hankel transform 中文意思是什麼
hankel transform
解釋
hankel變換-
The numerical calculation simulation shows that the fgb will change its shape upon propagation. ( 5 ) using the quasi - discrete hankel transform ( qdht ), the fast calculation code simulating the propagation of cylindrical symmetry laser beams passing through high power laser amplifier system is built up for the first time. the code is applied to
（ 3 ）明準訴散漢克爾變換編制寧旋轉對稱光束在高功率激光放大系統中傳輸的快冰汁彝摸擬程序，利用該程序對超高斯光束在多麟光放大系統中的傳輸和神光紅栩櫥化光傳。 -
The main work includes : for the torsional vibrations of a rigid disk on saturated media, first, the dynamic governing equations are solved by the use of hankel transform and the general solutions in the hankel transform fields are formulated. then, considering the mixed boundary - value condition, the dual integral equations of the torsional vibrations of a rigid disk on saturated grounds are obtained, which can be reduced to the fredholm integral equations of the second kind and solved by numerical procedures. consequently, the dynamic compliance coefficient curves and the torsional angle amplitude curves versus the dimensionless frequency are presented and contrasted to that of the elastic one
在前人研究的基礎上，本文基於陳龍珠等曾提出的一組實用飽和土波動方程，用解析或半解析的方法首次較系統而深入地研究了飽和半空間地基與基礎的扭轉振動問題，主要工作有：對于飽和地基上剛性圓板的扭轉振動，作者首先採用hankel變換求解了動力控制方程，得到了該控制方程在hankel變換域內的通解，然後由混合邊值條件建立了飽和地基上剛性基礎扭轉振動時的對偶積分方程，並將其化為易於數值求解的第二類fredholm積分方程，用數值方法計算了基礎的動柔度和扭轉角幅值與振動頻率的關系曲線，並將其與單相彈性介質情況進行了對比分析。 -
Thirdly, the method to calculate the 3 - d dynamic responding of layered transversely isotropic saturated soils to an arbitrary buried source in cylindrical coordinate as well as to an arbitrary harmonious source in rectangular coordinate is presented respectively. based on biot ' s wave theory, the 3 - d wave equations in cylindrical coordinate for transversely isotropic saturated poroelastic media are transformed into a group of governing different equations with 1 - order by the fourier expanding with respect to azimuth and hankel integral transform method or by the double fourier transform method with respect to horizontal coordinates in rectangular coordinate. then, transfer matrixes within layered media are derived under the continuous conditions, drainage conditions and the boundary conditions
基於飽和土的biot波動理論，通過fouricr變換，將橫觀各向同性飽和土三維非軸對稱波動方程轉化為一組一階常微分方程組，再經har止el變換，建立問題的狀態方程，求解狀態方程得到傳遞矩陣;利用傳遞矩陣，結合飽和層狀地基的邊界條件、排水條件及層間接觸和連續條件，首次給出層狀橫觀各向同性飽和地基在任意地展力作用下的三維非軸對稱動力響應的解析解。 -
7. propagation properties of flattened gaussian, bessel - super - gaussian and laguerre - gaussian beams are studied by using the collins formula in the frequency - domain and hankel transform. the results are compared with those by means of the collins formula in the space - domain, and the advantage of the method is discussed
用頻域collins公式和hankel變換研究了平頂高斯光束、貝塞耳?超高斯光束以及拉蓋爾?高斯光束的傳輸特性，並與空域collins公式計算結果作了比較，同時討論了該方法的優點。 -
Using the hankel transform, the state vector equations are reduced to a set of ordinary differential equations. according to the theory of ordinary differential equations and the cayley - hamilton theorem, an analytical solution of the problem is presented in the form of the product of initial state vector and transfer matrix, which is given for the four distinct eigenvalues each. applications of the solutions are discussed
利用hankel變換，將狀態變量方程轉化為一組常微分方程組；進而根據常微分方程組解的理論和cayley - hamilton定理，得到了以狀態變量和傳遞矩陣乘積表示的單層壓電壓磁彈性材料的解析解；並討論了4種不同特徵根的情況以及解的應用。 -
Fast hankel transform algorithm for zero - value
能算零點的快速漢克爾變換 -
Based on the transform of coordinate and principle of superposition, a generalized integral formula dealing with moving load problem is established. an impulse response function used in the integral is obtained by means of laplace and hankel transform
在論文中，基於線性系統的疊加原理和坐標變換，建立了求解移動荷載作用下粘彈性地基板的動力響應積分公式，把運動荷載問題轉化為獲取位移脈沖響應函數。 -
Finally, the torsional vibration of a rigid disk resting on the saturated grounds under the general torque is primarily discussed by the means of laplace - hankel transform. the general solutions of the torsional moment, stress and displacement are given and the numerical solutions in special cases are also obtained
最後，本文還採用laplace - hankel聯合變換技術初步分析了在一般動扭矩作用下飽和地基上剛性圓板的扭轉振動問題，給出了扭矩、應力和位移的通解，並給出了特例情況下的數值解。 -
The general stress and displacement solutions of non - axisymmetric problems are obtained by hankel transform, then the theoretical solutions of stress and displacement in transversely isotropic elastic half - space under arbitrary loading are put forward by introducing boundary conditions. the homogeneous elastic half - space solutions evolved from the theoretical solutions in the paper are in accord with classical ones. solutions under horizontal and vertical loading can be obtained respectively by specializing arbitrary loading ; by analogy, solutions under other loading can be also obtained
進而引入邊界條件得到一般荷載作用下橫觀各向同性彈性半空間的應力、位移分量理論解，此解經過退化后得到均質彈性半空間理論解與經典解吻合，對一般荷載的特殊化可以分別得到水平荷載下和豎直荷載下的理論解，如此類推，可以得到其它類型荷載的解答。
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