Abstract
Maritime structures in water always experience a mean hydrostatic pressure. This paper investigates the nonlinear vibration of a clamped circular thin plate subjected to a non-zero mean load. A set of coupled Helmholtz–Duffing equations is obtained by decomposing the static and dynamic deflections and employing a Galerkin procedure. The static deflection is parameterized in the linear and quadratic coefficients of the dynamic equations. The effects of the static load on the dynamics, i.e. stiffening, asymmetry and softening, are investigated by means of the numerical solution of the coupled multi-mode system. An analytical solution of the single-mode vibration near primary resonance is derived. The analytical solution provides a theoretical explanation and quick quantification of the influence of the static load on the dynamics. The numerical and analytical results compare well, especially for lower values of the static deflection, confirming the effectiveness of the analytical approach. The proposed analysis method for plate vibration can be applied to other structures such as beams, membranes and combination forms.
Highlights
Maritime structures in water are always exposed to a mean load in the form of the hydrostatic pressure
Little quantitative information is available on changes in structural dynamics due to uniformly distributed transverse static loads and its relation with the Helmholtz–Duffing equation, which motivates the authors to revisit the forced vibration of edge-clamped circular plates
This paper theoretically investigates the effects of a static transverse load on the nonlinear dynamic behavior of a clamped circular plate
Summary
Maritime structures in water are always exposed to a mean load in the form of the hydrostatic pressure. There are numerous prior studies on the nonlinear dynamics of plates with static in-plane pre-loads. [8,9] investigate the interaction of multiple modes of a rectangular plate vibrating under in-plane pre-loads. Their numerical results show branching in the frequency-imperfect amplitude-curve. The Helmholtz–Duffing equation is closely related to the nature of nonlinear plate vibrations subjected to complex transverse loads (see Section ). Little quantitative information is available on changes in structural dynamics due to uniformly distributed transverse static loads and its relation with the Helmholtz–Duffing equation, which motivates the authors to revisit the forced vibration of edge-clamped circular plates.
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