Mechanics of pressure cells

The accurate measurement of a stress field in a solid medium requires an understanding of the interaction between the pressure gage and the surrounding material. In this paper, the effects of shape and stiffness of the pressure gage are analyzed with a view to the prediction of pertinent static-calibration factors. The stress fields around isolated gages are evaluated as a means of estimating when closely spaced pressure cells might interact. The results of experiments performed with miniature semiconductor-type pressure transducers are presented. Good correlation between the experimental results and analytical predictions is obtained.     

Contact problems for a finitely deformed incompressible elastic halfspace

This paper examines the class of problems related to the interaction between a finitely deformed incompressible elastic halfspace and contacting elements that include smooth, flat rigid indenters with elliptical and circular shapes and a thick plate of infinite extent. The contact between the finitely deformed elastic halfspace and the contacting elements is assumed to be bilateral. The interaction between both the rigid circular indenter and the finitely deformed halfspace is induced by a Mindlin force that acts at the interior of the halfspace regions and by exterior loads. Similar considerations apply for the contact between the flexible plate of infinite extent and the finitely deformed elastic halfspace. The theory of small deformations superposed on large deformations proposed by Green et al. (Proc R Soc Ser A 211:128–155, 1952) is used as the basis for the formulation of the problem, and results of potential theory and integral transform techniques are used to develop the analytical results. In particular, explicit results are presented for the displacement of the rigid elliptical indenter and the maximum deflection of the flexible plate induced by the Mindlin forces, when the finitely deformed halfspace region has a strain energy function of the Mooney–Rivlin form.     

The effects of high pressure on foil strain gages on convex and concave surfaces

The present investigation was undertaken to determine whether a linear pressure-strain response could be obtained for gages mounted on convex and concave specimens subjected to hydrostatic pressures to 140 ksi. This is an extension of a previously reported work where flat surfaces only were considered. Linear pressure-strain curves were obtained for five different types of foil strain gage having gage lengths varying from 1/16 to 1/4 in. These were mounted on steel, aluminum and magnesium specimens having diameters ranging from 1/4 in. convex to 3/8 in. concave. The inverse slope of the pressure-strain curves was compared with the compressibility constant 1–2v)/E to determine a percent deviation. In this constant,v andE are Poisson's ratio and the modulus of elasticity respectively. Experimental results show the percent deviation to be a function of the compressibility constant of the material and the radius of curvature and that these two parameters are inter-related. The percent deviation was found to be essentially independent of gage length for the range of specimen configurations investigated except where the radius of curvature of the specimen induces problems in mounting the gages. Since a linear pressure-strain response was obtained, it is possible to correct the strain readings for gages mounted on specimens of varied hydrostatic compressibility and geometrical configuration.     

The influence of the soil stratification on free field traffic-induced vibrations

Summary  This paper deals with the influence of the soil stratification on the free field vibrations generated by the passage of a vehicle on an uneven road. A two-stage solution procedure is applied for the numerical prediction of the free field traffic-induced vibrations. First, a 2D vehicle model is used for the calculation of the axle loads from the longitudinal road profile. Next, the free field response is calculated with the dynamic Betti-Rayleigh reciprocity theorem, using a transfer function between the road and the receiver. The dynamic road-soil interaction problem is solved with a substructure method. The road is modelled as a beam of infinite length, while the boundary element method, based on the Green's functions for a horizontally layered linear elastic halfspace is used for the soil. The influence of the soil stratification is demonstrated by a numerical example where the free field vibrations during the passage of a vehicle on a traffic plateau are calculated. Three different cases are considered for the layering of the soil: a homogeneous halfspace, a layer built in at its base and a layer on a halfspace. Special emphasis goes to the dynamic interaction between the road and the soil. It is demonstrated that the stratification of the soil has a considerable influence on both the peak particle velocity and the frequency content of the free field vibrations. Received 28 November 2000; accepted 24 April 2001     

Response of foil strain gages to hydraulic pressure

A series of tests to determine the effect that hydraulic pressure has on the output of electrical-resistance foil strain gages is described. Tests were conducted on Micro-Measurements gages, type EA-13-125BT-120 for pressures up to 20.7 MPa and frequencies up to 150 Hz, both for purely dilatational strain as well as various combinations of dilatational and distortional strains. The results showed that gage performance due to the combined effects of hydrostatic pressure and distortion of the structure differed from the condition predicted when pressure and distortion were considered separately. Rate of pressurization (and, hence, strain rate) had no measurable effect within practical limits.     

Calibration of granular material parameters for DEM modelling and numerical verification by blade-granular material interaction

The discrete element method (DEM) is a promising approach to model blade-granular material interactions. The accuracy of DEM models depends on the model parameters. In this study, a calibration process was developed to determine the parameter values. The particle size was the same as the real material and the particle shape was modelled using two spherical particles rigidly clumped together to form a single grain. Laboratory shear tests and compressions tests were used to determine the material internal friction angle and stiffness, respectively. These tests were replicated numerically using DEM models with different sets of particle friction coefficients and particle stiffness values. The shear test results are found to be dependent on both the particle friction coefficient and the particle stiffness. The compression test results show that it is only dependent on the particle stiffness. The combination of shear test and compression test results can be used to determine a unique set of particle friction and particle stiffness values. The calibration process was validated experimentally and numerically by modelling a blade moving through granular material. Results show that the forces acting on the blade can be accurately modelled with DEM and the maximum error is found to be 26%. The relative particle-blade displacements were used to predict the position and shape of the shear lines in front of the blade. A good qualitative correlation was achieved between the experiments and the DEM simulations.     

Monitoring short fatigue cracks with miniature strain gages

An experimental technique to monitor the length and the opening level of a short fatigue crack is presented. It is based on the progressive decrease with crack length of the response of miniature strain gages installed on the surface near the crack plane. A first gage installed close to the crack plane can monitor cracks from 10 μm in depth to half a millimeter where the response saturates. Other gages at larger distances from the crack plane are less sensitive but can monitor longer cracks. The response is measured so that it is independent of strain-gage calibration, Young's modulus and Poisson's ratio. The paper first presents the basic principles and possibilities of the technique as well as a finite-element analysis performed on automatic welded joints with straight-fronted cracks for which the technique has been developed. The results give a correlation between gage response, crack length and gage location and the conditions of replacement of a gage reaching saturation. The practical exploitation of the technique has required further work to derive a continuous calibration of the gage response that includes corrections to account for the gage finite dimensions and the crack-plane inclination. This calibration is shown to give crack lengths that compare well with fractographic marks and typical results that have been obtained on short crack growth at the weld toe are presented. In particular, the resolution of the technique is put into evidence with results on the initial growth of a 0.1 mm nonpropagating crack. The paper finally points out the distinctive features that appear in current works to adapt the technique to the growth of semi-elliptical cracks of low and high aspect ratio.     

Design considerations and calibration of stress transducers for soil

Strain gage pressure transducers are most frequently used for soil stress state determinations. Their construction, rugged and mechanically resistant, enables them to measure stresses within a wide range (up to 500 kPa) in harsh conditions. Output signals are easily readable and stable. The accuracy of the measurements, however, depends upon proper design and calibration before use in soil. This paper contains information on design considerations and results from calibration tests of transducers of two membrane diameters: 20 and 30 mm. The calibration test stand, as well as calibration procedures, are described in detail. For calibration tests, natural soils were used, as well as steel balls, to simulate the effect of the aggregated structures of arable soils and grain materials. The calibration method considered different soil types as well as soil water content. Soil and its water content were found to have an effect on output scale factor.     

Inertial effects of quartz force transducers embedded in a split Hopkinson pressure bar

An aluminum split Hopkinson pressure bar is instrumented with quartz force transducers and used to test low impedance materials. Two transducers are used, one at the interface between the specimen and the incident bar and the other at the interface between the specimen and the transmitter bar. It is shown that the stress measured by the incident bar gage often contains a substantial acceleration component, i.e., a significant portion of the signal recorded by the gage is due to its own inertia and not representative of the stress within the sample. Attempts are made to actively compensate for this with measurements of the acceleration of the gage. This is done in three ways: (i) by differentiation of the interface velocity, as determined by a standard strain gage analysis; (ii) by a more direct determination of acceleration, using a measurement of the strain gradient within the bar; (iii) by adding a compensation crystal and mass to the gage to remove the inertial component from the output. It is shown that all three techniques successfully mitigate inertial effects.     

The effects of high pressure on foil strain gages

The purpose of this investigation was to determine whether a linear pressure-strain response was possible for gages subjected to hydrostatic pressures to 140 ksi. This was motivated by the desire to use this information to measure the elastic-plastic behavior of material at the inside surface of thick-walled cylinders subjected to high internal pressure. This paper shows the effects of fluid pressure to 140 ksi on four different types of foil strain gage. Linear pressure-strain curves were obtained for these gages mounted on flat surfaces of tungsten, steel and aluminum specimens. The linear strains of several materials due to pressure are compared with the compressibility constant (1–2ν)/E as calculated from experimentally determined values ofE and ν, whereE is defined as the modulus of elasticity and ν is Poisson's ratio. Experimental results show the percent deviation between the constants to be a function of the material, being greatest for tungsten and least for aluminum. The fact that a linear pressure-strain response was obtained makes it possible to correct the readings for strain gages mounted on flat surfaces of materials subjected to direct hydrostatic pressure. Temperature effects as a function of pressurization rate were investigated. Various gage failures encountered along with photomicrographs showing probable causes are presented.     

分析层状半空间对入射地震波响应的改进模型

采用层内位移线性近似的薄层元及基岩半空间刚度的Ｔａｙｌｏｒ级数展开技术，利用基岩地震动三分量反算入射波振幅，建立了层状半空间场地地震波响应分析的一种改进模型，分析了层状半空间对倾斜入射ＳＨ，ＳＶ和Ｐ波的动力响应．结果表明，本文模型不仅具有较高精度，而且非常便于数值处理和计算机编程     

The evaluation of a strain gage having long-time stability characteristics

A standardizing strain gage that meets the requirements for long-time stability of strain measurements is described in this paper. Statistical analyses of the strain calibration results taken over a period of 13 months showed no significant differences between successive calibrations at a 5-percent significance level. From the results of the strain calibrations of 134 gages, the resistance-deformation characteristicdR/dW had a mean of 120.31 ohms/in. with a coefficient of variation of 1.43 percent. Evaluation tests using 6×12 in. concrete cylinders compared the strains measured by the standardizing gage to those measured by the Berry gage. Statistical analyses of these results showed equivalent accuracy of strain measured by the standardizing strain gage at comparable precision.     

Mindlin??s Problem for a Halfspace Indented by a Flexible Plate

The paper deals with a contact problem for an isotropic elastic halfspace indented by a flexible circular plate and simultaneously subjected to a Mindlin-type axial force. The approach adopted is to solve the contact problem for the flexible circular plate and the elastic halfspace; this serves as the auxiliary solution to examine, via the Maxwell-Betti reciprocal theorem, the influence of the internal Mindlin force. The contact between the flexible plate and the elastic halfspace is solved using a variational approach. The net displacement of the flexible circular plate and the internal Mindlin force can be evaluated in analytical form. The result has applications to the in situ evaluation of the deformability characteristics of geologic media.     

Analysis of vibrating-wire stress gage in soft rock

An analysis for the in situ elastic response of a vibrating-wire stress gage in soft rock (E<10⁵ Mpa) has been accomplished with the use of the finite-element method and approximate analytical procedures. The vibrating-wire stress gage is not a true stressmeter in that it is somewhat dependent on rock-modulus changes. Conventional procedures for calibration include the assumption that this dependency is linear with respect to rock modulus. In this analysis, a nonlinear relationship is demonstrated and an approximate mathematical expression is derived for it. Good agreement is obtained between theoretical calibration factors and test results on laboratory-scale samples with the stressmeter.     

Large free vibrations of a beam carrying a moving mass

The focus of this work is to develop a technique to obtain numerical solution over a long range of time for non-linear multi-body dynamic systems undergoing large amplitude motion. The system considered is an idealization of an important class of problems characterized by non-linear interaction between continuously distributed mass and stiffness and lumped mass and stiffness. This characteristic results in some distinctive features in the system response and also poses significant challenges in obtaining a solution.

In this paper, equations of motion are developed for large amplitude motion of a beam carrying a moving spring–mass. The equations of motion are solved using a new approach that uses average acceleration method to reduce non-linear ordinary differential equations to non-linear algebraic equations. The resulting non-linear algebraic equations are solved using an iterative method developed in this paper. Dynamics of the system is investigated using a time-frequency analysis technique.     

Fracture of a burning solid propellant attenuated by a crack-type cavity

A plane steady problem of fracture mechanics for a burning deformable solid propellant attenuated by a crack-type cavity with a burning surface is considered. The crack-type cavity is assumed to have tip zones with bonds between the faces, and mixed boundary conditions are imposed on the propellant charge boundary. The problem of equilibrium of a propellant charge containing a crack-type cavity reduces to solving a system of nonlinear singular integrodifferential equations with a Cauchy-type kernel. Based on the solution obtained, the normal and tangential forces in the tip zones of the crack-type cavity are found. Local conditions determining stability (safety) of the solid propellant burning regime are found.     

Effects of ultrahigh vacuum on the response characteristics of strain gages

Strain gages are extensively used in spacesimulation research; yet, little if any information has been reported about the environmental effects on the gage installations themselves. Since ultrahigh vacuum affects the physical and chemical properties of materials, one may expect that the response characteristics of strain-gage installations will also be affected. A study was initiated to determine the behavior of a number of strain-gage installations subjected to ultrahigh-vacuum environments. This paper presents the results of the first phase of the program. The gages and adhesives were selected to provide optimum chance for failure in order to establish a time parameter for following tests and, more importantly, to verify the extent and nature of failure possible under the environmental test conditions. Data were obtained on a number of strain-gage-per-formance characteristics. The performances of the gage installations varied widely being dependent in part upon gage and adhesive composition, whether a gage was used as an active or inactive device, and the level of strain to which a gage was subjected. Detailed pre- and post-test examinations showed that there was little permanent damage to any of the installations.     

应变片技术在动态力学测量中的应用

本文详细讨论了应变片技术,特别是半导体应变片技术在动态力学测量中的若干技术问题,主要有应变片及起动态应变仪的频率响应问题,应变片灵敏系数的动态标定问题。文章指出,随着数据处理微机化的日益普及,半导体材料所存在的非线性特性及拉压不对称性将不再影响到半导体应变片技术的推广使用。相反地,灵敏系数极高这一优良特性将使该项技术获得日益广泛的应用。     

充液航天器液体晃动和液固耦合动力学的研究与应用

随着火箭运载能力、卫星工作寿命和深空探测器任务复杂度的不断提高, 液体推进剂占航天器总质量的比重也不断增加. 液体推进剂的晃动影响着航天器的运动稳定性和姿轨控系统的可靠性, 是航天器动力学中一个备受关注的问题. 充液航天器中晃动的液体是一个分布参数系统, 理论上是无穷维的, 而工程上希望建立的数学模型是简单、低维的, 因此对液体晃动等效力学模型的研究经久不衰. 另外, 液体推进剂对航天器的结构动特性有着重要的影响, 在建立充液航天器的结构动力学模型时需要考虑液体推进剂与贮箱等结构的耦合效应. 本文首先结合液体晃动动力学理论和航天工程实际, 从理论研究、数值研究和实验研究等三个方面综述了国内外在充液航天器液体晃动动力学领域的研究现状, 并以此为基础介绍了航天工程中液体晃动等效力学模型的应用进展情况; 然后, 以液体运载火箭为例概述了国内外在充液航天器液固耦合建模方面的成果,介绍了求解液固耦合问题的数值方法和应用软件; 最后, 根据航天器工程的发展需求, 对充液航天器液体晃动和液固耦合动力学的进一步研究方向提出了一些建议.      

高g值加速度传感器的标定

利用Hopkinson压杆装置,采用石英晶体片压力传感器对高g值加速度传感器进行了标定,并给出了加速度传感器灵敏度系数的标定公式。实验结果表明,本文中研制的利用石英晶体片压力传感器对高g值加速度传感器进行标定的实验装置可满足标定的精度要求,而且整个校准系统结构简单,易于操作。