profiles.…”

“…(28) and (38), respectively, are time invariant and it is not necessary to search for their maximum values as in the case of a stationary shell. However, these energies are not balanced at the finite strip level.…”

“…Closed-form solutions are now difficult to obtain. A number of investigations have been undertaken to tackle this problem [33][34][35][36][37][38][39]. One of the solutions was obtained by assuming the shell displacement field as a product of Fourier series in the axial direction, and trigonometric functions in the circumferential direction [36].…”

“…The problem of the free vibration of a rotating cylindrical shell having arbitrary boundary conditions can also be solved by employing the Rayleigh-Ritz method. Such a solution, using characteristic orthogonal polynomials for displacement variations along the axial direction, can be found in [38].…”