本文選題：Laplace變換　切入點(diǎn)：Laplace逆變換　出處：《西安建筑科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文求解出在任意豎向移動(dòng)荷載作用下橫觀各向同性彈性地基問題的通解。首先對(duì)胡海昌關(guān)于橫觀各向同性體的通解進(jìn)行Laplace變換,再利用雙重傅里葉變化及逆變換,求得橫觀各向同性彈性地基在直角坐標(biāo)系下的Laplace形式通解,再進(jìn)行Laplace逆變換可得其真實(shí)解。對(duì)于置于橫觀各向同性彈性地基上的四邊自由正交各向異性薄板在移動(dòng)荷載下的動(dòng)力響應(yīng)問題,先對(duì)薄板的邊界條件以及控制方程進(jìn)行Laplace變換,再對(duì)移動(dòng)荷載以及未知的地基反力進(jìn)行Laplace變換,最后進(jìn)行雙重傅里葉展開,引入變形協(xié)調(diào)方程,得出Laplace形式的通解,進(jìn)行Laplace逆變換求得真實(shí)解。對(duì)于置于橫觀各向同性彈性地基上的四邊自由正交各向異性的中厚板在移動(dòng)荷載下的動(dòng)力響應(yīng)問題,先求得含有未知地基反力板的Laplace形式通解,引入變形協(xié)調(diào)方程,得出Laplace形式的通解,進(jìn)行Laplace逆變換求得真實(shí)解。對(duì)于四邊自由正交各向異性的中厚板的穩(wěn)態(tài)振動(dòng)問題,基于橫觀各向同性彈性地基模型的通解,結(jié)合板的穩(wěn)態(tài)振動(dòng)控制方程,引入變形協(xié)調(diào)方程,得出解析解。編制Matlab程序,通過Matlab程序計(jì)算算例,計(jì)算所得結(jié)果與文獻(xiàn)吻合,證明本文方法的正確性。研究在移動(dòng)荷載下地基的參數(shù)、板的參數(shù)對(duì)板撓度與板彎矩的影響情況;研究在簡(jiǎn)諧激勵(lì)荷載作用下荷載的頻率對(duì)板撓度和彎矩幅值的影響情況。
[Abstract]:In this paper, the general solution to the problem of transversely isotropic elastic foundation under arbitrary vertical moving load is solved. Firstly, the general solution of Hu Haichang's general solution to transversely isotropic body is carried out by Laplace transform, and then the double Fourier transform and inverse transformation are used to solve the problem of transversely isotropic elastic foundation. The general solution of Laplace form for transversely isotropic elastic foundation in rectangular coordinate system is obtained. The real solution can be obtained by using Laplace inverse transformation. For the dynamic response of four free orthotropic thin plates on transversely isotropic elastic foundation under moving loads, the boundary conditions and governing equations of thin plates are firstly transformed by Laplace transform. Then the moving load and the unknown foundation reaction are transformed by Laplace, and then the double Fourier expansion is carried out, and the deformation coordination equation is introduced, and the general solution of Laplace form is obtained. The real solution is obtained by inverse Laplace transform. For the dynamic response of a plate with free orthotropic anisotropy of four sides on a transversely isotropic elastic foundation under moving load, the general solution of Laplace form with unknown foundation is first obtained. The general solution of Laplace form is obtained by introducing the deformation coordination equation, and the real solution is obtained by Laplace inverse transformation. For the steady state vibration problem of moderately thick plate with free orthotropic anisotropy on four sides, the general solution of transversely isotropic elastic foundation model is obtained. Combined with the steady state vibration control equation of the plate, the deformation coordination equation is introduced, and the analytical solution is obtained. The Matlab program is compiled, and an example is calculated by the Matlab program. The calculated results are in good agreement with the literature. The validity of this method is proved. The influence of the parameters of the foundation and the plate on the deflection and bending moment of the plate under moving load is studied, and the influence of the frequency of the load on the deflection and the amplitude of bending moment of the plate under harmonic excitation is studied.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TU470

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