Transient vibration analyses of structures with complex shapes are performed by finite element (FE) methods. Transient vibration analyses take long processing times for the systems having large number of degrees of freedom. A method performing the transient analyses very fast using the Fast Fourier Transform (FFT) is introduced in this work, and it is applied to a curved manipulator. Various analyses are required to determine the input parameters for vibration control, and each analysis takes long FE solution times.

In this work, an FFT method is developed where the samples of the impulse response of the system under study is obtained by the FE software ANSYS first. The samples of the transfer function are then obtained by FFT, and transient responses are found for various vibration control parameters by using FFT. Transient response results for the complex system considered in this study are obtained approximately in 1 s with FFT method, while it takes 36 h with ANSYS.

A one degree of freedom system is considered to verify the results of FFT method. Newmark's numerical, ANSYS, and FFT method results are compared, and it is observed that the results are in good agreement. A curved non-uniform steel manipulator with a complex shape is considered after the verification. The samples of the impulse response of the manipulator is found by ANSYS. Then, FFT method is used to obtain transient responses. A trapezoidal velocity profile is considered to analyze the residual vibration. The effect of the deceleration time on the root-mean-square (rms) values of the residual vibration is studied experimentally and using FFT method. It is observed that the results are in good agreement, and it is concluded that FFT method introduced in this study is very effective to study transient vibration problems in complex systems.

具有复杂形状的结构的瞬态振动分析通过有限元（FE）方法进行。对于具有大量自由度的系统，瞬态振动分析需要很长的处理时间。在这项工作中介绍了一种使用快速傅立叶变换（FFT）快速执行瞬态分析的方法，并将其应用于弯曲操纵器。需要进行各种分析才能确定振动控制的输入参数，并且每种分析都需要很长的有限元求解时间。

在这项工作中，开发了一种FFT方法，其中首先通过有限元软件ANSYS获得所研究系统的脉冲响应的样本。然后通过FFT获得传递函数的样本，并通过FFT找到各种振动控制参数的瞬态响应。本研究中考虑的复杂系统的瞬态响应结果通过FFT方法大约在1 s内获得，而使用ANSYS则需要36 h。

考虑一种自由度系统来验证FFT方法的结果。比较了Newmark的数值，ANSYS和FFT方法的结果，发现结果吻合良好。验证后，考虑使用形状复杂的弯曲非均匀钢机械手。机械手的冲激响应的样本可通过ANSYS找到。然后，使用FFT方法获得瞬态响应。梯形速度分布被认为可以分析残余振动。利用FFT方法，通过实验研究了减速时间对残余振动的均方根值的影响。可以看出，结果吻合良好，结论是，本文引入的FFT方法对于研究复杂系统的瞬态振动问题非常有效。