Abstract

This paper presents an analysis of the dynamic response of an undamped mechanical system with one degree of freedom subjected to disturbances which are described by antisymmetric forcing functions. The analysis was undertaken to throw light on the effect on the vibration of the wings caused by unsymmetric landing impact of an airplane. Two types of disturbances are considered; a full-sine-wave pulse, and a pulse which is the difference between two overlapping half sine waves. The results are presented in the form of dynamic-response curves and dynamic-response-factor curves. The numerically greatest dynamic-response factors, approximately 3.24 and −3.26, resulted for a full-sine-wave pulse disturbance with a ratio of duration of impact to natural period, Ti/T ≅ 1.11. When Ti/T is in the neighborhood of 1, the first positive peak of dynamic response is numerically less than the negative and positive peaks which follow it. For much of the range, the positive and negative dynamic-response factors are numerically approximately equal. The analysis was confined to values of Ti/T between 0.33 and 12. As Ti/T increases without limit, the positive and negative dynamic-response factors tend to 1 and −1, respectively.

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