A three-dimensional solution for plates and laminates

A general three-dimensional solution is presented for statics and dynamics of plates, homogeneous or laminated, of orthotropic materials. The solution is in series form. Using parts of the general solution a variety of problems, especially of rectangular configurations, can be solved. As Mindlin's approximate analysis for vibration of thick plates is often adequate for specific practical purposes, a general solution for Mindlin's analysis is also given.     

Nonlinear Vibration of Elastic Skew Plates Exhibiting Rectilinear Orthotropy

The governing equations for large amplitude flexural vibrations of orthotropic skew plates are obtained from the corresponding static equations derived in this paper. Making use of an approximation originally due to Berger, corresponding simplified equations are also derived. Considering the large amplitude free flexural vibration of orthotropic skew plates clamped along all the edges, it is shown that the Berger approximation leads to results good enough for engineering purposes. Amplitude vs period curves are presented for different aspect ratios and skew angles of the plate under two in-plane edge conditions. It is observed that the amplitude vs period behaviour is of the hardening type, i.e. period decreases with increasing amplitude.     

基于HEA方法的陕西省受损植被生态服务功能补偿评估

本文通过对HEA方法的改进,运用"中国生态系统生态服务价值当量因子表",推导出受损植被生态服务功能补偿评估计算公式。以相关统计资料为依据,应用公式,对陕西省森林和草地生态服务功能的受损量和补偿量进行了评估。发现,1986年~2004年,陕西省的森林生态服务功能水平每年递增1.7%,草地生态服务功能水平每年递减3.0%;1986年~2014年,陕西省草地的关键生态服务功能的受损量8090.7万当量,平均每年受损289.0万当量,相当于1986年、1994年、1999年、2004年4年草地关键生态服务功能价值当量平均值746.7万当量的38.7%;2005年~2014年,以耕地作为被转换的生态系统,陕西省最少需要2201.6×104hm2的耕地用于补偿受损草地。若以难利用土地作为被转换的生态系统,陕西省最少需要558.9×104hm2的难利用土地用于补偿受损草地。若把完成草地生态服务功能补偿的时间延长到2024年,则最少需要943.5×104hm2耕地用于补偿受损草地,或最少需要239.5×104hm2难利用土地用于补偿受损草地。     

Standing waves in thin plates tensioned by in-plane loads subject to high frequency excitation

The problem investigated is that of the response of thin plates subjected to pure tone or wide band frequency excitation. A point load is applied perpendicular to the plates. In the case of isotropic or orthotropic plates excited at high frequencies ring shaped standing wave patterns are observed. No classical explanation exists covering this phenomenon. The present analysis indicates that there are two waves radiating from the excitation point with the same frequency, but at different speeds. One wave, a bending wave, is separated from the other one, a membrane wave.     

矩形截面螺线管线圈磁场的计算

本文介绍了基于第一类和第二类椭圆积分的圆环磁场公式计算均匀电流密度分布下的矩形截面螺线管线圈磁场的空间分布。     

Radiant flux through apertures—I

Equations for the calculation of radiant power F through two apertures in series are well known. A characteristic of these formulae is that they give F as a small difference between two large terms. Evidently, the flux through the apertures must decrease as the spacing between them increases; and for large spacing, the inverse-square relation must hold. Instead of exhibiting this behaviour in an obvious manner, however, the traditional equations give the specious impression of an increase in F with increase in spacing. The paper develops an approximate formulae that applies to apertures in the shape of any regular polygon and that shows clearly how the inverse square relation is approached for large separation.     

Radiant Flux Through Apertures— II

Equations for the radiant flux through apertures are well-known. But the exact equations are cumbersome and give little direct insight into the behavior of aperture systems. The present paper considers simple approximate equations for rectangular apertures in parallel planes and in perpendicular planes. It extends the previous work (square apertures) to the general case of rectangular apertures.     

椭圆运动驱动技术及其在电火花加工中的应用

为了提高电火花加工的稳定性，提出了椭圆运动微驱动技术。基于李萨如图形的原理，利用压电晶体的逆压电效应进行工作．并进行了驱动本体和驱动电路设计。实验结果表明，椭圆运动驱动技术具有频率响应快、步距小和设计简单的优点。     

Transmission Line Circuit Models for Dielectric Waveguide

A general procedure is outlined for obtaining single or coupled transmission line models to represent the propagation of surface wave modes in conductively unshielded dielectric waveguides. The procedure uses a homogeneous electrically or magnetically walled waveguide having the same dimensions as the dielectric of the surface waveguide, to produce a set of orthogonal eigenfunctions. These eigenfunctions are projected upon Maxwell's equations resulting in a system of transmission lines coupled together through a wave immittance, which represents the ratio of a longitudinal and a transverse field component at the dielectric-air interface. Examples are given for various modes of the dielectric slab and the dielectric rod, in particular the HE_1n modes for the latter. The transmission line models derived for these examples consist of a single trasmission line found directly by projection or reduced from a coupled transmission line model by port elimination, or of two transmission lines coupled together. All circuit models derived preserve the basic properties of surface waves (e.g. no solution below cut-off), and any of the single line models can be solved to give explicit approximate algebraic formulae for the propagation constant as a function of frequency. Numerical results show that the dispersion curves calculated from the models versus exact values are generally excellent over the entire frequency spectrum.     

Recent progress in the plastic methods of structural analysis

The techniques described in Part I of this paper for the calculation of plastic failure loads under proportional loading are further exemplified by indicating solutions for a rectangular building frame, a Vierendeel girder, and a shed-type portal frame. A method for estimating deflections of a frame just as the collapse load is attained is then described, with some indications as to its reliability. More general conditions of loading than proportional loading are next discussed, and generalized load and failure concepts are defined. The theorems and techniques for determining critical shakedown loads under variable, repeated loading are then described and illustrated. The relation of the elastic-plastic shakedown analysis to the much simpler analysis for failure under single load applications is discussed.     

Unified Krylov-Bogoliubov-Mitropolskii method under a critical condition

A modified and compact form of Krylov-Bogoliubov-Mitropolskii (KBM) unified method is extended to obtain approximate solution of an nth order, n=2,3,…, ordinary differential equation with small nonlinearities when unperturbed equation has some repeated real eigenvalues. The existing unified method is used when the eigenvalues are distinct whether they are purely imaginary or complex or real. The new form is presented generalizing all the previous formulae derived individually for second-, third- and fourth-order equations to obtain undamped, damped, over-damped and critically damped solutions. Therefore, all types of oscillatory and non-oscillatory solutions are determined by suitable substitution of the eigenvalues in a general result. The formulation of the method is very simple and the determination of the solution is easy. The method is illustrated by an example of a fourth-order equation when unperturbed equation has two real and equal eigenvalues. The solution agrees with a numerical solution nicely. Moreover, this solution is useful when the differences between conjugate eigenvalues (real or complex) are small. Thus the method is a complement of the existing modified and compact form of KBM method.     

Two direct Tustin discretization methods for fractional-order differentiator/integrator

This paper deals with fractional calculus and its approximate discretization. Two direct discretization methods useful in control and digital filtering are presented for discretizing the fractional-order differentiator or integrator. Detailed mathematical formulae and tables are given. An illustrative example is presented to show the practically usefulness of the two proposed discretization schemes. Comparative remarks between the two methods are also given.     

Radiant Flux Through Apertures— III

This paper completes our treatment of radiant flux through pairs of apertures. In Part II, we obtained approximate equations for rectangular apertures in parallel planes, with the restriction that two apertures be identical and that one be directly above the other. Here we generalize to the case of any apertures that fit into a rectangular grid. The idea for this generalization originated with Ondracek but it is here expressed in matrix notation, which allows coefficients F_ij to be obtained rather simply.     

Regenerated isotropic wood

Construction of sustainable high-performance structural materials is a core part of the key global sustainability goal. Many efforts have been made in this field; however, challenges remain in terms of lowering costs by using all-green basic building blocks and improving mechanical properties to meet the demand of practical applications. Here, we report a robust and efficient bottom-up strategy with micro/nanoscale structure design to regenerate an isotropic wood from natural wood particles as a high-performance sustainable structural material. Regenerated isotropic wood (RGI-wood) exceeds the limitations of the anisotropic and inconsistent mechanical properties of natural wood, having isotropic flexural strength of ∼170 MPa and flexural modulus of ∼10 GPa. RGI-wood also shows superior water resistance and fire retardancy properties to natural pine wood. Mass production of large sized RGI-wood and functional RGI-wood nanocomposites can also be achieved.     

Tracking and separating non-stationary multi-component chirp signals

In this paper we are concerned with the problems of (1) tracking or estimating the unknown, time-varying instantaneous frequency (IF) of a chirp signal from a multi-component signal (we assume our multi-component signal to be formed of additive chirp signals, disjoint in the time–frequency domain, and Gaussian noise) and (2) reconstructing a specific chirp signal based on the estimate of its IF found at (1). The algorithm we developed is based on a previously proposed method adapted now for the case of multi-component signals. It combines an adaptive smoothing procedure with a noise resistant Fourier filter to generate an algorithm with an extremely fine frequency resolution. The method is non-parametric, that is, we assume no prior knowledge about the form of the time-varying IF of the chirp or about the chirp itself. We demonstrate how the method works on simulated data and compare its performance to other presently used procedures.     

The approximate frequency response of semi-active systems requiring no computer

Semi-active systems are those in which a passive, dissipative element (damper, friction clutch, fluid orifice) is modulated, via low power inputs, to enhance the performance of its associated dynamic system. This type of control is inherently nonlinear, thus forcing the closed-loop response of the total system to be determined numerically using a digital computer. Although, strictly speaking, the frequency response for nonlinear systems does not exist, it is typical to simulate semi-active systems with sinusoidal input and present results as frequency transmissibilities. This paper uses energy dissipation per cycle to determine an approximate frequency response of semi-active systems requiring only a calculator for numerical analysis.     

Automated learning of gravitational mass of elliptical galaxies

We present a 3-staged method for automated learning of the spatial density function of the mass of all gravitating matter in a real galaxy, for which, data exist on the observable phase space coordinates of a sample of resident galactic particles that trace the galactic gravitational potential. We learn this gravitational mass density function, by embedding it in the domain of the probability density function (pdf) of the phase space vector variable, where we learn this pdfas well, given the data. We generate values of each sought function, at a design value of its input, to learn vectorised versions of each function; this creates the training data, using which we undertake supervised learning of each function, to thereafter undertake predictions and forecasting of the functional value, at test inputs. We assume that the phase space that a kinematic data set is sampled from, is isotropic, and we quantify the relative violation of this assumption, in a given data set. Illustration of the method is made to the real elliptical galaxy NGC4649. The purpose of this learning is to produce a data-driven protocol that allows for computation of dark matter content in any example real galaxy, without relying on system- specific astronomical details, while undertaking objective quantification of support in the data for undertaken model assumptions.     

An optimum non-circular chainwheel design for a bicycle drive system

A new and systematic approach for the analysis and simulation of a non-circular chainwheel in a bicycle drive system is presented. The proposed leg-bicycle model is based on a five-bar linkage and explicit expressions for the kinematics and kinetics are derived. The generated shape of the chainwheel is smoothed to an ellipse, for practical reasons. The performance of this elliptical chainwheel is assessed by comparing the joint moments, leg angular accelerations, crank angular velocities, crank angular accelerations and output forces with those of a conventional circular chainwheel. The results suggest combining the elliptical and circular chainwheels into a single unit, in order to accommodate a wide range of pedalling speeds. At low speeds, the elliptical chainwheel is engaged, but as the speed increases, a switch over to the circular chainwheel is recommended.     

边界吸收中镶边法的评价

以均匀层状带凹陷特征的介质模型为例,分析镶边法在常规边界吸收问题中的独到优越性;采用均匀倾斜模型数值实例,详细探讨外侧镶边法在边界吸收中的弊端及其成因.综合数值试算分析表明,外侧镶边法会引入虚假反射波,其原因是边界处速度延拓产生了人为绕射点.提出了内侧镶边方法,即以牺牲局部有效波场来提高数值计算精度、信噪比和可信度,实例验证该方法正确可行.