Free vibration of paraboloidal dome/shell with arbitrary parabola meridian

Abstract

Dome can be considered as paraboloidal shells of revolution. Free vibration of the paraboloidal shells with arbitrary degree of parabola meridian have been formulated into an eighth-order partial differential equations (PDAs) with variable coefficients. In order to solve the PDAs, we introduce a displacement function U(r, φ) to represent the general solution of the PDAs. The vibration solutions are obtained in terms of series forms, respectively. The numerical simulations for free vibration shows that the spherical shape of dome performers better mechanics behaviors than other shape, this study is useful references for the optimization of the dome design.