harmonic boundary 中文意思是什麼
harmonic boundary
解釋
調和邊界-
Firstly, in spherical coordinate system, the sovp formulation for the time - harmonic electromagnetic fields of the current dipole in conductive infinite - space is derived, using reciprocity theorem and transforming relations between special functions. then, selecting appropriate coordinate system, using superposition principle, the boundary - value problem of modified magnetic vector potential on the problem of a time - harmonic current dipole in spherical conductor is solved and analytical solution is obtained. finally, by means of the addition formulas of legendre polynomial and spherical harmonics function of degree n and order 1, the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located
首先利用特殊函數間的轉化關系和互易定理推導得到了無限大導體空間中球坐標下時諧電流元電磁場的二階矢量位形式：然後利用疊加原理，選擇合適坐標系，求解了導體球中時諧電流元的修正磁矢量位邊值問題，得到了問題的解析解；最後依據不同坐標系下電磁場解的轉化原理，藉助勒讓德多項式和n次1階球諧函數的加法公式，將坐標系特殊安放時的電磁場解析解變換到坐標系一般安放時的解析解，給出了球內電場和球外磁場的並矢格林函數。 -
First, in virtual of identification of flaws is a typical of in - verse problems, proceeding from time - harmonic electromagnetic maxwell ' s equa - tion and helmholtz equation, the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given. second, the uniqueness and existence of inverse scattering problems and the theory of ill - posed integral equation are briefly looked back upon. finally, indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects, meanwhile, the proof of possibility for near - field measurements and nu - merical simulation are given
由於缺陷的識別是一類典型的反問題，因而首先從時諧電磁maxwell方程和helmholz方程出發，具體地闡述了求解正散射問題的有關方法，包括各種（夾雜）邊界條件下的數值解法，就解的存在性唯一性給予了肯定的回答；隨后對逆散射問題的理論作了簡短的回顧，包括解的唯一性以及非線性不適定積分方程的處理等；然後對均勻介質和非均勻介質的逆散射問題建立了在各種邊界條件下的邊界識別的指示函數方法，鑒于近場數據獲得的重要性，對近場測試時邊界識別的方法給予了相應的證明，並且實現了數值模擬。 -
The main original work is as the followings : 1. longitudinal vibration of an integral pile in an uniform soil with end bearing boundary or elastic bottom boundary undergoing vertical harmonic load is theoretically investigated
主要工作如下： 1 、分別對均質土中完整端承樁和彈性支承樁在垂直諧和激振力作用下的縱向振動特性進行了研究。 -
Fourthly, the solutions for non - axisymmetical dynamic responding of elastic circular plate ( thin and thick plate ) rested on transversely isotropic saturated half - space / layered ground subjected to arbitrary harmonic loading are presented. under the contact conditions, the problem leads to a pair of dual integral equations which describs the mixed boundary - value problem
首先建立直角坐標系下波動問題的狀態方程，經雙重fo吐er變換求解狀態方程后得到傳遞矩陣:利用遞矩陣給出直角坐標系下層狀橫觀各向同性飽和地基在任意分佈簡諧荷載作用下穩態動力響應的一般解。 -
The main work includes : based on biot ' s dynamic consolidation equations, by the method of integral transform and matrix transfer, two - dimensional consolidation of layered saturated soils is studied. then, the general integral solutions of stress ( including pore pressure ) and displacement ( including fluid flow ) of any point were obtained under harmonic vibration loads according to staunch boundary condition. second, a program to verify the correctness of this dissertation is developed
主要工作有：本文根據biot平面動力固結方程，運用積分變換和矩陣傳遞的方法，研究了成層飽和地基的二維biot固結問題，根據下邊界為不透水基巖的邊界條件，獲得了地基表面作用簡諧振動荷載時，任意點應力（包括孔壓） 、位移（包括流體流量）的一般積分形式解。 -
In this thesis, studies are made on the problem of time - harmonic electromagnetic fields excited by an arbitrary current dipole in spherical conductor. the problem is presented in eddy - current nondestructive test and geophysical prospecting. under the condition of magnetic quasi - static state, the boundary - value problem about modified magnetic vector potential is solved and the analytical solution is obtained
本論文針對渦流無損檢測和地球物理勘探領域用到的球導體中時諧電流元的電磁問題做了研究，在磁準靜態近似下，求解了修正磁矢量位的邊值問題，獲得了問題的解析解，並利用通用有限元分析軟體做了數值驗證。 -
Finally, the wave equation of the electromagnetic field of this kind damper is derived from the maxwell ' s equation. the magnetic flux density at the boundary is assumed to be harmonic, so the analytical result of the wave equation is solved. when the rotor rotates, eddy currents flowing inside the conducting material field are caused
最後，應用ahrens的電磁軸承簡化模型，從maxwell方程出發推導了應用於本文所述的被動式電磁阻尼器的波動方程，並用傅立葉級數把矩形磁場展開的諧變磁場作為磁場的邊界條件，通過求解波動方程得到磁場的解析解，從而計算了阻尼器對轉子的電磁力和由渦流引起的切向力產生的阻尼器附加功耗。 -
The series solution for boundary value problem of nonhomogeneous harmonic equation with variable coefficient is obtained
使變系數非齊次調和方程邊值問題的求解有了新的進展。 -
Chapter 3 introduces the main ideas of the probabilistic numerical method and applies it to the harmonic boundary value problem over bounded plane domains
第三章首先介紹概率數值方法總的思路，然後對平面有界區域上，調和方程的第一邊值問題提出了概率數值方法。 -
There were troubles in the continuity of the function and of its - derivative divided by band - mass on the boundary. in the theoretical calculation, the wave function is relative to the physical properties of the impurity greatly, the envelop function f ( x, y ) is expanded in terms of the one - dimensional linear harmonic oscillator function in this paper. it satisfies the continuity of the function and of its - derivative divided by the band - mass, so it improves the precision of the function and binding energy
與以往工作不同的是，以前選用的x ， y方向電子的包絡函數f （ x ， y ）是一維有限深量子阱中波函數的乘積，在邊界上波函數的連續性和粒子流的守恆條件存在問題；而在理論計算中，波函數的選取與雜質的物理性質有密切關系，本文選取的電子的包絡函數是用一維線性諧振子的波函數展開而成的，在邊界上能夠同時滿足波函數的連續性及粒子流（ 1 / m ~ * ） f ' （ x ， y ）的守恆條件，從而使得波函數和束縛能的精確度得到了改進。 -
Evolution analysis of ts wave and high - order harmonic waves in boundary layers
波及其高階諧波的演化
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