论文标题
广义的Bagley-Torvik方程和分数振荡器
Generalized Bagley-Torvik Equation and Fractional Oscillators
论文作者
论文摘要
在本文中，Bagley-torvik方程式被允许在一到两个之间的阻尼术语的顺序考虑。发现该溶液可以用作驱动力的三角和指数函数的卷积。还研究了有效衰减速率和振荡频率相对于分数阻尼阶的特性。发现有效的衰减速率和振荡频率对阻尼项的导数的顺序具有复杂的依赖性，并且表现出人们可能对状态热力学方程式可能期望的特性：临界点，相变和lambda转变。
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of state: critical point, phase change, and lambda transition.
