Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A F
Department of Physics, Sri KGS Arts College, Srivaikuntam, Tamilnadu, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046608. doi: 10.1103/PhysRevE.80.046608. Epub 2009 Oct 20.
We analyze the occurrence of vibrational resonance in a damped quintic oscillator with three cases of single well of the potential V(x)=1/2omega(0)(2)x(2)+1/4betax(4)+1/6gammax(6) driven by both low-frequency force f cos omegat and high-frequency force g cos Omegat with Omega >> omega. We restrict our analysis to the parametric choices (i) omega(0)(2), beta, gamma > 0 (single well), (ii) omega(0)(2), gamma > 0, beta < 0, beta(2) < 4omega(0)(2)gamma (single well), and (iii) omega(0)(2) > 0, beta arbitrary, gamma < 0 (double-hump single well). From the approximate theoretical expression of response amplitude Q at the low-frequency omega we determine the values of omega and g (denoted as omega(VR) and g(VR)) at which vibrational resonance occurs. We show that for fixed values of the parameters of the system when omega is varied either resonance does not occur or it occurs only once. When the amplitude g is varied for the case of the potential with the parametric choice (i) at most one resonance occur while for the other two choices (ii) and (iii) multiple resonance occur. Further, g(VR) is found to be independent of the damping strength d while omega(VR) depends on d. The theoretical predictions are found to be in good agreement with the numerical result. We illustrate that the vibrational resonance can be characterized in terms of width of the orbit also.
我们分析了一个阻尼五次振荡器中振动共振的发生情况，该振荡器具有势(V(x)=\frac{1}{2}\omega_0^2x^2+\frac{1}{4}\beta x^4+\frac{1}{6}\gamma x^6)的三种单阱情形，由低频力(f\cos\omega t)和高频力(g\cos\Omega t)（其中(\Omega\gg\omega)）驱动。我们将分析限制在参数选择上：(i) (\omega_0^2,\beta,\gamma>0)（单阱）；(ii) (\omega_0^2,\gamma>0,\beta<0,\beta^2<4\omega_0^2\gamma)（单阱）；以及(iii) (\omega_0^2>0,\beta)任意，(\gamma<0)（双峰单阱）。从低频(\omega)处响应振幅(Q)的近似理论表达式，我们确定了发生振动共振时(\omega)和(g)的值（记为(\omega_{VR})和(g_{VR})）。我们表明，对于系统参数的固定值，当(\omega)变化时，要么不发生共振，要么只发生一次共振。当振幅(g)变化时，对于参数选择(i)的势的情形，最多发生一次共振，而对于其他两种选择(ii)和(iii)，会发生多重共振。此外，发现(g_{VR})与阻尼强度(d)无关，而(\omega_{VR})取决于(d)。理论预测与数值结果吻合良好。我们还表明，振动共振也可以用轨道宽度来表征。
