摘要 於反算振動問題中，本文將應用李群打靶法經由位移的輸入，進行估測擁有時變阻尼和時變勁度參數之力振動問題的時變外力。首先我們先將常微分方程式轉換成偏微分方程式。再經由半離散的方法將其改寫成常微分方程組的兩點邊界值問題，後透過一步保群算法得到非耦合的代數方程，其中未知時變外力可寫成閉合型式。李群打靶法的關鍵點，是基於一步李群元素 的建構與廣義中點李群元素 的建立。接著利用 ，我們可經由調整常數 ，找出打靶誤差最小的的 進行一步保群算法。經由數個例子的操作，可由估算結果看出應用此數值方法於力源反算振動工程問題的高效率和高準確度。 Abstract For the inverse vibration problem, we will propose a Lie-group shooting method (LGSM) to simultaneously estimate the unknown time-dependent external forces of a generalized force vibration problem which have the time-dependent damping and stiffness coefficients by using displacements as input. First, we transform these ODEs into PDEs. Then, we formulate them as two-point boundary value problems and apply one-step group preserving schemes (one-step GPS) for the semi-discretizations of PDEs to obtain uncoupled algebraic equations, in which the estimation of the unknown time-dependent external forces can be written in a close-form. The key point of the LGSM is based on the construction of a one-step Lie group element and the establishment of a generalized mid-point Lie group element . Then, by imposing we can search of the minimum trial error to integrate by GPS, of which .From the numerical examples examined, the estimated results appear to have high efficiency and high accuracy for in the problems of the inverse forced vibration engineering.