Instability Analysis of Rotating Convex and Concave Circular Nano-plate by Considering Surface Residual Stress
Based on the theory of the surface residual stress of nanomaterials and small deflection of elastic plate,the transverse vibration differential equation of rotating convex-concave circular nanoplate was established.The variation of dimensionless complex frequency of convex-concave circular nanoplate with dimensionless angular speed and surface residual stress under different conditions was obtained by using the differential quadrature method.The results show that the first-order divergence instability of rotating convex-concave circular nanoplate was observed in both clamped and simply supported conditions.When other parameters are constant,the critical instability angular speed of the clamped concave circular nanoplate is smaller than that of the convex circular nanoplate,and the critical instability angular speed of the simply supported concave circular nanoplate is greater than that of the convex circular nanoplate.The critical instability angular speed increases with the increasing of surface residual stress,and the critical surface residual stress increases with the increasing of dimensionless angular speed.
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