Influence of nonlinear rigidity of elastic elements on the $L$-$L$ type two-mass micromechanical gyroscope dynamics in a forced-oscillation regime

In this paper, an $L$-$L$ type micromechanical gyroscope is considered in a forced-oscillation regime. The main purpose is to analyze the effect of nonlinearity on the gyroscope dynamics. In this case, the nonlinearity is caused by difference in the rigidity of elastic elements. A distinctive feature of this work is that the angular velocity of the base is supposed to be arbitrary. A mathematical model of the micromechanical gyroscope, which is characterized by two active masses, is developed assuming that the mass of the frame is far less than that of the sensitive element. The problem solution is obtained using the Van der Pol variables. The differential equations of motion of the $L$-$L$ type two-mass micromechanical gyroscope are solved numerically with an application of the mathematical package "Mathematica". The amplitudefrequency responses are plotted on the basis of calculated results. The obtained data allowed one to analyze the system behavior and to make an appropriate conclusion. It was revealed that when the frequency of driving force approaches the system natural frequencies, one of the amplitudes rapidly increases while another tends to zero.