Abstract In this paper, the critical axial speeds of three types of sigmoid, power law and exponential law functionally graded plates for both isotropic and orthotropic cases are obtained via a completely analytic method. The plates are subjected to lateral white noise excitation and show evidence of large deformations. Due to randomness, the conventional deterministic methods fail and a statistical approach must be selected. Here, the probability density function is evaluated analytically for prescribed plates and used to investigate the critical axial velocity of them. Specifically the effect of in-plane forces, mean value of lateral load and the material property on the critical axial speed are studied and discussed for both isotropic and orthotropic functionally graded plates. Since the governing equation is transformed to a non dimensional format, the results can be used for a wide range of plate dimensions. It is shown that the material heterogeneity palys an essential and significant role in increasing or decreasing the critical speed of both isotropic and orthotropic functionally graded plates.

In this paper the response of a microgrid to the interfaced harmonic distorted load is analyzed. A new control algorithm to mitigate harmonic distortion is considered for distributed generators (DGs) and the effect of this control scheme is shown in the currents of DGs and other loads. The proposed control algorithm is compared with the conventional control strategy for harmonic distorted loads that is sinusoidal source current strategy based on the instantaneous reactive power (IRP) theory. PSCAD simulation results for IRP theory control show high total harmonic distortion (THD) and 3rd harmonic percent. In comparison inner voltage and current controllers of the proposed control scheme with their disturbance rejection capability, mitigate THD and 3rd harmonic percent. For this control system MATLAB simulation results are shown. By demonstrating the traditional sinusoidal source current control strategy based on IRP theory, it is concluded that ignoring the distortion power (D) in compensating process and also sub-harmonics of Pap crossing from the controller interior high pass filter cause the presence of some harmonic components and high THD.