Nonlinear effects in thermal wave propagation near zero absolute temperature

The nonlinear theory of thermal wave propagation at low temperatures, i.e. in the realm of hyperbolic heat conduction, is discussed with regard to implications of experimental data and numerical calculations. Simplifying assumptions of earlier approaches are replaced by a consequent nonlinear thermodynamics. The effects of nonlinearity on the solution behavior are investigated. In particular, Lax conditions on shock waves are analyzed and temperature ranges of admissibility for discontinuities are identified.     

Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.     

Shock-induced thermal wave propagation and response analysis of a viscoelastic thin plate under transient heating loads

This paper is devoted to the thermal shock analysis for viscoelastic materials under transient heating loads. The governing coupled equations with time-delay parameter and nonlocal scale parameter are derived based on the generalized thermo-viscoelasticity theory. The problem of a thin plate composed of viscoelastic material, subjected to a sudden temperature rise at the boundary plane, is solved by employing Laplace transformation techniques. The transient responses, i.e. temperature, displacement, stresses, heat flux as well as strain, are obtained and discussed. The effects of time-delay and nonlocal scale parameter on the transient responses are analyzed and discussed. It can be observed that: the propagation of thermal wave is dynamically smoothed and changed with the variation of time-delay; while the displacement, strain, and stress can be rapidly reduced by nonlocal scale parameter, which can be viewed as an important indicator for predicting the stiffness softening behavior for viscoelastic materials.     

Nonlinear wave propagation in discrete and continuous systems

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.     

Nonlinear wave propagation along periodic-loaded transmission line

A high frequency transmission line periodically loaded with varactor diodes is presented to study nonlinear wave propagation. The nonlinearity and dispersion characteristics are experimentally and theoretically analysed. Experimental results on shock wave formation and harmonic frequency generation are found to be in good agreement with theoretical predictions. The influence of dispersion on second-harmonic frequency generation is particularly discussed yielding large values of the efficiency.     

Elastic wave propagation and scattering in solids with uniaxially aligned cracks

In this article, elastic wave propagation and scattering in a solid medium permeated by uniaxially aligned penny-shaped microcracks are studied. The crack alignment refers to the case in which the unit normals of all cracks are randomly oriented within a plane of isotropy. The analysis is restricted to the limit of the noninteraction approximation among individual cracks. Explicit expressions for attenuations and wave speeds of the shear horizontal, quasilongitudinal, and quasishear vertical waves are obtained using stochastic wave theory in a generalized dyadic approach. The ensemble average elastic wave response is governed by the Dyson equation, which is solved in terms of the anisotropic elastic Green's dyadic. The analysis of expressions is limited to frequencies below the geometric optics limit. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence. In particular, the attenuations are simplified considerably within the low frequency Rayleigh regime. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters.     

Thermal wave methods in investigation of thermal properties of solids

A short review of thermal wave measuring methods is presented in the paper. Based on fundamental laws of heat transport, experimental methods for determination of thermal properties of solids are divided into two groups – steady flux techniques and variable flux ones. Special attention is paid to the wave methods belonging to the second group and methods used by the author in his experiments. The idea of ?ngstr?m's method for determination of the thermal diffusivity of metals is reminded. Then different modifications of this classical technique using in investigations of bulk materials and thin films are described. Examples of a few thermal wave measurements are also presented.     

Heat of the martensitic transformation in CuAlMn alloy subjected to thermal cycling under constrained deformation conditions

The calorimetric study of Cu-Al-Mn alloy under constrained deformation conditions shows a 9–15% decrease in the heat of the γ′₁ ? β₁ martensitic transformation as compared to the free state, and this decrease takes place against the background of an increase in the transformation temperature. This effect is explained by a load-induced change in the symmetry of the crystal lattice.     

Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads

This paper aims at proposing an analytical model for the vibration analysis of horizontal beams that are self-weighted and thermally stressed. Geometrical nonlinearities are taken into account on the basis of large displacement and small rotation. Natural frequencies are obtained from a linearization of equilibrium equations. Thermal force and thermal bending moment are both included in the analysis. Torsional and axial springs are considered at beam ends, allowing various boundary conditions. A dimensionless analysis is performed leading to only four parameters, respectively, related to the self-weight, thermal force, thermal bending moment and torsional spring stiffness. It is shown that the proposed model can be efficiently used for cable problems with small sag-to-span ratios (typically , as in Irvine's theory). For beam problems, the model is validated thanks to finite element solutions and a parametric study is conducted in order to highlight the combined effects of thermal loads and self-weight on natural frequencies. For cable problems, solutions are first compared with existing results in the literature obtained without thermal effects or bending stiffness. Good agreement is found. A parametric study combining the effects of sag-extensibility, thermal change and bending stiffness is finally given.     

Anharmonism of lattice vibrations and of acoustic wave propagation velocity in quasi-isotropic solids

Linear correlation is established in glasses between the Grüneisen parameter and the ratio of propagation velocities of the longitudinal and transverse acoustic waves. An interpretation is given within the Pineda-Kuz’menko model to the relation between the harmonic and anharmonic quantities.     

Nonlocal plate model for nonlinear bending of single-layer graphene sheets subjected to transverse loads in thermal environments

This paper investigates the nonlinear bending behavior of a single-layer rectangular graphene sheet subjected to a transverse uniform load in thermal environments. The single-layer graphene sheet (SLGS) is modeled as a nonlocal orthotropic plate which contains small scale effect. Geometric nonlinearity in the von Kármán sense is adopted. The thermal effects are included and the material properties are assumed to be size dependent and temperature dependent, and are obtained from molecular dynamics (MD) simulations. The small scale parameter e ₀ a is estimated by matching the deflections of graphene sheets observed from the MD simulation results with the numerical results obtained from the nonlocal plate model. The numerical results show that the temperature change as well as the aspect ratio has a significant effect on the nonlinear bending behavior of SLGSs. The results reveal that the small scale parameter reduces the static large deflections of SLGSs, and the small scale effect also plays an important role in the nonlinear bending of SLGSs.     

弱界面分层结构中的非线性兰姆波

对弱界面分层结构中兰姆波的非线性效应进行了研究。在二阶微扰近似条件下,将兰姆波传播过程中的非线性效应处理成兰姆波线性波动响应的一个二阶微扰。采用界面弹簧模型对分层结构的弱界面性质进行描述。根据模式展开分析方法,伴随基频兰姆波传播所发生的二次谐波可视为由一系列二倍频兰姆波模式叠加而成。弱界面性质的变化将从多个方面对二倍频兰姆波模式的展开系数产生影响,尤其是弱界面性质变化导致的兰姆波相速度的改变可显著地影响到二倍频兰姆波模式随传播距离的积累增长程度。分析结果表明,兰姆波的非线性效应可有效地表征分层结构的弱界面特性。     

Nonlinear wave processes of crack propagation in brittle and brittle-ductile fracture

The paper reports on theoretical and experimental studies which demonstrate that crack propagation in solids in brittle and brittle-ductile fracture is a nonlinear wave process. The effect of the structural phase state and stress-strain stiffness of material on the crack type (opening, sliding, or tearing mode) and on the character of wave fracture is described.     

Dynamic behaviour of reactor structures subjected to impulsive loads

A reactor is modeled as a thin cylinder with one end capped by a solid circular plate and the dynamic behaviour of this structure is investigated when it is subjected to an impulsive load uniformly distributed over the circular plate. To simplify calculations, the load is assumed to be a step function with respect to time. As the fundamental equation of the cylinder under an axisymmetrical load, Donnell's equation is used and it is solved by the Laplace transformation method. From the results of the theoretical analysis, it becomes evident that large hoop stresses are induced in the neighbourhood of the junction of the plate and the cylinder.     

Dynamic non-linear response of beams subjected to impact loads

A non-linear theory is presented for plane deformation of beams which allows for longitudinal stretching as well as for cross-sectional stretching and shearing. The exact strain measures for this theory are also deduced. The longitudinal and flexural motions are coupled in the theory. If the cross section is constrained from stretching, the resulting theory may be classified as a non-linear Timoshenko beam theory. The equations of the latter theory are used to study the motion of beams under impact loads.     

Response of cork compounds subjected to impulsive blast loads

The experimental characterisation of the dynamic (blast) behaviour of micro-agglomerated cork is presented. A 4-cable ballistic pendulum system was used to measure the transmitted impulse to a target subjected to a shock-wave originated from the detonation of an explosive. The displacement of the pendulum and the transmitted impulse were measured and the coefficient of restitution of the whole system when the cork compound is used was determined. A numerical study of the problem using the finite element method gave very good correlation with the experimental analysis leading to the development of a material constitutive model suited to the dynamic behaviour of these cork compounds in such solicitations.