Two simple methods to suppress the residual vibrations of a translating or rotating flexible cantilever beam

In this paper, two methods for controlling the residual vibrations of a translating or rotating Euler–Bernoulli cantilever beam are considered. Although a beam has an infinite number of vibration modes, when it simply changes its position by translation or rotation the first mode is the main contributor to the total response. Thus, the problem can be reduced to the base acceleration excitation of a single-degree-of-freedom system. Two simple methods are suggested for suppressing the residual vibration of such a system without considering any control algorithms. Both methods are based on the transient response of the system—namely, the shock response spectrum (SRS). The first method is simple and can be used for lightly damped systems, while the second method can be applied to more general situations. The result of the second method is similar to that of the input shaping method; however, in the method proposed here, both position and time to move from one position to another can be controlled simultaneously.