FEA for vibrated structures with non-linear concentrated spring having hysteresis

This paper describes vibration analysis using finite element method for structures connected with non-linear concentrated spring. The restoring force of the spring is assumed to be expressed as power series of displacement. The restoring force also has linear hysteresis damping. Thus, complex stiffness is introduced for the linear component of the restoring force. Finite element for the spring is expressed and is connected to viscoelastic structures modelled by linear solid finite elements. Further, the discretised equations in physical coordinate are transformed into the non-linear ordinary coupled equations using normal coordinate corresponding to linear natural modes. Note that modal damping is also transformed in this procedure. The transformed equations were integrated numerically in fairly small degree of freedom. This transformation yields computation efficiency. Effectiveness of this analysis was shown for a basic block-spring model. And then, this numerical method was applied for a sophisticated measurement system named as the Levitation Mass Method proposed by Fujii for evaluating viscoelastic parameters.     

Tilt stiffness and damping of externally pressurized porous gas journal bearings

The dynamic behaviour of an externally pressurized porous gas journal bearing is analysed by assuming one-dimensional flow through the porous bushing. A periodic disturbance (angular displacement) about the transverse axis is imposed on the bearing and the resulting dynamic pressure distribution is determined by small perturbations of the Reynolds equation. A finite difference method is used to determine the dynamic pressure. Design data for tilt stiffness and damping as a function of squeeze number, feeding parameter, supply pressure and porosity parameter are calculated numerically using a digital computer and are presented in tables and figures.     

Pressure between elastic bodies having a slender area of contact and arbitrary profiles

A numerical method is presented for calculating the pressure distribution and contact area shape between two elastic bodies of arbitrary profile which make contact over a slender contact area, i.e. where the relative curvature of the two profiles is much smaller in the longitudinal direction than in the transverse. The pressure distribution is assumed to be piecewise-linear in the longitudinal direction and semi-elliptical in the transverse. No a priori relationship is assumed between the shape of the contact area and the longitudinal variation in pressure; they are found simultaneously from dual integral equations for the compatibility of (a) the normal displacement and (b) the transverse curvature along the longitudinal axis of the contact zone.In cases where the profiles of the contacting bodies are smooth and continuous up to, and beyond, the ends of the contact area, the method gives a very reliable measure of the contact pressure distribution. Where discontinuities in profile are present, at roller ends for example, stress singularities are to be expected and like any numerical method, only approximate values of the stress concentration can be found. In the cases studied, the concentration of pressure associated with a “sharp” edge of contact is found to be very local.The method has been applied to both cylindrical and variously “crowned” rollers, also to a ball “over-riding” the edge of a closely conforming groove.     

Resonance measurement technique for viscoelastic properties of damping materials of the porous closed cellular PE foam type

Theoretical and experimental studies of longitudinal and lateral vibrations in a 2D cavity filled with foam viscoelastic material were performed; measurement methods of Lame parameters, as well as viscosity parameters with longitudinal and lateral resonance vibrations in cellular polypropylene loaded by a final mass were proposed. Measurements of the visco-elastic properties of samples from the porous closed cellular polyethylene of a PE foam and EVA ultrathene types were made.     

Pore-scale visualization of gas trapping in porous media by X-ray CT scanning

Entrapment of the non-wetting phase in porous media has been observed in a variety of fields such as petroleum engineering, geological storage of carbon dioxide, and remediation of ground water. We investigated gas trapping in porous media from a microscopic point of view. High-resolution, three-dimensional images of pore structure and trapped gas bubbles in Berea sandstones were obtained using a micro-focused X-ray CT scanner. We used vertical and horizontal Berea sandstone cores, 8 mm in diameter and 15 mm long. Based on the three-dimensional image analysis, the statistical distribution of the trapped gas volume was estimated. Trapped bubbles have a pore-network scale size and distribute over several pores. In the case of the vertical core, the porosity fluctuates along the flow direction due to the layered structure. The residual gas saturation also fluctuates with porosity along the flow direction. The higher gas saturation in porous layers at the end of gas injection results in a higher trapped gas saturation compared to dense layers. On the other hand, in dense layers the gas saturation at the end of gas injection is almost the same as residual gas saturation. Therefore, most of the gas injected into the dense layers would be trapped. In the case of the horizontal core, the gas saturation at the irreducible water condition is lower than that for the vertical core, because the injected gas selectively passes through the more permeable layers. However, the residual gas saturation is 29.2% for the horizontal core, which is comparable with that for the vertical core (30.9%). Finally, the effect of capillary number on stability of trapped gas bubbles has been estimated. Trapped gas bubbles are stable against the increased flow rate up to a capillary number of 1.0×10^?5.     

Design of externally pressurized gas bearings for stiffness and damping

A design method for flat, circular thrust bearings is presented in this paper. The design method is based upon a new dynamic model of the bearing and permits the selection of stiffness and damping for applications of bearings in vibrating environments. Application of the design method to the tuning of bearing dynamics is emphasized here, while the development of the dynamic model is discussed in other references. Design constraints are considered in the iterative design procedure and are illustrated in a bearing design example.     

A new quasi-steady method to measure gas permeability of weakly permeable porous media

A new quasi-steady method for the determination of the apparent gas permeability of porous materials is presented in this paper along with the corresponding interpretative physical model derived from the unsteady flow equations. This method is mainly dedicated to the measurement of very low permeability of thin porous media, although thicker but more permeable samples may also be analyzed. The method relies on quasi-steady flow resulting from a (quasi) constant pressure maintained at the inlet face of the sample. Gas flow-rate, as low as 3 × 10(-10) m(3)/s, is determined from the record of pressure increase in a reservoir connected to the outlet face of the sample. An estimate of the characteristic time, t(c), to reach quasi-steady flow after imposing a constant pressure at the inlet is derived. It is validated by direct numerical simulations of the complete unsteady flow, clearly defining the required experimental duration for the method to apply. Experimental results obtained on rather permeable and thick rock samples are reported showing an excellent agreement of the measured permeability with that determined independently on the same sample whereas the experimental value of t(c) is also in very good agreement with the predicted one. The method is further employed on a composite material sheet allowing the identification of an apparent gas permeability of about 10(-23) m(2).     

多体结构瑞利阻尼系数的确定

多体结构时域动响应分析广泛采用瑞利比例阻尼,其阻尼系数一般根据系统的质量和初始刚度确定,其确定过程有很多不确定因素。从基本概念出发,推导瑞利阻尼的基本表达形式,提出了用线性插值方法计算阻尼比,来获取多组数据,做图拟合推算出较为准确的阻尼系数。并结合算例说明该方法可行。     

Effective elastic properties of randomly distributed void models for porous materials

Many 2D analytical models are available for estimating the effective elastic properties of porous materials. Most of these models adopt circular voids of a uniform diameter in superlattice arrays, such as unit void or periodically positioned models. There are two principal issues in a realistic representation of porous materials: the random distribution of a statistically sufficiently large number of voids in the model, and the random distribution of the size and position of the voids. Numerical schemes such as the FEM or the BEM have also been presented to cater for regular patterned circular voids. However, due to the large number of elements needed to produce sufficient accuracy for the curved boundary of circular voids or modelling a statistically sufficient number of voids with a random distribution in both the void size and the position, no such model has yet been produced.Modelling based on an FEM approach using a simplified approximation for void geometry is proposed here for the calculation of the effective elastic properties of porous solids. A plane strain model of a square geometry is adopted for a 2D array of voids. This simplified square shape allows a large number of voids to be simulated with a random distribution for both void sizes and their locations. The problem of anisotropy, which arises from the square shape, is discussed. It is verified that along the two principal directions (parallel to the sides of the square voids), the elastic properties remain the same as those predicted by using a circular void geometry. This square-shaped approximation, with its reduced requirement for FE analysis, has the potential to be extended to 3-dimensional modelling for a realistic simulation of engineering materials.     

悬臂薄板结构阻尼特性几种测试方法的比较

在振动和噪声控制中,阻尼的测试有着重要的工程及学术意义.在明确阻尼辨识原理的基础上,以悬臂薄板结构为研究对象,搭建了锤击、振动台、压电陶瓷激励三种测试系统,分别采用半功率带宽法和时域自由振动衰减法进行了阻尼测试.并从重复性、测试精度、测试阻尼的频率范围和测试效率等方面,将各种阻尼测试结果进行了比较.最终认为,宜采用振动台扫频激励的方式和半功率带宽法对所研究的薄板进行阻尼测试和辨识.可为悬臂薄板结构后续的响应预估和阻尼优化设计提供重要的参考.     

Stability of elastic and viscoelastic systems under action of random stationary narrow-band loads

The stability is considered of the equilibrium state of elastic and viscoelastic systems, subjected to random parametric loads, with respect to perturbations of initial conditions. The stability is explored in the sense of Liapunov. The loads are assumed in the form of random narrow-band stationary processes. A numerical method for the analysis of the stability of such systems is offered, which is based on a method of statistical simulation of random processes, and on the determination of maximum Liapunov exponents. With the help of the method proposed the influence of the form of probability distributions, and of characteristics of the material, on the asymptotic stability of elastic and viscoelastic rods is investigated.     

Serial sectioning and digitization of porous media for two- and three-dimensional analysis and reconstruction

A procedure is proposed for serial sectioning of impregnated porous media, for photographing the sections under the microscope, and for digitizing the image using an IBM PC (XT) with a digitizing board. The result is a three-dimensional matrix containing the enhanced digitized image in a binary form of O's and I's which represent solid and pore spaces respectively. The procedure was tested on three different porous materials: (1) a pack of glass beads, 170–350 μm; (2) Berca sandstone; and (3) Elora clay loam soil. Each of these was impregnated, forty-six to eighty cross-sections were prepared by close parallel polishing of 10–50 μm per section, and then the sections were photographed and digitized. Examples of the real and digitized cross-sectioned samples are given as well as an example of reconstructed images in a plane perpendicular to the plane of sampling. It is proposed that the method of serial sectioning and automated digitization of porous media provides a powerful tool for further three-dimensional geometrical and topological investigation of pore space to be used in models of fluid transport phenomena.     

Modeling of porous structures for rapid prototyping of tissue engineering scaffolds

Rapid prototyping techniques are increasingly used to build porous scaffolds for the regeneration of biological tissues. This paper deals with one of the most critical tasks involved by this option, i.e., the preparation of geometric data for layered fabrication. Compared to other existing approaches, this work aims at both reducing the required effort in interactive modeling and allowing a standard use of commercial prototyping systems without resorting to special treatments. The proposed method adds a porous structure to the geometric model of tissue surface in polygon format. The structure is of the Cartesian type and consists of an interconnected network of rectilinear channels, whose dimensions can be varied according to desired porosity and pore size. The algorithmic procedures needed for the generation of the porous structure have been implemented in a demonstrative software tool. Sample models of scaffolds have been generated and used to build prototype parts by different fabrication processes and systems.     

A model for micro-slip between flat surfaces based on deformation of ellipsoidal elastic bodies

Micro-slip is a phenomenon that occurs between contacting surfaces when a frictional load, less than that necessary to produce macro-slip, is applied to the contacting surfaces. A model is presented for micro-slip between a flat smooth surface and a flat rough surface. The rough surface is covered with uniformly distributed ellipsoidal elastic bodies. The results from two test cases show that anisotropy of the contacting surfaces influences the tangential stiffness at zero displacement, the length of the micro-slip zone and the energy dissipated in the contact.     

Finite element model updating of vibrating structures under free-free boundary conditions for modal damping prediction

A method to predict resonance frequencies and modal loss factors of bare and damped samples, using constrained layer damping treatment, under free-free boundary conditions is proposed. In a first phase, measurements of the frequency response functions of these two specimens are performed. In a second phase, a finite element model of the undamped sample is developed. The novelty lies in the consistent modelling of the suspension with spring-damper elements defined with stiffness and damping coefficients with fixed values over the whole considered frequency range. By updating these, the agreement between experiments and simulation is further improved. In a third phase, a finite element model of the damped sample, with constrained layer damping material, is realized. A good agreement with experimental results is obtained thanks to an optimization algorithm used to determine the material parameters of the viscoelastic layer at various frequency. A comparison with experimental results, from a Dynamic Mechanical Analysis, confirms the consistency of the results from the optimization process.     

Computerized characterization of the geometry of real porous media: their discretization,analysis and interpretation

Real or reconstructed porous media can be discretized as a series of elementary cubes, which are filled either with a solid or a fluid phase. Various algorithms, based on pseudo-diffusion processes, are proposed to determine the connected and percolating components of the pore space. The graph of the pore space is obtained by two different methods; the most efficient is based upon homotopic thinning. Topological characteristics, such as the number of loops, are derived. Systematic applications of these algorithms are illustrated on computer reconstructions of various sandstones.     

Parametric investigation of particulate flow in interconnected porous media for central particle-heating receiver

Journal of Mechanical Science and Technology - An interconnected porous structure can be utilized to regulate the particle mass flow rate for central Solar particle-heating receivers (SPR) in...     

High sensitivity non-contact method for dynamic quantification of elastic waves and strains in transparent media

This paper presents time resolved quantitative evaluation of elastic stress waves in solid media by utilising an adaptation of the well-established laser Doppler vibrometry method. We show that the introduction of elastic stress waves in a transparent medium gives rise to detectable and quantifiable changes in the refractive index, which is proportional to stress. The method is tested for mechanical excitation at frequencies from 10 to 25 kHz in an acrylic bar. This refractometric quantification can measure internal strains as low as 1 × 10⁻¹¹. Additionally, finite element analysis is conducted to gauge the validity of the results. In the presented work an acrylic bar is used, this method however should be applicable to any transparent solid.     

A new algorithm for solving the multi-indentation problem of rigid bodies of arbitrary shapes on a viscoelastic half-space

In this paper the contact problem between rigid indenters of arbitrary shapes and a viscoelastic half-space is considered. Under the action of a normal force the penetration of the indenters changes and a few contact areas appeared. We wish to find the relations which link the pressure distribution, the resultant forces on the indenters and the penetration on the assumption that the surfaces are frictionless. For indenters of arbitrary shapes the problem may be solved numerically by using the matrix inversion method, extended to viscoelastic cases [1]. But when the problem involves a large number of points the matrix inversion method can become very time-consuming. Here the problem is solved using an alternative scheme, called the two-scale iterative method. In this method the local matrix inversion method is used at the micro-scale for each contact area to compute the pressure distribution taking into account interacting effect (the forces on the other contact areas which can be calculated at the macro-scale) between indenters. Two algorithms were proposed. The first algorithm takes into account the distribution of forces on the other contact areas and the second is the approximation of the first algorithm and takes into account the resultant forces on the other contact areas. The method was implemented for a simple configuration of seven spherical indenters, seven spherical-ended cylindrical indenters and seven flat-ended cylindrical indenters as well as for a more complex configuration of 12 randomly positioned indenters of arbitrary shapes: spherical-ended cylindrical, flat-ended cylindrical, conical and cylindrical indenters (finite cylindrical shape with its curved face). This last case is more difficult as the indenting geometry does not have an axisymmetric profile. For all these cases the two-scale iterative method permits to find the pressure distribution and the contact forces versus the penetration. It can be validated by comparing the numerical results to the numerical results obtained with the matrix inversion method.