Variational formulation and differential quadrature finite element for freely vibrating strain gradient Kirchhoff plates

In this paper, we apply the energy variational principle to arrive at the differential equation of motion and all appropriate boundary conditions for strain gradient Kirchhoff micro‐plates. The resulting sixth‐order boundary value problem of free vibration is solved by a thirty‐six‐DOF four‐node differential quadrature plate finite element. The C 2 ‐continuity condition of the deflection is guaranteed by devising a sixth‐order differential...