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51.
Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder 总被引:1,自引:0,他引:1
By virtue of the introduction of a dependent variable and the separation of variables technique, the axisymmetric plane strain electroelastic dynamic problem of a special non-homogeneous piezoelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solutions of displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow cylinder with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are finally presented. 相似文献
52.
从辽河油区的地质条件和开发特征出发.立足单因素分析,在着重研究渗进率、净总厚度比和单层厚度对原油采收率影响的基础上。利用《价值工程》中的“功能重要评价法”,优化出不同类型稠油油藏蒸汽吞吐和蒸汽驱开发阶段的采收率计算公式.经实际资料验证,该公式对油田开发前期确定采收率丰和可采储量,具有较好的适用性。 相似文献
53.
邹光远 《水动力学研究与进展(A辑)》1993,8(2):219-226
对于用层平均速度势(或速度)与波高给出的非线性等水深Boussinesq方程,与KdV方程一样,存在两类永形波—孤立波和周期波。不同的是,对于Boussinesq方程,孤立波和周期波一样,是以反函数的积分形式给出的,这在使用上是不方便的。本文对这两类波,分别给出了相应的级数形式的正函数解。对于孤立波,级数的收敛速度是十分快的,且文中还给出了一个具有高精度的十分简单的近似解,对于周期波,只要有关参数选得合适,解的收敛速度也是相当快的。这就有效地克服了反函数形式解在使用上的不方便。 相似文献
54.
When freshly etched samples of various types of copper were exposed in moderately acid, aerated chloride solutions, two phenomena were observed. First the corrosion potential and the pH of the solution decreased over a shorter time, then the potential increased over a long period (600-1500 min), following an s-shaped pattern. Increase in pH during the second stage was avoided using a pH-stat. The corrosion rate increased little or not at all over the entire period. A tentative interpretation of the short-term behaviour is presented with some reservation. The long-term development of the potential suggests phase formation or transformation following the Avrami pattern. By suitable derivations it was possible to fit the development of potentials to the Avrami equation. Subsequent examinations by Auger spectroscopy proved the presence of thin layers of Cu2O on the copper surfaces, increasing in thickness with exposure time. The dissolution kinetics can be described in terms of two parallel electrochemical reactions and a simultaneous non-electrochemical dissolution reaction. 相似文献
55.
In general, this paper deals with general nonlinear oscillations of a nonconservative and single degree-of-freedom system with odd nonlinearity and, in particular, it presents accurate higher-order analytical approximate solutions to van der Pol damped nonlinear oscillators having odd nonlinearity and the Rayleigh equation. By combining the linearization of the governing equation with harmonic balancing and the method of averaging, we establish accurate analytical approximate solutions for the general weakly damped nonlinear systems. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. The combination of these two methods results in very accurate transient response of the periodic solution. In addition and for the first time, this paper also presents a method for deducing fourth-, fifth- and higher-order linearized governing equations from the lower-order equations without the requirement of formulating the problem from the first principle. Three examples including the van der Pol damped nonlinear oscillator are presented to illustrate the excellent agreement with approximate solution using the exact frequency. 相似文献
56.
This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated. 相似文献
57.
A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers 总被引:1,自引:0,他引:1
Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems. 相似文献
58.
In the present work, the ohmic resistance of an integrated planar-SOFC (IP-SOFC) has been evaluated by developing a model
whose equations have been solved numerically through an FEM method. The model allows to estimate the distribution of voltage
and current density in the cell. A comparison between simulated and experimental data of area specific resistance is reported,
which shows satisfactory agreement. The mathematical model has also been used to carry out some parametric studies for optimisation
purposes. Indeed, a reduction in cell pitch length and an increase in electrode thickness are predicted to lead to a reduction
in ohmic losses in IP-SOFCs. 相似文献
59.
A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes,
is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the
small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically
derive the Butler–Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to
a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter)
model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the
dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations
of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated
electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited
reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer
region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state)
numerical solutions of the inner equations are presented. 相似文献
60.
This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions 相似文献