The nonlinear geometrical responses in large deflection of an unsymmetrically piezo-electric layered plate under initial tension are studied. von Karman plate theory for large deflection is utilized and extended to an un-symmetrically layered plate including a piezoelectric layer. The nonlinear governing equations are derived, first, in a non-dimensional form in terms of lateral slope and radial force resultant. These equations are solved using a numerical finite difference method with the aid of the clamped-ended boundary conditions of the problem and an iteration procedure, by taking the associated linear analytical solution of lateral slope as the initial guess. For a nearly monolithic plate under a very low applied voltage, the results agree well with available solutions for a singlelayered case due to uniform lateral load in literature and thus the present approach is validated. For a two-layered un-symmetric plate made of typical silicon-based materials, the results show that piezoelectric effect seems to be apparent only up to a moderate initial tension and a moderate lateral pressure. Under this circumstance, the higher the applied voltage, the greater the central deflection; and hence the plate may transit to a membrane in a relatively low pretension condition. For a relatively high pretension or a severe lateral load, however, the piezoelectric effect becomes insignificant. Moreover, the effects of initial tension and lateral load may merge to become dominant, yielding nearly the same responses, regardless of the magnitude of the applied voltage.

No abstract

Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.

No abstract