Method of separation of variables and boundaryvalue problem of the isosceles - right triangular waveguide 分離變量法與等腰直角三角形波導的邊值問題
By using the method of separation of variables and limited fourier and laplace transform , the analytical results are obtained 運用分離變量法和有限傅立葉變換和拉普拉斯變換,將系統(tǒng)運動微分方程轉(zhuǎn)換為線性方程組,求出撓度和內(nèi)力解析解。
According to thinking the joints of plates as elastic boundary supports to plates and by using of the method of separation of variables , betti ' s reciprocal theorem of work , the solution of dynamic equation can be deserved 運用變分法,分離變量法,互等功定理等數(shù)學工具求解板的運動方程,可得出彈性地基上考慮接縫傳荷能力的道面板在移動荷載下的動力響應(解析解) 。
By adopting appropriate transformation , this paper transform the heat conduction equation with internal heat source into a non - source heat conduction equation , and then solve the problem successfully by the method of separation of variables 其關(guān)鍵方法是:通過將電場量引入溫度場方程,作適當變換,把含內(nèi)熱源的熱傳導方程轉(zhuǎn)化為不含內(nèi)熱源的熱傳導方程,然后采用分離變量法進行求解。
The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils . because " the surface current source is placed at the interface , the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation . by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants , the expressions for the magnetic vector potential of the three regions are solved out 在求解過程中,假定放置式圓柱線圈是由無窮多個對稱圓環(huán)線圈密饒而成,首先求解含有有限長磁芯的通電對稱圓環(huán)線圈的電磁場:以有限長圓柱磁芯的側(cè)面和圓環(huán)線圈所在圓柱面為分界面將場域劃分為三個小區(qū)域,由于場源放置在內(nèi)邊界面上,使得關(guān)于矢量磁位的非齊次約束方程轉(zhuǎn)化成齊次亥姆霍茲方程,利用分離變量法求解,根據(jù)分界面鄭州大學碩十研究生畢業(yè)論文摘要條件以及無限遠條件確定待定常數(shù),從而得到各場區(qū)矢量磁位的表達式。