Initial energy input in system by impulsive force

The scale of the eventual debris flow is several times larger than the start-up scale, and the larger scale of debris flows can cause devastating damage to structures.

Erosion and deposition of the debris flow mixture composed of particles and fluids will produce great kinetic energy that will impact the flow path. Coupled numerical analysis can assess the potential effect of erosion and sedimentation, making a significant contribution to the assessment of the impact of debris flow and the design of retaining structures.Дebris flow disasters occur all over the world. The study also found that the dynamic response considering the debris flow impact and the retaining structures of erosion and sedimentation is more pronounced than when not considering erosion and sedimentation. The results of this study are similar to existing literature and data, with the numerical analysis being consistent with the physical simulation tests in the existing literature, verifying the applicability of the SPH-DEM-FEM coupling analysis for assessing the debris flow impact retaining structures of erosion and sedimentation. The impact process of the debris flow, the impact height behind the retaining dam, the deposition thickness, and the debris flow dynamic response significantly influence both with and without considering the effects of erosion.

The coupled numerical analysis completely reproduces the debris flow erosion test, fitting the debris flow shape and thickness profile well. The strain-softening model was adopted to simulate the transformation of the debris flow body from the solid state to the transition state and finally into the liquid state. This paper adopted the coupled SPH-DEM-FEM to establish a complex dynamic model of the particle-fluid-erosion-structure of the debris flow and to assess the impact of erosion and sedimentation and analyse the dynamic response of the retaining structure of the debris flow. Yes, I get that in theory you have cases BEFORE and AFTER, but I am only interested in (to ensconce this) what happens AFTER you slug the ball.The erosion of debris flows on the material source will affect the movement and impact of the debris flow. Would you be so kind as to run that by me again, but explain this a, b, c, d, in terms of initial quiescent conditions? It's essentially the linear 2nd order ODE:egin It seems so strange to me: as if I skirted the complexity of a nonhomogeneous differential equation (I cheated). Would I get the same results by solving the original equation with a convolution or numerical method? Initial momentum + (integral of force over time) = Final momentumДЄnd now I turn my original differential equation to thisД¬an someone explain in words (sorry, I am embarrassed) what I am doing (if this is correct)? However, I cannot readily integrate this differential equation. This is a second order differential equation with a forcing function. May I ask if the following process is correct?ДЄpply an impulsive force using the dirac delta near 0 (with F nearly constant over the tiny impulsive interval)

Initial energy input in system by impulsive force