New closed-form solutions for flexural vibration of microplates based on a modified strain gradient theory

In this work, the flexural vibration of size-dependent Kirchhoff microplates has been investigated analytically following a modified strain gradient theory. A displacement-based variational formulation is established to derive the governing differential equations and all possible boundary conditions, including both essential and natural ones, for general curved boundaries. In particular, the natural boundary conditions are expressed in terms of force quantities in a concise form.