Determination of the natural frequencies of axially moving beams by the method of multiple scales

The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.

Bearing capacity analysis using the method of characteristics

Using the method of characteristics,the bearing capacity for a strip footing is analyzed.The method of characteristics leads to an exact true limit load when the calculations of the three terms in the bearing capacity formula are consistent with one collapse mechanism and the soil satisfies the associated flow rule.At the same time,the method of characteristics avoids the assumption of arbitrary slip surfaces,and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses.The exact solution without superposition approximation can still be expressed by Terzaghi＇s equation of bearing capacity,in which the bearing capacity factor N γλ is dependent on the dimensionless parameter λ and the friction angle φ.The influence of groundwater on the bearing capacity of the shallow strip footing is considered,which indicates that when the groundwater effect is taken into account,the error induced by the superposition approximation can be reduced as compared with dry soil condition.The results are presented in the form of charts which give the modified value（Nwγλc /Nγλc） of bearing capacity factor.Finally,an approximated analytical expression,which provides results in close agreement with those obtained by numerical analysis in this paper,has been suggested for practical application purposes.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)--CANTILEVER RECTANGULAR PLATES

In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates,the figures and tables of number value of bending moment and the deflection amplitudes as well.

APPLICATION OF THE METHOD OF THE RECIPROCAL THEOREM TO FINDING DISPLACEMENT SOLUTIONS OF CUBES

In this paper the method of reciprocal theorem is extended to find solutions of three-D problems of elasticity.First we give the basic solution of the cube with six surfaces fixed as the basic system and then using the reciprocal theorem between the basic system acted on by unit concentrated loads and the actual system with prescribed surface displacements, we find displacement solution of the actual system.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅱ)——RECTANGULAR PLATES WITH TWO ADJACENT CLAMPED EDGES

In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.

ON THE METHOD OF RECIPROCAL THEOREM TO FIND SOLUTIONS OF THE PLANE PROBLEMS OF ELASTICITY

In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.

Study on the Method of Setting the Mountain on Fire on the Experimen

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The Method of Moving Planes for Integral Equation in an Extremal Case

In this paper, we study the symmetry results and monotonicity of solutions for an integral equation u（x）=-cn∫RNeu（y）log｜x-y｜dy in an external case.

Preliminary Research on the Mathematical Methods and Order of Problems in the“Fungcheng”Chapter of Yang Hui's Mathematical Methods(1261 CE)

Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.

Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas

We study the existence of global-in-time classical solutions for the one-dimensional nonisentropic compressible Euler system for a dusty gas with large initial data.Using the characteristic decomposition method proposed by Li et al.(Commun Math Phys 267:1–12,2006),we derive a group of characteristic decompositions for the system.Using these characteristic decompositions,we find a sufficient condition on the initial data to ensure the existence of global-in-time classical solutions.

Well-Posedness of Equations with Fractional Derivative via the Method of Sum

We study the well-posedness of the equations with fractional derivative D^αu（t）= Au（t） ＋ f（t） （0 ≤ t ≤ 2π）, where A is a closed operator in a Banach space X, 0 〈 α 〈 1 and D^αis the fractional derivative in the sense of Weyl. Although this problem is not always well-posed in L^P（0, 2π; X） or periodic continuous function spaces Cper（[0, 2π]; X）, we show by using the method of sum that it is well-posed in some subspaces of L^P（0, 2π; X） or Cper （[0, 2π]; X）.

One modified method of characteristics used to analyze the multiconductor transmission lines

To solve the coupling effect of multiconductor transmission lines excited by external electromagnetic wave, the modified method of characteristics is proposed. The modified method of characteristics which can compute the terminal induced voltages excited by the external electromagnetic wave when the terminal networks or intereonnection networks contain the dynamic elements is introduced. The simulation results indicate that the modified method can analyze the terminal induced voltages when the terminal networks or the interconnection networks contain the dynamic elements excited by the external electromagnetic wave. And the results are compared with the results acquired by FDTD method, the two results are completely same. So one effective modified method is implemented to compute the transmission lines.

A comparative study of the aromaticity in some typical conjugated six-membered rings by the method of localized molecular orbital

The localized molecular orbitals and energy levels for four typical conjugated six-membered ring systems C_6H_6, C_3N_3H_3, B_3N_3H_6, and (B_3O_6)^(3-) as well as a non-aromatic reference molecule N_3Cl_6 have been calculated by using Edmiston-Ruedenberg energy localization technique under the CNDO/2 approximation in order to investigate the nature of aromaticity or quasi-aromaticity of the six-membered ring systems studied. The contour maps for π-type localized MO's (LMO) have been plotted to illustrate the bonding characteristics of the five ring systems studied. These LMO calculations show that for all the conjugated six-membered ring systems considered there exists local delocalization of π-bonds or three-centered and occasionally four-centered two-electron π-bonds in our terminology, and the cooperative effect among these π-bonds leading to the formation of a closed continuous x-conjugation system around the ring, which is necessary for the creation of aromaticity in the systems studied. We have been able to discuss the properties of these three-centered π-bonds in terms of the constituent atoms and electrons and the relevant orbitals involved.

On the Application of “Red Culture” in Urban Parks

In recent years, with the support of national policies and the people’s demand for cultural life, a wave of red tourism has been in full swing throughout the country. The revolutionary martyrs opened up new heavens and earth with their flesh and blood, and the great spirit of the Red Revolution carried forward the precious material and spiritual wealth of our socialist country. As the successor of socialism in the new era, inheriting the great spirit of the Chinese revolution and praising the red culture are important tasks for our contemporary people. Therefore, in the development and construction of urban parks, the red cultural connotation of urban parks should be given, which plays a very important role in improving the quality of the city and enhancing the charm of the city.

Studies on the method of total synthesis of koumine——Ⅰ.4-Substituted 1,2-dihydropyridine derivatives and their function as a conjugated diene in Diels-Alder reaction

A route to the total synthesis of koumine has been suggested.Five 4-substituted 1,2- dihydropyridine derivatives,which are supposed to be a conjugated diene of Diels-Alder reaction to produce the isoquinuclidine ring of koumine,have been synthesized.Only two of them were found to be able to undergo the Diels-Alder reaction.The stereochemistry of the reaction product has also been examined.

A Comparison of Cultures between China and the West——Taking Chinese Clothing and British Clothing as an Example

This paper attempts to do study on the comparison of differences between Chinese and western cultures by taking the Chinese and British clothing as an example. This comparison is made form two aspects about clothing culture. One is the separate characteristics of the Chinese and British clothing. The other is the common features of the Chinese and British clothing.The paper aims at making the Chinese confidently promote the clothing culture of China to make efforts to realize the great rejuvenation of China and enrich the culture of all mankind.

Investigation on the threshold control of safety blasting vibration velocity for the extraction of complicated orebody under railway

The threshold control of safety blasting vibration velocity is a significant process for the underground mining of complicated ore deposit under construction,road,and water.According to the equivalent principle of displacement and velocity of mass point,differential evolution is put forward based on 3DEC dynamic analysis,making the calculation more efficient and accurate.The 3DEC model of the complicated orebody under railway is established according to the topographic maps and geological data of the eastern Pyrite Mine.The stimulus-response distribution of internal stress and displacement fields are demonstrated by analyzing the on-site monitoring vibration displacement and velocity data of the mass point.The reliability of parameter selection,such as blasting simulation waveforms,rock damping,is identified.The safety vibration velocity of railway is set to 4.5 cm/s in line with the requirement of safety blasting rules.Thus,the maximum amount of single-stage explosive in this region is 44.978 kg.The simulation result is in good agreement with the on-site monitoring datum.No displacement and settlement of the 701 railway special line was achieved by choosing the critical amount of the single-stage explosive.

Reliability analysis on bolt support structure of coal roadway under the influence of mining

Based on the features of the serious deformation of coal roadway,many random variables of the mechanics of the surrounding rocks and the influence of mining, the reliability analysis model of the support structure of coal roadway under the influence of mining is established,and the calculating formulas of reliability of the support structure is obtained with the engineering structure reliability theory. And the reliability is calculated based on the method of Monte Carlo to the coal roadway which is exampled on the influence of mining or not. The relationship between support parameters and reliability, the mining influence coefficients and reliability is established, which provides theory foundations for the design of the coal roadway bolt support.