It is generally acknowledged that the disturbance of rotating speed will cause parametric resonance for blades, and the presence of rotor displacement also can make the blade vibrate transversely. However, the coupled resonance mechanism of blades under the combined action of rotating speed disturbance and rotor displacement is not yet clear. To answer this question, this article investigates the nonlinear coupled resonance behavior of rotating blades in two cases: typical tuned (the frequency ratio of parametric and forced excitations equals 2:1) and frequency ratio detuned. A nonlinear vibration equation for rotating blades is established based on Euler beam theory in conjunction with geometric nonlinearity. The mixing rule and modified Halpin-Tsai model are used to calculate the effective properties of GPLRMF materials. Subsequently, using the method of varying amplitudes (MVA), an approximate analytical solution of the coupled resonance response is derived, the Jacobian matrix is used to determine the stability of non-trivial solutions, and the accuracy of the analytical results is verified with the aid of numerical solutions. Finally, the steady-state response of typical tuned and detuned coupled resonance is analyzed, and the influence mechanism of factors such as excitation amplitude, excitation phase angle and other parameters on coupled resonance is studied in detail. The results indicate that the supercritical coupled resonance curve exhibits double resonance peaks and jumps. Meanwhile, the steady-state response of coupled resonance highly depends on the excitation phase angle.
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