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Dynamic amplification factor in the problem of inclined impact

Results show that this method gives a solution which is more general than the solutions illustrated in the textbook of Strength of Materials. The developed formulations may expand the applied sphere of the dynamic amplification factor (DAF), kd, as in the case of driving inclined piles. | Vietnam Journal of Mechanics, NOST of Vietnam Vol. 22, 2000, No 2 (124 - 128) Short Communication DYNAMIC AMPLIFICATION FACTOR IN THE PROBLEM OF INCLINED IMPACT PHAN VAN KHOI Inst£tute of Mechanics, 264 Doi Can, Hanoi ABSTRACT. The purpose of this article is to investigate an advanced method for presentation of the impact problem between the rigid body and the .elastic beam. Results show that this method gives a solution which is more general than the solutions illustrated in the textbook of Strength of Materials . The developed formulations may expand the applied sphere of the dynamic amplification factor (DAF), kd, as in the case of driving inclined piles. 1. Formulation of the problem In the ordinary textbooks of Strength of Materials, the problem of impact is presented with its two particular cases: - impact body with the weight of Q moves in the vertical direction (vertical impact, Fig. la and 1b) and - impact body moves in the horizontal direction (horizontal impact, Fig. le and ld), where the beams may be located horizontally or vertically only. Q' Q l;t------•v:~ = o<. oo ft= 900 C) o(. = 90° /3= oo d) Fig.1 It is obvious that the obtained results may not be applied to general cases, which are often encountered in practice, when the impact body moves in arbitrary direction and the beam axis is inclined at an arbitrary angle. On the other hand, the presentation of two particular cases of a problem with 124 the same principle is not advisable according to teaching methodology. Hence, the above problem of impact may be formulated generally as follows: A rigid body of the mass Q / g impinges on the beam with the velocity v, where g is the acceleration of gravity. At the impact point in the beam there may already exist another body of the mass Q' / g. This mass may also be a reduced mass of the beam at the impact point, Fig. 2. Find the dynamic amplification factor, kd. 2. Solutions x We denote a - angle between the moving direction of the