Vibrational resonance (VR) is a phenomenon wherein the response of a nonlinear oscillator driven by biharmonic forces with two different frequencies, $\omega$ and $\Omega$, such that $\Omega \gg \omega$, is enhanced by optimizing the parameters of high-frequency driving force. In this paper, an counterintuitive scenario in which a biharmonically driven nonlinear oscillator does not vibrate under the well known VR conditions is reported. This behaviour was observed in a system with an integrable and asymmetric Toda potential driven by biharmonic forces in the usual VR configuration. It is shown that with constant dissipation and in the presence of biharmonic forces, VR does not take place, whereas with nonlinear displacement-dependent periodic dissipation multiple VR can be induced at certain values of high-frequency force parameters. Theoretical analysis are validated using numerical computation and Simulink implementation in MATLAB. Finally, the regime in parameter space of the dissipation for optimum occurrence of multiple VR in the Toda oscillator was estimated. This result would be relevant for experimental applications of dual-frequency driven laser models where the Toda potential is extensively employed.

振动共振（VR）是一种现象，其中非线性振荡器的响应由具有两个不同频率的双谐波力驱动， $\omega$ 和 $\Omega$，这样 $\Omega \gg \omega$通过优化高频驱动力的参数来增强。在本文中，报告了一种违反直觉的情况，其中在众所周知的VR条件下，双谐波驱动的非线性振荡器不会振动。在具有常规VR配置中由双谐波力驱动的可积分和不对称Toda电位的系统中观察到了此行为。结果表明，在恒定耗散且存在双谐波力的情况下，不会发生VR，而在非线性位移相关的周期性耗散的情况下，可以在某些高频力参数值下诱发多个VR。使用数值计算和MATLAB中的Simulink实现对理论分析进行了验证。最后，估算了Toda振荡器中多个VR最佳出现的耗散参数空间中的状态。该结果与广泛使用Toda电位的双频驱动激光模型的实验应用有关。