Size-dependent Response of Rectangular Micro-plates Subjected to Random Base Excitation Incorporating the Packaging Effect

The objective of the present paper is to investigate the size-dependent response of a fully clamped rectangular micro-plate under random base excitation. The size-dependent Kirchhoffchr('39')s plate model based on the modified couple stress theory is utilized in the theoretical formulation. The equations of motion which account for the packaging effect and axial residual stresses are derived using Hamiltonchr('39')s principle. To find the spectral density and mean square value of the micro-plate deflection, the standard modal summation method is employed where the micro-plate mode-shapes are extracted using the extended Kantorovich method. A convergence study is conducted to find the number of modes which must be included in the response. It is found that using the first six symmetric mode-shapes for the present micro-plate leads to very accurate results, while single-mode solution gives the mean square value of the response with a maximum error of 10%. Furthermore, the results reveal that the size effect on the mean square value of the mid-point deflection is usually negligible when the ratio of the plate thickness to its material length scale parameter becomes larger than 15.