非線形ばね特性(hardening/softening)が動吸振器の制振挙動に与える影響評価

抄録

Research is being conducted on nonlinear dynamic vibration absorbers (NDVAs) to suppress vibrations over a broader frequency range compared to traditional dynamic vibration absorbers (DVAs). Typical nonlinear springs can be categorized into two types: hardening springs and softening springs. In this study, we consider springs with cubic nonlinearity stiffness. The coefficient of the cubic term in the restoring force-displacement characteristic of nonlinear springs is defined as the strength of the nonlinearity. The vibration transmissibility of an NDVA with hardening spring decreases in the high-frequency range, while that of an NDVA with softening spring decreases in the low-frequency range. Using an approximate solution to the equations of motion for NDVAs discussed in previous studies, we investigate the phenomena occurring when the vibration transmissibility of the NDVA. Our investigation focused on the derivative of the primary system's amplitude with respect to the strength of the nonlinearity in the range of valid frequency. As a result, it was found that this derivative is negative within the range of nonlinear spring characteristics where the vibration does not diverge, except that the strength of the nonlinearity is large in hardening type NDVA. This indicates that as the strength of the nonlinearity increases, the vibration transmissibility of the NDVA decreases in the high-frequency range for the hardening type and in the low-frequency range for the softening type. Although this derivative is not negative in hardening type occasionally, this value is so small that the nonlinear characteristic is not sensitive to the vibration transmissibility on such situation.