正方形膜の多モード共振

抄録

The problem of the nonlinear forced oscillations of a square membrane is considered. For theoretical analysis, modal equations are first derived from the governing nonlinear partial differential equaions. Then, based on these modal equations, the characteristics of oscillations induced by harmonic excitation near a primary resonance point are discussed. Numerical calculation is conducted for a typical case in which the excitation frequency comes near the resonance point of the mode with one nodal line. It is shown that near this resonance point, two modes which exist with the same natural frequency and with the same modal form are excited simultaneously due to nonlinear coupling, and thus two-mode oscillations can occur. It is also shown that two kinds of two-mode oscillations are possible, one in which two modes are excited with a time lag of nearly π/2 and the other without a time lag. The former implies the occurrence of oscillations of the rolary type, and the latter the occurrence of oscillations with its nodal line shifted from that of the linear harmonic oscillation. Experimental analysis is also conducted, which confirms the validity of the theoretical analysis.