Structural Instability Of A Parallel Array Of Mutually Attracting Simply-Supporting Microplates

Based on the rigorous theory of elasticity,we investigate the structural instability of a parallel array of identical simply-supported elastically isotropic microplates and piezoelectric microplates.In both cases,the major forces between the two adjacent microplates are surface attractive forces such as van der Waals force,electrostatic force,capillary force or Casmir force.By means of a linear perturbation analysis,the critical interaction coefficient can be determined by solving the resulting generalized eigenvalue problem for the microplate array.The structural instability can be avoided by controlling the critical separation at the beginning of the design or in the process of design.First,we investigate the structural instability of a parallel array of mutually attracting identical simply-supported elastically isotropic microplates.One plate interacts with the neighboring plates through surface attractive forces.The proposed method is based on the 2x2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array.Analytical expressions of the critical interaction coefficients for two,three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored.The influence of the end-effect and the surface energy on the critical interaction coefficient is also numerically studied.Our solution is valid whether the plates are thin or extremely thick.Second,we investigate the structural instability of a parallel array of mutually attracting identical simply-supported piezoelectric rectangular microplates.The upper and lower surfaces of each plate can be either insulating or conducting.By considering the fact that the shear stresses and the normal electric displacement(or electric potential)are zero on the two surfaces of each plate,a 2x2 transfer matrix for a plate can be obtained directly from the 8x8 fundamental piezoelectricity matrix without resolving the original Stroh eigenrelation.The critical interaction coefficient can be determined by solving the resulting generalized eigenvalue problem for the piezoelectric plate array.Also considered in our analysis is the in-plane uniform edge compression acting on the four sides of each piezoelectric plate.Our results indicate that:the stabilizing influence of the piezoelectric effect on the structural instability is unignorable;the edge compression always plays a destabilizing role in the structural instability of the plate array with interactions.