Artificial boundary conditions for Euler–Bernoulli beam equation

In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treat- ments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection co- efficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to nu- merical implementations. The ALEX （almost EXact） bound- ary condition is numerically more effective.

A micro-kinetic model of enhanced foam stability under artificial seismic wave

To get a deeper understanding on the synergistic enhancement effect of low frequency artificial seismic wave on foam stability,a micro-kinetic model of enhanced foam stability under low frequency artificial seismic wave is established based on a vertical liquid film drainage model and elastic wave theory.The model is solved by non-dimensional transformation of the high order partial differential equations and a compound solution of implicit and explicit differences and is verified to be accurate.The foam film thickness,surfactant concentration distribution and drainage velocity under the action of low frequency artificial seismic wave are quantitatively analyzed.The research shows that low-frequency vibration can reduce the difference between the maximum and minimum concentrations of surfactant in the foam liquid film at the later stage of drainage,enhance the effect of Marangoni effect,and improve the stability of the foam liquid film.When the vibration frequency is close to the natural frequency of the foam liquid film,the vibration effect is the best,and the best vibration frequency is about 50 Hz.The higher the vibration acceleration,the faster the recovery rate of surfactant concentration in the foam liquid film is.The higher the vibration acceleration,the stronger the ability of Marangoni effect to delay the drainage of foam liquid film and the better the foam stability is.It is not the higher the vibration acceleration,the better.The best vibration acceleration is about 0.5 times of gravity acceleration.Reasonable vibration parameters would greatly enhance the effect of Marangoni effect.The smaller the initial concentration of surfactant,the better the vibration works in enhancing Marangoni effect.

Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation

The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.

Numerical method for wave height distribution within the artificial harbor with water depth of steep variation

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Research career of an astronomer who has studied celestial mechanics

Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20th century. However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings, asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group.

Efficient Procedure for Seismic Analysis of Soil-Structure Interaction System

A simplified and efficient procedure, based on the viscous-spring artificial boundary and the modal superposition method, is developed to analyze the dynamic soil-structure interaction system in the time domain. The viscous-spring artificial boundary introduced in this procedure transforms the infinite soil-structure interaction system to an approximately finite system. A seismic wave input method is used to transform the wave scattering problem into the wave source problem. The modal superposition method is then applied to this approximate finite system. The results show that this method with only a few modes can significantly reduce the computational time with almost the same precision as the traditional direct integration method. Comparison of results from different loading times demonstrates that the advantages of this method are evident in computing with long loading time.

Theoretical and numerical investigations of wave resonance between two floating bodies in close proximity

A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model（ε） and that devised for the modified potential flow model（μ_p） is established, namely, μ_p=3πεω_n/8 （where ω_n is the natural frequency）. This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.