物理代写|理论力学代写theoretical mechanics代考|PHYS2201

statistics-lab™ 为您的留学生涯保驾护航 在代写理论力学theoretical mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写理论力学theoretical mechanics代写方面经验极为丰富，各种代写理论力学theoretical mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

物理代写|理论力学代写theoretical mechanics代考|Basic Linear Relations of Electro Elasticity

In the future, we will consider only electroacoustic interaction in piezoelectric media, where the complete system of quasistatic equations can be conveniently represented as
$$c_{i j k m} \frac{\partial^{2} u_{k}^{(n)}}{\partial x_{i} \partial x_{m}}+e_{i j m} \frac{\partial^{2} \varphi_{n}}{\partial x_{i} \partial x_{m}}=\rho_{n} \frac{\partial^{2} u_{j}^{(n)}}{\partial t^{2}} ; e_{i j m} \frac{\partial^{2} u_{j}^{(n)}}{\partial x_{i} \partial x_{m}}-\varepsilon_{i m} \frac{\partial^{2} \varphi_{n}}{\partial x_{i} \partial x_{m}}=0 .$$
in which the physicomechanical characteristics of the material form the tensors describing a specific anisotropy of the piezoelectric material $\left{\left(\hat{c}{i j n k}\right){6 \times 6} ;\left(\hat{e}{i j m}\right){3 \times 6} ;\left(\hat{e}{m i j}\right){6 \times 3} ;\left(\hat{\varepsilon}{n k}\right){3 \times 3}\right}_{9 \times 9}$, and determine the structural composition of the coupled electroelastic wave field $\left{u_{i}\left(x_{k}, t\right) ; \varphi\left(x_{k}, t\right)\right}$.

Formally, the role of the conjugation conditions of mechanical fields in the adjoining electro- (magneto-thermo-) elastic media is played by the conditions of continuity of mechanical stresses $\sigma_{i j}^{(m)}$ and elastic displacements $u_{k}^{(m)}$ at the media interface $\Sigma_{m}\left(x_{i}\right)$
$$\left.\left(\sigma_{i j}^{(1)}-\sigma_{i j}^{(2)}\right) \cdot n_{j}\right|{\Sigma{m}\left(x_{i}\right)}=0 ;\left.\quad u_{k}^{(1)}\right|{\Sigma{w}\left(x_{i}\right)}=\left.u_{k}^{(2)}\right|{\Sigma{w}\left(x_{i}\right)}$$
In electro-elastic media, the conjugacy conditions at the interface of the media are represented as continuity of the tangential components of the electric field strength and normal components of the electric displacements in the adjacent media. In the media interface $\Sigma_{m}\left(x_{i}\right)$, these conditions are written as
$$\left.\left(D_{j}^{(1)}-D_{j}^{(2)}\right) \cdot n_{j}\right|{\Sigma{w}\left(x_{i}\right)}=0 ;\left.\quad \varphi^{(1)}\right|{\Sigma{m}\left(x_{i}\right)}=\left.\varphi^{(2)}\right|{\Sigma{m}\left(x_{i}\right)^{0}}$$
In the problems of electro elasticity (magneto elasticity), the vacuum is also considered as an interacting “medium”, on the outer surfaces of the waveguide. In these cases, the conditions of mechanically open borders are written as
$$\left.\sigma_{i j}^{(1)} \cdot n_{j}\right|{\Sigma{0}\left(x_{i}\right)}=0 .$$
In the case of a rigidly clamped outer surface of the waveguide, we will have the fixing conditions for elastic displacements
$$\left.u_{k}^{(1)}\right|{\Sigma{0}\left(x_{i}\right)}=0 .$$

物理代写|理论力学代写theoretical mechanics代考|The Connection of Two Piezoelectric Layers

When the roughness surfaces of two bodies are joined with the piezoelectric glue (Fig. 1), a near-surface thin non-uniform three-layer with mixed physico mechanical properties is formed $[14,15]$. Take into account a thinness of the near-surface zone,

the piecewise-homogeneous three-layer is modeled as an internal meta-surface of a two-layer waveguide, with unique physical and geometric characteristics (Fig. 1).
The thickness of the adhesive layer is also small compared to the effective thickness of the adjacent layers. In studies of the propagation of the wave signal electroactive antiplane deformation, in the internal adhesive gap of variable width $\Omega_{3}=\left{|x|<\infty, h_{2}(x) \leq y \leq h_{1}(x),|z|<\infty\right}$, as well as in each half space $\Omega_{1}=\left{|x|<\infty, h_{1}(x) \leq y<\infty,|z|<\infty\right}$ and $\Omega_{2}=\left{|x|<\infty,-\infty<y \leq h_{2}(x),|z|<\infty\right}$ quasistatic equations of electroactive antiplane deformation are solved
$$\begin{gathered} c_{44}^{(m)} \frac{\partial^{2} \mathrm{w}{m}}{\partial x^{2}}+e{15}^{(m)} \frac{\partial^{2} \varphi_{m}}{\partial x^{2}}+\frac{\partial \sigma_{y z}^{(m)}}{\partial y}=\rho_{m} \frac{\partial^{2} \mathrm{w}{m}}{\partial t^{2}} ; \ e{15}^{(m)} \frac{\partial^{2} \mathrm{w}{m}}{\partial x^{2}}-\varepsilon{11}^{(m)} \frac{\partial^{2} \varphi_{m}}{\partial x^{2}}+\frac{\partial D_{y}^{(m)}}{\partial y}=0 \end{gathered}$$
Taking into account the effective thickness of the adjacent layers, the solutions of Eqs. (3.1) and (3.2) in each half space have the following form
$$\begin{gathered} \mathrm{w}{n}(x, y, t)=W{0 n} \exp \left[(-1)^{n} \alpha_{n} k y\right] \cdot \exp [i(k x-\omega t)] \ \varphi_{n}(x, y, t)=\left{\begin{array}{l} \Phi_{0 n} \exp \left[(-1)^{n} k y\right] \ +\left(e_{n} \backslash \varepsilon_{n}\right) \cdot W_{0 n} \exp \left[(-1)^{n} \alpha_{n} k y\right] \end{array}\right} \cdot \exp [i(k x-\omega t)] \end{gathered}$$
The function of the distribution of the wave field is chosen so that it simply and completely (without loss of physical phenomena) describes the nature of the change of the desired quantities on surfaces and along the thickness of the adhesive layer.

物理代写|理论力学代写theoretical mechanics代考|Smoothing the Roughness of the Surfaces

Smoothing the roughness of the surfaces of the piezoelectric layer by pouring different materials (Fig. 2), in the near-surface zones, thin non-uniform double layers with mixed physical and mechanical properties are formed $[16,18,19]$. Different fills lead to the formation of heterogeneous electromechanical meta-surfaces of the piezoelectric base layer.

Let us assume that the waveguide surface irregularities $y=h_{+}(x)$ are filled to the level $y=h_{0}\left(1+\gamma_{+}\right)$with a good dielectric, and the waveguide’s surface irregularities $y=h_{-}(x)$ are filled to the level $y=-h_{0}\left(1+\gamma_{-}\right)$with a good electrical conductor.
Here $\gamma_{\pm} \ll 1$ are the heights of the profiles of irregularities and $h_{0}$ is a half of the base thickness of the homogeneous piezoelectric layer. So we have a composite waveguide, which consists of five layers:

• the base layer $\Omega_{0}{x, y}$ of a constant thickness $-h_{0}\left(1-\gamma_{-}\right) \leq y \leq h_{0}\left(1-\gamma_{+}\right)$
• an electrically conductive layer $\Omega_{-}^{c}{x, y}$ of thickness $\xi_{c}(x)=$ $\left|h_{0}\left(1+\gamma_{-}\right)+h_{-}(x)\right|$
• nonhomogeneous piezoelectric thin layer $\Omega_{-}^{p}{x, y}$ of thickness $\xi_{p-}(x)=$ $\left|-h_{0}\left(1-\gamma_{-}\right)-h_{-}(x)\right|$
• nonhomogeneous piezoelectric thin layer $\Omega_{+}^{p}{x, y}$ of thickness $\xi_{p+}(x)=$ $\left|h_{+}(x)-h_{0}\left(1-\gamma_{+}\right)\right|$
• a dielectric thin layer $\Omega_{+}^{d}{x, y}$ of thickness $\xi_{d}(x)=h_{0}\left(1+\gamma_{+}\right)-h_{+}(x)$.
Thus, near the surface area $y=h_{-}(x)$ we have a composite layer, which consists of transversely inhomogeneous piezoelectric and homogeneous, perfectly conducting materials. The same way, near the surface area $y=h_{+}(x)$ we have a composite layer, which consists of homogeneous dielectric and transversely inhomogeneous piezoelectric materials. The homogeneous piezoelectric waveguide with filled surface irregularities is modeled as a multilayer waveguide made of different materials.

物理代写|理论力学代写theoretical mechanics代考|Basic Linear Relations of Electro Elasticity

C一世jķ米∂2在ķ(n)∂X一世∂X米+和一世j米∂2披n∂X一世∂X米=ρn∂2在j(n)∂吨2;和一世j米∂2在j(n)∂X一世∂X米−e一世米∂2披n∂X一世∂X米=0.

(σ一世j(1)−σ一世j(2))⋅nj|Σ米(X一世)=0;在ķ(1)|Σ在(X一世)=在ķ(2)|Σ在(X一世)

(Dj(1)−Dj(2))⋅nj|Σ在(X一世)=0;披(1)|Σ米(X一世)=披(2)|Σ米(X一世)0

σ一世j(1)⋅nj|Σ0(X一世)=0.

物理代写|理论力学代写theoretical mechanics代考|The Connection of Two Piezoelectric Layers

C44(米)∂2在米∂X2+和15(米)∂2披米∂X2+∂σ是和(米)∂是=ρ米∂2在米∂吨2; 和15(米)∂2在米∂X2−e11(米)∂2披米∂X2+∂D是(米)∂是=0

\begin{聚集} \mathrm{w}{n}(x, y, t)=W{0 n} \exp \left[(-1)^{n} \alpha_{n} k y\right] \cdot \exp [i(k x-\omega t)] \ \varphi_{n}(x, y, t)=\left{\begin{array}{l} \Phi_{0 n} \exp \left[( -1)^{n} k y\right] \ +\left(e_{n} \反斜杠 \varepsilon_{n}\right) \cdot W_{0 n} \exp \left[(-1)^{n} \alpha_{n} k y\right] \end{array}\right} \cdot \exp [i(k x-\omega t)] \end{聚集}\begin{聚集} \mathrm{w}{n}(x, y, t)=W{0 n} \exp \left[(-1)^{n} \alpha_{n} k y\right] \cdot \exp [i(k x-\omega t)] \ \varphi_{n}(x, y, t)=\left{\begin{array}{l} \Phi_{0 n} \exp \left[( -1)^{n} k y\right] \ +\left(e_{n} \反斜杠 \varepsilon_{n}\right) \cdot W_{0 n} \exp \left[(-1)^{n} \alpha_{n} k y\right] \end{array}\right} \cdot \exp [i(k x-\omega t)] \end{聚集}

物理代写|理论力学代写theoretical mechanics代考|Smoothing the Roughness of the Surfaces

• 基础层Ω0X,是厚度不变的−H0(1−C−)≤是≤H0(1−C+)
• 导电层Ω−CX,是厚度XC(X)= |H0(1+C−)+H−(X)|
• 非均匀压电薄层Ω−pX,是厚度Xp−(X)= |−H0(1−C−)−H−(X)|
• 非均匀压电薄层Ω+pX,是厚度Xp+(X)= |H+(X)−H0(1−C+)|
• 介电薄层Ω+dX,是厚度Xd(X)=H0(1+C+)−H+(X).
因此，在地表附近是=H−(X)我们有一个复合层，它由横向不均匀的压电材料和均匀的完美导电材料组成。同样的方法，靠近表面积是=H+(X)我们有一个复合层，它由均匀的电介质和横向不均匀的压电材料组成。具有填充表面不规则性的均匀压电波导被建模为由不同材料制成的多层波导。

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。