标题： 分数阻尼振荡器脉冲响应的闭式近似 显示英文标题

标题： A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators

摘要： 我们考虑一个分数阻尼振子，其中阻尼项由阶数为$\beta\in (0,1).$的 Caputo 分数导数表示。该振子的脉冲响应可以用包含双重无限级数的双变量 Mittag-Leffler 函数来表示。尽管该级数一致收敛，但其数值实现存在计算不稳定性。在本文中，我们提出了一种近似闭式解，避免了这些数值问题，同时保持了合理的精度。所得的近似解计算效率高且稳健，适用于实际工程应用。 显示英文摘要

摘要： We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $\beta\in (0,1).$ The impulse response of this oscillator can be expressed in terms of the bivariate Mittag-Leffler function consisting of a double infinite series. Although this series is uniformly convergent, its numerical implementation suffers from computational instabilities. In this contribution, we propose an approximate closed-form solution that avoids these numerical pitfalls while maintaining a reasonable accuracy. The resulting approximation is computationally efficient and robust, making it suitable for practical engineering applications.