Forced Vibrations of The System with Two Degrees of Freedom with Coulomb Damping

Abstract

In this paper, we analysed the motion affected by harmonic disturbing displacement of the system which has two masses suspended by two springs and a constant friction between masses or between the mass and the supporting ceiling, and obtained an analytical solution in the domain of vibrations with or without stops. Some experiments were carried out, showing close agreements with the theoretical analysis. By these studies, the fol1owing results were obtained, (1) In the resonance (at the natural frequencies of two degrees system), when the friction is smaller than a certain definite value, the amplitudes of masses become infinitely large, and the friction which is larger, than this value causes the motion with stops or the motion without the relative displacement of masses. (2) At 1/3, 1/5, 1/7, ……of natural fretuencies, any smallest friction causes the motion with stops. (3) At infinitely high frequency, in the case that the friction between two masses is larger than a certain definite value, the motion with stops or the motion without relative displceament will exist, and in the case that the friction exists between the mass and the supporting ceiling, any friction does not cause the stop motion.