Fig。 2 : FFT of a triangle-shape time history
The Fig。 3 shows two wave trains on either side of the point of load discontinuity and propagating in opposite directions。 The Fig。 4 reveals a series of inpidual waves, which are characteristic of a dispersion phe- nomenon。
Fig。 3 : Amplified deformed shape 240 ms after the shock
Fig。 4 : Zoom of the amplified deformed shape after 1 s
Close to the starting point of the waves (coinciding with the point of load discontinuity), every inpidual waves are spatially concentrated, what leads to a peak of bend- ing moment (see Fig。 5)。 On the contrary, far from this point, the time histories of the bending moment clearly show the dispersion phenomenon (see Fig。 6), as indi- vidual waves have had time to separate from each other。 This is inevitably accompanied by a decrease of the global amplitude。 Furthermore, it is noteworthy that these signals seem to be made of two groups, which are distinguished by both their amplitudes and frequencies。 This is quite in agreement with the c() relation (see Fig。 1), which indicates that some low frequency indi- vidual waves and some high frequency ones propagate with the roughly same celerity cT。 It has been also veri- fied that the celerity of the most fast inpidual waves was of the order of clim=c(lim), what confirms the abil- ity of the time scheme to capture such complex phe- nomena。
Fig。 5 : Time history of the bending moment at several points close to the starting point of the waves
Fig。 6 : Time history of the bending moment at several points far from the starting point of the waves
Simulation of the Response of a Finite Homoge- neous Beam
Model
The previous test enabled to confirm that the main phe- nomena expected were reproduced correctly。
Then, the same kind of simulation was performed on a beam of the hull-girder type, with characteristics typical of a passenger ship (length = 280 m, cross-section area
= 9。1 m2, moment of inertia of cross-section = 1000 m4,
material : steel)。 At this stage, the aim was more to analyze the phenomena than to obtain precise results。 Thus, for example, section area and moment of inertia of the cross-section were first taken uniform along the girder。 The latter was uniformly discretized in 100 Ti- moshenko elements。 One end was clamped as no restor- ing hydrostatic or hydrodynamic force was modelized, voluntarily in order to isolate phenomena more easily。 A transverse pressure was uniformly applied on a quarter length, from the free end。 The time history was a isosce- les triangle-shape。 This is not a realistic spatiotemporal load of course but its simplicity contributes to provide guidelines。
Role of the load duration for identical impulse
An impulse (integral of the time history) of 105 kg。m。s-1, and 1 and then 10 ms durations were first tested。 The Fig。 7 shows several fast dynamic effects。 Similarly to the semi-infinite case, two trains of flexural waves propagate in opposite directions from the point of load discontinuity (at a quarter length from the free end) : one, Gc, towards the clamped end (1), and the other one, Gf, towards the free end。 Quickly, the Gf group reflects with opposite sign for bending moment (2)。 Later, the Gc group reflects also, but at the clamped end, with same sign (3), etc。 As they propagate, these groups
distort due to dispersion, and thus their total duration increases。 The fastest harmonic wave (flim = 49 Hz) travels with a celerity clim of about 3900 m/s, what cor- responds to 54 ms for it to reach the fixed end (or 72 ms to cover the full length)。 The high frequency phenomena in question are expected to vanish quickly because of damping effects。 Therefore, the initial peak is of main interest。 According to Fig。 7, its level is higher for the 1 ms signal。 横向载荷冲击下船体梁的瞬态响应英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_94988.html