An integrated model of rolling tyre vibrations on a smooth road

We describe new results on the vibrations of rolling tyres, aimed at noise prediction for tyres of given design on a smooth road surface. This new approach incorporates our existing models, of smooth road-tyre interaction and belt vibration but includes additional features that are required for real tyre patterns. To this end, the model allows variable tread block size and grooves along the belt circumference; the density and angle of these grooves may also vary laterally. The key innovation is to treat the tyre belt as a laterally stacked series of rings, each of which is equipped with a set of viscoelastic springs around its circumference. It is shown how to use this construction to mimic the details of actual tyre patterns and, in conjunction with existing models, predict belt vibrations. The construction is applied to develop a ring discretisation for a real tyre that shows strong lateral variations. It is shown that the vibration amplitude is concentrated on a set of parallel lines in frequency-wavenumber space and that the tread pattern dictates the occurrence and spacing of these lines. Linkage to a boundary element calculation then allows quantification of the influence of tread parameters on radiated noise. Keywords: Vibration, tread pattern, tyre noise. Copyright © (2011) by the Institute of Noise Control Engineering.

Vibrations of coupled cylindrical-conical shells

The free vibrational characteristics of coupled conical-cylindrical shells is presented. The equations of motion for the cylindrical shell are solved using a wave approach while the equations of motion for the conical shells are solved using a power series solution. The use of both Donnell-Mushtari and Flügge equations of motion are investigated and their limitations are discussed. Results are presented in terms of natural frequencies for different boundary conditions and the purely torsional mode solution is described. The results from the analytical model presented are compared with those obtained from a finite element model solved with Nastran and other data available in literature.

The vibrations of bubbles and balloons

Bubbles and balloons are two examples of structures that feature a pressure difference across the skin, a thin, tensioned membrane, and a doubly curved interface surface. While mathematical models have been formulated for bubble vibrations, no such model exists for balloon vibrations. This paper reviews a model of bubble vibrations, and compares its predicted natural frequencies and modeshapes to those of a rubber balloon. It is shown that the bubble model consistently underpredicts the balloon's natural frequencies, and it is concluded that the nonlinear elasticity present in the balloon skin accounts for this result.

Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials

The paper presents a multiscale procedure for the linear analysis of components made of lattice materials. The method allows the analysis of both pin-jointed and rigid-jointed microtruss materials with arbitrary topology of the unit cell. At the macroscopic level, the procedure enables to determine the lattice stiffness, while at the microscopic level the internal forces in the lattice elements are expressed in terms of the macroscopic strain applied to the lattice component. A numeric validation of the method is described. The procedure is completely automated and can be easily used within an optimization framework to find the optimal geometric parameters of a given lattice material. © 2011 Elsevier Ltd. All rights reserved.

Structural optimization of lattice materials

Lattice materials are characterized at the microscopic level by a regular pattern of voids confined by walls. Recent rapid prototyping techniques allow their manufacturing from a wide range of solid materials, ensuring high degrees of accuracy and limited costs. The microstructure of lattice material permits to obtain macroscopic properties and structural performance, such as very high stiffness to weight ratios, highly anisotropy, high specific energy dissipation capability and an extended elastic range, which cannot be attained by uniform materials. Among several applications, lattice materials are of special interest for the design of morphing structures, energy absorbing components and hard tissue scaffold for biomedical prostheses. Their macroscopic mechanical properties can be finely tuned by properly selecting the lattice topology and the material of the walls. Nevertheless, since the number of the design parameters involved is very high, and their correlation to the final macroscopic properties of the material is quite complex, reliable and robust multiscale mechanics analysis and design optimization tools are a necessary aid for their practical application. In this paper, the optimization of lattice materials parameters is illustrated with reference to the design of a bracket subjected to a point load. Given the geometric shape and the boundary conditions of the component, the parameters of four selected topologies have been optimized to concurrently maximize the component stiffness and minimize its mass. Copyright © 2011 by ASME.

Spin-cluster effect and lattice-deformation-induced Kondo effect, spin-glass freezing, and strong phonon scattering in La 0.7 Ca 0.3Mn 1-xCr xO 3

Besides the Kondo effect observed in dilute magnetic alloys, the Cr-doped perovskite manganate compounds La0.7 Ca0.3 Mn1-x Crx O3 also exhibit Kondo effect and spin-glass freezing in a certain composition range. An extensive investigation for the La0.7 Ca0.3 Mn1-x Crx O3 (x=0.01, 0.05, 0.10, 0.3, 0.6, and 1.0) system on the magnetization and ac susceptibility, the resistivity and magnetoresistance, as well as the thermal conductivity is done at low temperature. The spin-glass behavior has been confirmed for these compounds with x=0.05, 0.1, and 0.3. For temperatures above Tf (the spin-glass freezing temperature) a Curie-Weiss law is obeyed. The paramagnetic Curie temperature θ is dependent on Cr doping. Below Tf there exists a Kondo minimum in the resistivity. Colossal magnetoresistance has been observed in this system with Cr concentration up to x=0.6. We suppose that the substitution of Mn with Cr dilutes Mn ions and changes the long-range ferromagnetic order of La0.7 Ca0.3 MnO3. These behaviors demonstrate that short-range ferromagnetic correlation and fluctuation exist among Mn spins far above Tf. Furthermore, these interactions are a precursor of the cooperative freezing at Tf. The "double bumps" feature in the resistivity-temperature curve is observed in compounds with x=0.05 and 0.1. The phonon scattering is enhanced at low temperatures, where the second peak of double bumps comes out. The results indicate that the spin-cluster effect and lattice deformation induce Kondo effect, spin-glass freezing, and strong phonon scattering in mixed perovskite La0.7 Ca0.3 Mn1-x Crx O3. © 2005 American Institute of Physics.

The predicted compressive strength of a pyramidal lattice made from case hardened steel tubes

A sandwich panel with a core made from solid pyramidal struts is a promising candidate for multifunctional application such as combined structural and heat-exchange function. This study explores the performance enhancement by making use of hollow struts, and examines the elevation in the plastic buckling strength by either strain hardening or case hardening. Finite element simulations are performed to quantify these enhancements. Also, the sensitivity of competing collapse modes to tube geometry and to the depth of case hardening is determined. A comparison with other lattice materials reveals that the pyramidal lattice made from case hardened steel tubes outperforms lattices made from solid struts of aluminium or titanium and has a comparable strength to a core made from carbon fibre reinforced polymers. © 2013 Elsevier Ltd. All rights reserved.

Fracture of brittle lattice materials: A review

The mechanics of failure for elastic-brittle lattice materials is reviewed. Closed-form expressions are summarized for fracture toughness as a function of relative density for a wide range of periodic lattices. A variety of theoretical and numerical approaches has been developed in the literature and in the main the predictions coincide for any given topology. However, there are discrepancies and the underlying reasons for these are highlighted. The role of imperfections at the cell wall level can be accounted for by Weibull analysis. Nevertheless, defects can also arise on the meso-scale in the form of misplaced joints, wavy cell walls and randomly distributed missing cell walls. These degrade the macroscopic fracture toughness of the lattice. © 2010 Springer Science+Business Media B.V.

Non linear constitutive models for lattice materials

We use a computational homogenisation approach to derive a non linear constitutive model for lattice materials. A representative volume element (RVE) of the lattice is modelled by means of discrete structural elements, and macroscopic stress-strain relationships are numerically evaluated after applying appropriate periodic boundary conditions to the RVE. The influence of the choice of the RVE on the predictions of the model is discussed. The model has been used for the analysis of the hexagonal and the triangulated lattices subjected to large strains. The fidelity of the model has been demonstrated by analysing a plate with a central hole under prescribed in plane compressive and tensile loads, and then comparing the results from the discrete and the homogenised models. © 2013 Elsevier Ltd.