The vibration of a single-story frame with bilinear hysteresis supporting a rotating machine is analyzed. The excitation force caused by the rotating unbalanced mass of the machine has a frequency dependent amplitude. The bilinear hysteresis of the resisting force of the frame to the motion is derived from the bilinear moment-curvature relationship of the frame columns. Solving the equation of motion of the system by the method of slowly varying parameters, the system exhibits unbounded resonance when the product of the machine unbalanced mass and its eccentricity exceeds a critical value. For the purpose of design and analysis of this type of structures, the displacement amplitude is plotted against arguments of the frequency for various values of two parameters involved.

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