Comparative study on three dynamic modulus of elasticity and static modulus of elasticity for Lodgepole pine lumber

The dynamic and static modulus of elasticity （MOE） between bluestained and non-bluestained lumber of Lodgepole pine were tested and analyzed by using three methods of Non-destructive testing （NDT）, Portable Ultrasonic Non-destructive Digital Indicating Testing （Pundit）, Metriguard and Fast Fourier Transform （FFT） and the normal bending method. Results showed that the dynamic and static MOE of bluestained wood were higher than those of non-bluestained wood. The significant differences in dynamic MOE and static MOE were found between bulestained and non-bluestained wood, of which, the difference in each of three dynamic MOE （Ep. the ultrasonic wave modulus of elasticity, Ems, the stress wave modulus of elasticity and El, the longitudinal wave modulus of elasticity） between bulestained and non-bluestained wood arrived at the 0.01 significance level, whereas that in the static MOE at the 0.05 significance level. The differences in MOE between bulestained and non-bluestained wood were induced by the variation between sapwood and heartwood and the different densities of bulestained and non-bluestained wood. The correlation between dynamic MOE and static MOE was statistically significant at the 0.01 significance level. Although the dynamic MOE values of Ep, Em, Er were significantly different, there exists a close relationship between them （arriving at the 0.01 correlation level）. Comparative analysis among the three techniques indicated that the accurateness of FFT was higher than that of Pundit and Metriguard. Effect of tree knots on MOE was also investigated. Result showed that the dynamic and static MOE gradually decreased with the increase of knot number, indicating that knot number had significant effect on MOE value.

On dynamics of elastic rod based on exact Cosserat model

The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.

Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod

In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.

Theoretical Research and Experimental Validation of Elastic Dynamic Load Spectra on Bogie Frame of High-speed Train

When a train runs at high speeds, the external exciting frequencies approach the natural frequencies of bogie critical components, thereby inducing strong elastic vibrations. The present international reliability test evaluation standard and design criteria of bogie frames are all based on the quasi-static deformation hypothesis. Structural fatigue damage generated by structural elastic vibrations has not yet been included. In this paper, theoretical research and experimental validation are done on elastic dynamic load spectra on bogie frame of high-speed train. The construction of the load series that correspond to elastic dynamic deformation modes is studied. The simplified form of the load series is obtained. A theory of simplified dynamic load–time histories is then deduced. Measured data from the Beijing–Shanghai Dedicated Passenger Line are introduced to derive the simplified dynamic load–time histories. The simplified dynamic discrete load spectra of bogie frame are established. Based on the damage consistency criterion and a genetic algorithm, damage consistency calibration of the simplified dynamic load spectra is finally performed. The computed result proves that the simplified load series is reasonable. The calibrated damage that corresponds to the elastic dynamic discrete load spectra can cover the actual damage at the operating conditions. The calibrated damage satisfies the safety requirement of damage consistency criterion for bogie frame. This research is helpful for investigating the standardized load spectra of bogie frame of high-speed train.

ON SOME BASIC PRINCIPLES IN DYNAMIC THEORY OF ELASTIC MATERIALS WITH VOIDS

According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids,but also to derive systematically the complementary functionals for the eight-field,six-field, four-field and two-field simplified Gurtin-type variational principles.Furthermore,with this approach,the in- trinsic relationship among various principles can be explained clearly.

Dynamic Elastic Modulus of Cement Paste at Early Age based on Nondestructive Test and Multiscale Prediction Model

This paper introduced a nondestructive testing method to evaluate the dynamic elastic modulus of cement paste. Moreover, the effect of water-cement ratio and conventional admixtures on the dynamic elastic modulus of cement paste was investigated, in which three kinds of admixtures were taken into account including viscosity modifying admixture （VMA）, silica.fume （SF）, and shrinkage-reducing admixture （SRA）. The experimental results indicate that the dynamic elastic modulus of cement paste increases with decreasing water-cement ratio. The addition of SF increases the dynamic elastic modulus, however, the overdosage of VMA causes its reduction. SRA reduces the dynamic elastic modulus at early age without affecting it in later period. Finally, a multiscale micromechanics approach coupled with a hydration model CEMHYD3D and percolation theory is utilized to predict the elastic modulus of cement paste, and the predictive results by the model are in accordance with the experimental data.

Static and dynamic snap-through behaviour of an elastic spherical shell

The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to estimate the influence of the dynamic effects on the response. A table tennis ball is considered as an example of a thin-walled elastic shell. It is shown that the increase of the impact velocity leads to a variation of the deformed shape thus resulting in larger de- formation energy. The increase of the contact force is caused by both the increased contribution of the inertia forces and contribution of the increased deformation energy. The contact force resulted from deformation/inertia of the ball and the shape of the deformed region are calcu- lated by the proposed theoretical models and compared with the results from both the finite element analysis and some previously obtained experimental data. Good agreement is demonstrated.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

Dynamic analysis of new type elastic screen surface with multi degree of freedom and experimental validation

A feasible method was proposed to improve the vibration intensity of screen surface via application of a new type elastic screen surface with multi degree of freedom(NTESSMDF). In the NTESSMDF, the primary robs were coupled to the main screen structure with ends embedded into the elastomers, and the secondary robs were attached to adjacent two primary robs with elastic bands. The dynamic model of vibrating screen with NTESSMDF was established based on Lagrange's equation and the equivalent stiffnesses of the elastomer and elastic band were calculated. According to numerical simulation using the 4th order Runge-Kutta method, the vibration intensity of screen surface can be enhanced substantially with an averaged acceleration amplitude increasing ratio of 72.36%. The primary robs and secondary robs vibrate inversely in steady state, which would result in the friability of materials and avoid stoppage. The experimental results validate the dynamic characteristics with acceleration amplitude rising by62.93% on average, which demonstrates the feasibility of NTESSMDF.

Dynamic Design of Thick Orthotropic Cantilever Plates with Consideration of Bimoments

The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments;and the theory takes into account nonlinear law of displacements distribution in cross section of the plate. The methods for constructing bimoment theory are based on Hooke’s Law, three-dimensional equations of the theory of dynamic elasticity and the method of displacements expansion into Maclaurin series. The article gives the expressions to determine the forces, moments and bimoments. Bimoment theory of plates is described by two unrelated two-dimensional systems with nine equations in each. On each edge of the plate, depending on the type of fastening, nine boundary conditions are given. As an example, the solution of the problem of dynamic bending of thick isotropic and orthotropic plate under the influence of transverse dynamic loads in the form of the Heaviside function is given. The equations of motion of the plate are solved by numerical method of finite differences. The numerical results are obtained for isotropic and orthotropic plate. The graphs of changes of displacements and stresses of faces surfaces of the plate are presented. Maximum values of these displacements are found and analyzed. It is shown that by Timoshenko theory numerical values of stresses are much smaller compared to the ones obtained by bimoment theory of plates. Maximum numerical values of generalized displacements, forces, moments, and bimoments are obtained and presented in tabular form. The analysis of numerical results is done and the conclusions are drawn.

Low embankment dynamic response under vehicle traffic loads in arid-oasis areas

The use of low embankments is of significant concern for ecological protection in aridoasis areas.Based on the project of Sansha Expressway located in Kashgar City,Xinjiang,China,physical model tests were conducted in this study to investigate the dynamic response of the low embankment as per the effects of road structure,load amplitude,load frequency,load cycle,and moisture content.The dynamic stress is shown to increase with load amplitude while the dynamic elastic modulus decreases with load amplitude under short-term loading.The load frequency slightly influences the soil’s dynamic behavior;higher frequencies can improve the dynamic elastic modulus of the subgrade soil.The moisture content has greater influence on the mechanical properties of the subsoil than that of subgrade layer.The subgrade bears the majority of the traffic load as the stress dissipates to 37%of the whole value on its surface.The number of load cycles has the greatest effect on the dynamic response among the influencing factors tested.The dynamic elastic modulus with the type of long-term dynamic loading is only 40%-52%of that with static loading across the entire depth range.The dynamic stress shows significant accumulation with load cycles over the long-term dynamic loading test and becomes stable after 8×10~4 cycles of loading.An equation is established to quantify the cumulative dynamic stress in the low embankment under long-term dynamic loading conditions.

Elastic Dynamic Stability of Big-Span Power Transmission Tower Subjected to Seismic Excitations

By combining the time-history response analysis and the eigenvalue buckling analysis, this paper developed a computational procedure to study the elastic dynamic stability of a transmission tower by APDL language in ANSYS. The influences of different input directions of seismic excitations and damping ratio on the elastic dynamic stability of tower were discussed. The following conclusions were obtained： （ 1 ） Longitudinal direction of the transmission lines is the worst input direction of seismic excitation for the transmission tower. （2） Dead load has no significant effect on the critical load and the occurrence time of buckling. （3） Vertical input of seismic excitations has no great effect on the dynamic stability of the transmission tower. （4） Damping effect has an influence on the dynamic stability of the transmission tower; however, the inherent characteristics of dynamic buckling is not changed.

Pressure Effect on Elastic and Lattice Dynamic Properties of Beryllium Selenide from First Principles

The lattice dynamic, elastic, and thermodynamic properties of Be Se were investigated with first principles calculations. The phase transition pressure from the zinc blende（B3） to the nickel arsenide（B8） structure of Be Se was determined. The elastic stability analysis suggests that the B3 structure Be Se is mechanically stable in the applied pressure range of 0-50 GPa. Our lattice dynamic calculations show that the B3 structure is lattice dynamically stable under high pressure. Within the quasiharmonic approximation, the thermodynamic properties including the constant volume heat capacity and constant pressure heat capacity are predicted.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Detection of Frost-Resistance Property of Large-Size Concrete Based on Impact-Echo Method

The dynamic elasticity modulus(Ed)is the most commonly used indexes for nondestructive testing to represent the internal damage of hydraulic concrete.Samples with a specific size is required when the transverse resonance method was used to detect the Ed,resulting in a limitation for field tests.The impact-echo method can make up defects of traditional detection methods for frost-resistance testing,such as the evaluation via the loss of mass or strength.The feasibility of the impact-echo method to obtain the relative Ed is explored to detect the frost-resistance property of large-volume hydraulic concretes on site.Results show that the impact-echo method can replace the traditional resonance frequency method to evaluate the frost resistance of concrete,and has advantages of high accuracy,easy to operate,and not affecting by the aggregate size and size effect of samples.The dynamic elastic modulus of concrete detected by the impact-echo method has little difference with that obtained by the traditional resonance method.The one-dimensional elastic wave velocity of concrete has a good linear correlation with the transverse resonance frequency.The freeze-thaw damage occurred from the surface to the inner layer,and the surface is expected to be the most vulnerable part for the freeze-thaw damage.It is expected to monitor and track the degradation of the frost resistance of an actual structure by frequently detecting the P-wave velocity on site,which avoids coring again.

Assessment of flexural properties of different grade dimension lumber by ultrasonic technique

The dimension lumber （45mm×90mm×3700mm） of plantation Chinese fir （Cunninghamia lanceolata （Lamb.） Hook.） was graded to four different classes as SS, No. 1, No.2 and No.3, according to national lumber grades authority （NLGA） for structure light framing and structure joists and planks. The properties of apparent density was determined at 15% moisture content, bending strength and stiffness were tested according to American Society for Testing and Materials （ASTM） D198-99, and dynamic modulus of elasticity （Eusw） was measured by ultrasonic technique, for predicting the flexural properties of different grade lumbers. The results showed that Eosw was larger than the static MOE. The relationship between Eusw and static MOE was significant at 0.01 level, and the determination coefficients （R2） of the four grade lumbers followed the sequence as R^2No.2 （0.616）〉 R^2ss （0.567）〉 R^2No1 （0.366）〉 R^2No.3 （0.137）. The R^2 of Fusw and MOR were lower than that of the Etru and MOR for each grade. The Eusw of all the grade lumbers, except No.3-grade, had significant correlation with the static MOE and MOR, thus the bending strengthof those grade lumbers can be estimated by the E The Etru valuesof four grade lumbers followed a sequence as No.2-grade （10.701 GPa） 〉 SS-grade （10.359 GPa） 〉 No.l-grade （9.840 GPa） 〉 No.3-grade （9.554 GPa）. For the same grade dimension lumber, its Eusw value was larger than static MOE. Mean values of MOR for four grade lumbers follow a sequence as No.2-grade （48.67 MPa） 〉 SS-grade （48.16 MPa） 〉 No.3-grade （46.55 MPa） 〉 No. 1-grade （43.39MPa）.

Effect of Li addition on mechanical properties and ageing precipitation behavior of extruded Al-3.0 Mg-0.5 Si alloy

The effect of Li(2.0 wt%)addition on mechanical properties and ageing precipitation behavior of Al-3.0 Mg 0.5 Si was investigated by tensile test,dynamic elasticity modulus test,scanning electron microscopy(SEM),transmission electron microscopy(TEM)and high-resolution transmission electron microscopy(HRTEM)images.The results show that the tensile strength of the Li-containing alloy can be significantly improved;however,the ductility is sharply decreased and the fracture mechanism changes from ductile fracture to intergranular fracture.The elasticity modulus of the Li-containing alloy increases by 11.6%compared with the base alloy.The microstructure observation shows that the Li addition can absolutely change the precipitation behavior of the base alloy,andδ′-Al_(3)Li phase becomes the main precipitates.Besides,β′′-Mg_(2)Si andδ′-Al_(3)Li dual phases precipitation can be visibly observed at 170℃ ageing for 100 h,although the quantity ofδ′-Al_(3)Li phase is more thanβ′′-Mg_(2)Si phase.The width of the precipitate-free zone(PFZ)of the Li-containing alloy is much wider at the over-ageing state than the base alloy,which has a negative impact on the ductile and results in the decrease of elongation.

BEHAVIOR OF AIR-ENTRAINED CONCRETE AFTER FREEZE-THAW CYCLES

The experimental study of air-entrained concrete specimens subjected to different cycles of freeze-thaw was completed. The dynamic modulus of elasticity, weight loss, the cubic compressive strength, compressive strength, tensile strength and cleavage strength of air-entrained concrete were measured after 0, 100, 200, 300, 400 cycles of freeze-thaw. The experimental results showed that the dynamic modulus of elasticity and strength decreased as the freeze-thaw was repeated. The influences of freeze-thaw cycles on the mechanical properties, the dynamic modulus of elasticity and weight loss were analyzed according to the experimental results. It can serve as a reference for the maintenance, design and the life prediction of dams, hydraulic structures, offshore structures, concrete roads and bridges in northern cold regions.

Brine-freeze-thaw Durability and Crack Density Model of Concrete in Salt Lake Region

The brine-freeze-thaw durability (defined as the durability under freeze-thaw cycles in Qinghai salt lake brine) of concrete (ordinary Portland cement concrete (OPC), high performance concrete (HPC-a), high performance concrete with steel fiber (HPC-b), and high performance concrete with high Young's modulus polyethylene fiber (HPC-c)) was systematically investigated by the relative dynamic elastic modulus, the relative mass, the appearance, the scanning electron microscopy, and the X-ray diffraction. In addition, the low-temperature physical and chemical corrosion mechanism and a crack density model after the modified relative dynamic elastic modulus being taken into consideration were proposed. The results show that the deterioration of OPC is the severest, followed by HPC-a, HPC-c and HPC-b. The admixture or the fiber is mixed into concrete, which can improve the brine-freeze-thaw durability of concrete. The critical mass growth of the failure of concrete is 3.7%. The cause of the deterioration of concrete under the brine-freeze-thaw cycles is physical and chemical corrosion, not freezing and thawing. The crack density model can effectively describe the deterioration evolution of concrete.

Correlations between ultrasonic pulse wave velocities and rock properties of quartz-mica schist

Physico-mechanical properties are critically important parameters for rocks. This study aims to examine some of the rock properties of quartz-mica schist（QMS） rocks in a cost-effective manner by establishing correlations between non-destructive and destructive tests. Using simple regression analysis, good correlations were obtained between the pulse wave velocities and the properties of QMS rocks. The results were further improved by using multiple regression analysis as compared to those obtained by the simple linear regression analysis. The results were also compared to the ones obtained by other empirical equations available. The general equations encompassing all types of rocks did not give reliable results of rock properties and showed large relative errors, ranging from 23% to 1146%. It is suggested that empirical correlations must be investigated separately for different types of rocks. The general empirical equations should not be used for the design and planning purposes before they are verified at least on one rock sample from the project site, as they may contain large unacceptable errors.