Subharmonic Oscillations of a Slender Beam

Abstract

Various types of nonlinear steady forced vibrations are expected to occur in a beam subjected to harmonic excitation. This paper concerns among them the subharmonic oscillations of order 1/2 and of order 1/3. Theoretical analysis for them is carried out by assuming the deflection as a superposition of linear mode shapes. The theoretical analysis proves the occurrence of the subharmonic oscillations. For a subharmonic oscillation of order 1/2 to occur, a constant term is necessary in the excitation. The transition to the state in which this oscillation occurs from the state in which only a harmonic oscillation occurs is made continuously by increasing the excitation frequency. For a subharmonic oscillation of order 1/3, the constant term is not necessary. The transition to the state in which this oscillation occurs, cannot be made by varying the excitation frequency. Experimental analysis is also made. The experimental results confirm the results of the theoretical analysis.