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(dǎo)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(yùn)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(yùn)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(yùn)用變分法,分離變量法,互等功定理等數(shù)學(xué)工具求解板的運(yùn)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(yīng)(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(dāng)變換,把含內(nèi)熱源的熱傳導(dǎo)方程轉(zhuǎn)化為不含內(nèi)熱源的熱傳導(dǎo)方程,然后采用分離變量法進(jìn)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(xué)碩十研究生畢業(yè)論文摘要條件以及無限遠(yuǎn)條件確定待定常數(shù),從而得到各場區(qū)矢量磁位的表達(dá)式。
The governing equations of the problem are derived in hamiltonian form by using variable substitution and variational principle . then the methods of separation of variables and conjugate symplectic eigenfunction expansion are developed to solve the equations of plate bending problem . the result can be derived by analytical method 在平面彈性問題中,由變量代換及變分原理,方程可導(dǎo)向哈密頓體系,從而通過分離變量法及共軛辛本征函數(shù)向量展開法,以解析的方法來進(jìn)行求解。
The vector magnetic potential of a system consisting a line electric current and an infinite long magnetic dielectric column is calculated with the method of separation of variables and method of images , it is pionted out that the vector magnetic potential of a system consisting a line electric current and a magnetic dielectric plane , an ideal paramagnetic column , a superconductor column , and a line electric current in homogeneous magnetic field can all be deduced from our calculation 摘要用鏡象電流法和分離變量法計(jì)算了線電流與無限長磁介質(zhì)圓柱系統(tǒng)的磁矢勢,指出線電流與無限大磁介質(zhì)分界平面、線電流與超導(dǎo)體圓柱、均勻外磁場中有磁介質(zhì)圓柱系統(tǒng)時的磁矢勢都可以由線電流與磁介質(zhì)圓柱系統(tǒng)的磁矢勢的極限情形給出。
By using the method of separation of variables , a recursive formula was derived for the electromagnetic fields in a circular coaxial cable with a radial conductor plate and filled with multilayered homogeneous isotropic media , and the relationship between the first and the nth layers of the electromagnetic fields was determined 摘要采用分離變量方法,推導(dǎo)了有徑向?qū)w板、填充均勻的多層各向同性介質(zhì)的同軸線各層電磁場之間的遞推關(guān)系,得到了第1層與第n層介質(zhì)中電磁場的關(guān)系方程。