Font Size: 

A meshfree method based on moving least square (MLS) approximation is used to study the vibration of the strain gradient plates. A high-order shifted and scaled polynomial basis is proposed to deal with the strain gradient elastic plates described by higher order differential equation. The natural frequencies of the strain gradient plates and classic Kirchhoff plates with elastically supported boundary are obtained by the MLS method. The natural frequencies of the strain gradient plates obtained by the meshfree method are in good agreement with the theoretical results for all boundaries simply supported case. Finally, the MLS method is used to study the vibration of the strain gradient plates with different boundary conditions and the nonlocal parameter which show the small scale effects.

Shifted and scaled polynomial basis, MLS method, Strain gradient, Scale effect, Elastic boundary condition