fourier expansion 中文意思是什麼
fourier expansion
解釋
傅里葉級數展開-
So this base isolation technique has profound prospects. unfortunately there exist definite difficulties in the calculation because of the nonlinear of the base friction force. now, both the equivalent damping method and the numerical calculatin of the vibration response of the base - isolated buildings are frequently used in the calculation of the seismic response of the base - isolated building. however both of them have certain drawbacks. in this paper, the response of the building with base - isolation system is derived by the method of fourier expansion for the friction force and the earthquake response. at the same time, the sliding vibration character of inertia of a single mass structure and the sliding vibration response of a muti - mass structure are discussed. the stable condition of the sliding base isolation system of a structure is given. in the end, two circes of base fixation and base sliding are analyzed by adopting ansys
本文利用對摩擦力和地震響應進行付氏級數展開的方法導出了基底具有摩擦隔震系統的地震反應。同時，文中從研究單質點結構的滑動振動慣性力入手，進而對多質點結構體系滑動振動反應進行探討，分別給出了結構滑動隔震的自身穩定條件。最後，本文利用ansys對基礎固定和基礎滑移隔震兩種工況進行了動力模擬模擬分析，進一步證實了基礎滑移隔規律。 -
The main results achieved in this thesis can be summarized as follows : 1. by means of the fourier series expansion, an approximate analytical propagation equation of flattened gaussian beams ( fgbs ) passing through an apertured paraxial abcd optical system is derived, and illustrated with numerical examples, when the transmissivity of the aperture is t ( x ) = cos ( x )
用傅立葉級數展開法研究了平頂高斯光束通過有光闌限制的近軸abcd光學系統的傳輸特性，導出了光闌透射率為t （ x ） = cos （ x ）時的近似解析傳輸公式，硬邊光闌的情況可作為= 0的特例得到。 -
In this paper, dynamic stability of parametrically excited flexible cam - follower system on the weakly nonlinear condition is investigated by using the combination of both the method of multiple scales and the technique of fourier series expansion. the equations of approximate transition curves in the plane of the dimensionless frequency and excitation ( amplitude ) parameter that separate stable from unstable solution are derived
隨后，本文採用多尺度法並結合fourier級數展開，分析了不同的凸輪從動件運動規律和不同的凸輪的升程、停程以及回程的時間分配規律下，無間隙的周期時變凸輪系統模型的穩定性，獲得了各種規律下的凸輪系統的穩定區間圖。 -
The obtained results in the paper are as follows : ( 1 ) the expansion of fourier series of orthogonal trigonometric polynomial for conditional mathematical expectation and function of random variable ; ( 2 ) the best approximation of trigonometric polynomial about another random variable for function of a random variable ; ( 3 ) the best approximation order of trigonometric polynomial for function of random variable
摘要獲得了如下結果： （ 1 ）條件數學期望及隨機變量函數的三角多項式級數表達； （ 2 ）一個隨機變量關于另一個隨機變量的三角多項式的最佳逼近； （ 3 ）隨機變量函數被隨機變量三角多項式最佳逼近的階。 -
When studying the basis expansion approach, a new scheme utilizing pilot signals is proposed, which takes full advantage of high processing gain of dpcch. utilizing fourier transform, the frequencies and the coefficients of basis can be estimated
在基展開方法中，充分利用對dpcch解擴后的系統處理增益為24db的優點，結合基展開的思路，提出了基於基展開的通道非盲估計。 -
The submarine structure is simplified to single or double infinite cylindrical shell stiffened with rings, bulkheads and stringers, focusing on underwater sound radiation from the single shell. the shell motion is described by donnell ' s theory including excitation forces and reactions of rings, bulkheads, stringers and fluid, which leads to the fluid - structure coupling vibration equation. expressing displacements by velocities, applying modal expansion circumferentially and fourier transformation longitudinally result in the shell ' s modal equations of motion
殼體的運動方程採用較為簡單的donnell理論描述，運動方程中包括了激勵力、加筋結構（環肋、艙壁和縱骨）和流場對殼體的作用力，從而組成流場-結構的耦合振動方程，並進一步將方程中的位移用速度表示，然後沿軸線方向進行fourier變換，將速度和各項荷載沿圓周方向進行模態展開，得到了殼體振動的模態運動方程。 -
From 1920s up to now, various techniques and methods for wave field decomposition, propagation and migration / imaging have been well developed, such as the kirchhoff asymptotic method, frequency - wavenumber domain phase - shift and phase - shift - plus - interpolation methods, and the one - way wave equation based phase - screen and generalized screen methods, etc. wave field extrapolation in these methods is implemented based on the expansion of the wave field by sets of basic functions like spatial fourier harmonies, modes, and green ' s functions
自上個世紀二十年代至今，波場分解、傳播與偏移成像技術經歷了將近一個世紀的發展，形成了多種不同的方法，如kirchhoff波動方程高頻近似解方法，頻率-波數域的相移（ phase - shift ）方法和相移-內插（ pspi ）方法，以及在混合域中基於單向波動方程的相位屏、廣義屏方法等。 -
In this paper a newly develoed helical coordinates is used to make out the solution of electromagnetic fields in the helix gap and calculate dispersion characteristics of tape helix slow wave structure for the first time. strict boundary conditions for magnetic fields are adopted and are treated rigorously by fourier expansion. besides, the radial propagation constant of every layer in the dielectric - loaded region is differentiated. some of practical tape helix slow wave structures have been calculated for dispersion characteristics and the calculated values accord with measured values very well. the authors also compare the calculated results with experiments for different structures by changing tape thickness or other structure parameters and find that the theory in the paper is universal
本文首次運用螺旋坐標系給出了帶狀螺旋線縫隙內的電磁場解，並據此計算了帶狀螺旋慢波結構的色散特性.文中採用了嚴格的邊界條件，並以傅立葉展開進行了嚴格的數學處理.另外還首次對有介質區域內各層的徑向傳輸系數作了區別.本文使用這種方法計算了我們已研製的一些寬帶高功率行波管所用的慢波線結構的色散特性，理論與實驗符合得很好.我們還計算了不同結構參數對色散特性的影響，並與實驗作了對照，發現本文的理論有一定的普適性 -
Based on the assumption of periodic rubbing force in rotor system, the rubbing forces onto each node of rotor system are estimated by modal expansion technique and the sub - harmonic decomposition of residual matrix between faulty and faulty - free vibration signals of rotor system through fft ( fast fourier transformation )
基於轉子系統碰摩力的周期性假設，利用模態擴展方法，對故障和健康轉子系統振動信號的殘差矩陣進行傅立葉級數的分頻諧波近似，估算得到轉子軸承各節點的碰摩力。 -
We consider a neutral particle with magnetic moment antiparallel to the field. with the interaction potential energy between the magnetic moment of the particle and the magnetic field, we obtain the classical motion equation of the neutral particles in the loffe trap. in some limit conditions, by using the perturbative method, the equations may take on concise forms. of which the two equations about x and y are mathieu equations. if we properly set the parameters and have the condition a > > q > 0, we can solve the mathieu equation with the traditional wkbj method. as a new attemptation, with fourier series expansion we solve the mathieu equation and obtain the classical motion law of the neutral particles
若阱的參數設置使得條件> > q 0成立時，我們可以利用傳統的wkbj方法近似求解馬丟方程。作為一種新的嘗試，本文還採用傅立葉級數展開的辦法來對馬丟方程進行求解，從而得到中性粒子在阱中的經典運動規律。在研究ioffe阱對中性粒子的囚禁問題時，實際上我們更感興趣的是馬丟方程的周期解，而要想獲得這種周期解，和q必須滿足一定的關系，亦即必須選擇阱的特定的參數和粒子的特定初始條件，對這一問題我們進行了嘗試性的研究。
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