On the theorem of Reichert

This paper reworks and amplifies Reichert's proof of his theorem (1969) which asserts that any impedance function of a one-port electrical network which can be realised with two reactive elements and an arbitrary number of resistors can be realised with two reactive elements and three resistors. © 2012 Elsevier B.V. All rights reserved.

Deformation and fracture of impulsively loaded sandwich panels

Light metal sandwich panel structures with cellular cores have attracted interest for multifunctional applications which exploit their high bend strength and impact energy absorption. This concept has been explored here using a model 6061-T6 aluminum alloy system fabricated by friction stir weld joining extruded sandwich panels with a triangular corrugated core. Micro-hardness and miniature tensile coupon testing revealed that friction stir welding reduced the strength and ductility in the welds and a narrow heat affected zone on either side of the weld by approximately 30%. Square, edge clamped sandwich panels and solid plates of equal mass per unit area were subjected to localized impulsive loading by the impact of explosively accelerated, water saturated, sand shells. The hydrodynamic load and impulse applied by the sand were gradually increased by reducing the stand-off distance between the test charge and panel surfaces. The sandwich panels suffered global bending and stretching, and localized core crushing. As the pressure applied by the sand increased, face sheet fracture by a combination of tensile stretching and shear-off occurred first at the two clamped edges of the panels that were parallel with the corrugation and weld direction. The plane of these fractures always lay within the heat affected zone of the longitudinal welds. For the most intensively loaded panels additional cracks occurred at the other clamped boundaries and in the center of the panel. To investigate the dynamic deformation and fracture processes, a particle-based method has been used to simulate the impulsive loading of the panels. This has been combined with a finite element analysis utilizing a modified Johnson-Cook constitutive relation and a Cockcroft-Latham fracture criterion that accounted for local variation in material properties. The fully coupled simulation approach enabled the relationships between the soil-explosive test charge design, panel geometry, spatially varying material properties and the panel's deformation and dynamic failure responses to be explored. This comprehensive study reveals the existence of a strong instability in the loading that results from changes in sand particle reflection during dynamic evolution of the panel's surface topology. Significant fluid-structure interaction effects are also discovered at the sample sides and corners due to changes of the sand reflection angle by the edge clamping system. © 2012 Elsevier Ltd. All rights reserved.

Mechanical response of carbon fiber composite sandwich panels with pyramidal truss cores

The combination of light carbon fiber reinforced polymer (CFRP) composite materials with structurally efficient sandwich panel designs offers novel opportunities for ultralight structures. Here, pyramidal truss sandwich cores with relative densities ρ̄ in the range 1-10% have been manufactured from carbon fiber reinforced polymer laminates by employing a snap-fitting method. The measured quasi-static shear strength varied between 0.8 and 7.5 MPa. Two failure modes were observed: (i) Euler buckling of the struts and (ii) delamination failure of the laminates. Micro-buckling failure of the struts was not observed in the experiments reported here while Euler buckling and delamination failures occurred for the low (ρ̄≤1%) and high (ρ̄>1%) relative density cores, respectively. Analytical models for the collapse of the composite cores by these failure modes are presented. Good agreement between the measurements and predictions based on the Euler buckling and delamination failure of the struts is observed while the micro-buckling analysis over-predicts the measurements. The CFRP pyramidal cores investigated here have a similar mechanical performance to CFRP honeycombs. Thus, for a range of multi-functional applications that require an "open-celled" architecture (e.g. so that cooling fluid can pass through a sandwich core), the CFRP pyramidal cores offer an attractive alternative to honeycombs. © 2012 Elsevier Ltd. All rights reserved.

Compressive response of glass fiber composite sandwich structures

Sandwich panels with crushable foam cores have attracted significant interest for impulsive load mitigation. We describe a method for making a lightweight, energy absorbing, glass fiber composite sandwich structure and explore it is through thickness (out-of-plane) compressive response. The sandwich structure utilized corrugated composite cores constructed from delamination resistant 3D woven E-glass fiber textiles folded over triangular cross section prismatic closed cell, PVC foam inserts. The corrugated structure was stitched to 3D woven S2-glass fiber face sheets and infiltrated with a rubber toughened, impact resistant epoxy. The quasi-static compressive stress-strain response of the panels was experimentally investigated as a function of the strut width to length ratio and compared to micromechanical predictions. Slender struts failed by elastic (Euler) buckling which transitioned to plastic microbuckling as the strut aspect ratio increased. Good agreement was observed between experimental results and micromechanical predictions over the wide range of core densities investigated in the study.

Corrugated all-composite sandwich structures. Part 2: Failure mechanisms and experimental programme

A novel corrugated composite core, referred to as a hierarchical corrugation, has been developed and tested experimentally. Hierarchical corrugations exhibit a range of different failure modes depending on the geometrical properties and the material properties of the structures. In order to understand the different failure modes the analytical strength model, developed in part 1 of this paper, was used to make collapse mechanism maps for the different corrugation configurations. If designed correctly, the hierarchical structures can have more than 7 times higher weight specific strength compared to its monolithic counter part. The difference in strength arises mainly from the increase in buckling resistance of the sandwich core members compared to the monolithic version. The highest difference in strength is seen for core configurations with low overall density. As the density of the core increases, the monolithic core members get stockier and more resistant to buckling and thus the benefits of the hierarchical structure reduces. © 2008 Elsevier Ltd. All rights reserved.

Corrugated all-composite sandwich structures. Part 1: Modeling

An analytical model for the compressive and shear response of monolithic and hierarchical corrugated composite cores has been developed. The stiffness model considers the contribution in stiffness from the bending- and the shear deformations of the core members in addition to the stretching deformation. The strength model is based on the normal stress and shear stress distribution over each core member when subjected to a shear or compressive load condition. The strength model also accounts for initial imperfections. In part 1 of this series, the analytical model is described and the results are compared to finite element predictions. In part 2, the analytical model is compared to experimental results and the behaviour of the corrugated structures is investigated more thoroughly using failure mechanism maps. © 2008 Elsevier Ltd. All rights reserved.

Hybrid core carbon fiber composite sandwich panels: Fabrication and mechanical response

Carbon fiber reinforced polymer (CFRP) composite sandwich panels with hybrid foam filled CFRP pyramidal lattice cores have been assembled from a carbon fiber braided net, 3D woven face sheets and various polymeric foams, and infused with an epoxy resin using a vacuum assisted resin transfer process. Sandwich panels with a fixed CFRP truss mass have been fabricated using a variety of closed cell polymer and syntactic foams, resulting in core densities ranging from 44-482kgm-3. The through thickness and in-plane shear modulus and strength of the cores increased with increasing foam density. The use of low compressive strength foams within the core was found to result in a significant reduction in the compressive strength contributed by the CFRP trusses. X-ray tomography led to the discovery that the trusses develop an elliptical cross-section shape during pressure assisted resin transfer. The ellipticity of the truss cross-sections increased, and the lattice contribution to the core strength decreased as the foam density was reduced. Micromechanical modeling was used to investigate the relationships between the mechanical properties and volume fractions of the core materials and truss topology of the hybrid core. The specific strength and moduli of the hybrid cores lay between those of the CFRP lattices and foams used to fabricate them. However, their volumetric and gravimetric energy absorptions significantly exceeded those of the materials from which they were fabricated. They compare favorably with other lightweight energy absorbing materials and structures. © 2013.

The low velocity impact response of sandwich beams with a corrugated core or a Y-frame core

The low speed impact responses of simply-supported and clamped sandwich beams with corrugated and Y-frame cores have been measured in a drop-weight apparatus at 5 m s-1. The AISI 304 stainless steel sandwich beams comprised two identical face sheets and represented 1:20 scale versions of ship hull designs. No significant rate effects were observed at impact speeds representative of ship collisions: the drop-weight responses were comparable to the ones measured quasi-statically. Moreover, the corrugated and Y-frame core beams had similar performances. Three-dimensional finite element (FE) models simulated the experiments and were in good agreement with the measurements. The simulations demonstrated correctly that the sandwich beams collapsed by core indentation under both quasi-static loading and in the drop-weight experiments. These FE models were then used to investigate the sensitivity of impact response to (i) velocity, over a wider range of velocities than achievable with the drop-weight apparatus, and (ii) the presence of the back face sheet. The dynamic responses of sandwich beams with both front and back face sheets were found to be within 20% of the quasi-static responses for speeds less than approximately 5 m s-1. This suggests that quasi-static considerations are adequate to model the collision of a sandwich ship hull. By contrast, beams without a back face collapsed by Brazier buckling under quasi-static loading conditions, and by core indentation at a loading velocity of 5 m s-1. Thus, dynamic considerations are needed in ship hull designs that do not employ a back face. © 2014 Elsevier Ltd. All rights reserved.

Response of clamped sandwich beams subjected to high-velocity impact by sand slugs

The dynamic response of end-clamped sandwich and monolithic beams of equal areal mass subjected to loading via high-velocity slugs of dry and water-saturated sand is measured using a novel laboratory-based method. The sandwich beams comprise aluminium face sheets and an aluminium honeycomb core: the effect of sandwich core strength and beam thickness on the dynamic beam deflection is investigated by varying the orientation and height of the anisotropic aluminium honeycomb core material. High-speed imaging is used to measure the transient transverse deflection of the beams and to record the dynamic modes of deformation. The measurements show that sandwich beams with thick, strong cores are optimal and that these beams significantly outperform monolithic beams of equal mass. The water-saturated sand slugs cause significantly higher deflections compared to the dry sand slugs having the same mean slug velocity and we demonstrate that this enhanced deflection is due to the larger mass of the water-saturated slugs. Finally, we show that the impact of sand slugs is equivalent to the impact of a crushable foam projectile. The experiments using foam projectiles are significantly simpler to perform and thus represent a more convenient laboratory technique. © 2014 Elsevier Ltd. All rights reserved.

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

High temperature direct double side cooled inverter module for hybrid electric vehicle application

In this paper a novel approach to the design and fabrication of a high temperature inverter module for hybrid electrical vehicles is presented. Firstly, SiC power electronic devices are considered in place of the conventional Si devices. Use of SiC raises the maximum practical operating junction temperature to well over 200°C, giving much greater thermal headroom between the chips and the coolant. In the first fabrication, a SiC Schottky barrier diode (SBD) replaces the Si pin diode and is paired with a Si-IGBT. Secondly, double-sided cooling is employed, in which the semiconductor chips are sandwiched between two substrate tiles. The tiles provide electrical connections to the top and the bottom of the chips, thus replacing the conventional wire bonded interconnect. Each tile assembly supports two IGBTs and two SBDs in a half-bridge configuration. Both sides of the assembly are cooled directly using a high-performance liquid impingement system. Specific features of the design ensure that thermo-mechanical stresses are controlled so as to achieve long thermal cycling life. A prototype 10 kW inverter module is described incorporating three half-bridge sandwich assemblies, gate drives, dc-link capacitance and two heat-exchangers. This achieves a volumetric power density of 30W/cm3.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Compact double-side liquid-impingement-cooled integrated power electronic module

This paper presents a compact integrated power electronic module (IPEM) which seeks to overcome the volumetric power density limitations of conventional packaging technologies. A key innovation has been the development of a substrate sandwich structure which permits double side cooling of the embedded dies whilst controlling the mechanical stresses both within the module and at the heat exchanger interface. A 3-phase inverter module has been developed, integrating the sandwich structures with high efficiency impingement coolers, delink capacitance and gate drive units. Full details of the IPEM construction and electrical evaluation are given in the paper. © 2007 IEEE.

The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.