Vertical dynamic behaviour of a railway track on an elastic halfspace or on a layered halfspace is investigated by a frequency domain analysis. The results are compared with those for a simpler model, where ballast and subgrade are considered as a viscoelastic foundation. In the low- and medium-frequency range up to 250 Hz, great differences are observed between the results of the halfspace model and the results of the viscoelastic foundation model. This is because the damping due to wave propagation and coupling between sleepers cannot be modelled correctly by a viscoelastic foundation. Contradictions observed in the past between measured and calculated results can be explained with the new halfspace model. For frequencies higher than 250 Hz, the influence of the subgrade is negligible, so that here the simpler viscoelastic foundation model can be used.
We discuss the Hill principle's role and applications in modern micromechanics of industrial composite materials. Uniform boundary conditions, fundamental in micromechanics, are introduced as a class of Hill solutions. Mixed uniform conditions, basic for experimental testing, are analysed. Domains of application of the Hill principle are reviewed, like homogeneization of heterogeneous media, definition of effective properties and size effect in heterogeneous materials. Generalization of the Hill condition is realized for arbitrary materials, in particular for nonlinear inelastic composites with imperfect interfaces.
Nonlinear dynamics of one-mode approximation of an axially moving continuum such as a moving magnetic tape is studied. The system is modeled as a beam moving with varying speed, and the transverse vibration of the beam is considered. The cubic stiffness term, arising out of finite stretching of the neutral axis during vibration, is included in the analysis while deriving the equations of motion by Hamilton's principle. One-mode approximation of the governing equation is obtained by the Galerkin's method, as the objective in this work is to examine the low-dimensional chaotic response. The velocity of the beam is assumed to have sinusoidal fluctuations superposed on a mean value. This approximation leads to a parametrically excited Duffing's oscillator. It exhibits a symmetric pitchfork bifurcation as the axial velocity of the beam is varied beyond a critical value. In the supercritical regime, the system is described by a parametrically excited double-well potential oscillator. It is shown by numerical simulation that the oscillator has both period-doubling and intermittent routes to chaos. Melnikov's criterion is employed to find out the parameter regime in which chaos occurs. Further, it is shown that in the linear case, when the operating speed is supercritical, the oscillator considered is isomorphic to the case of an inverted pendulum with an oscillating support. It is also shown that supercritical motion can be stabilised by imposing a suitable velocity variation.
A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.
We call piezoelectromechanical (PEM) truss beam a truss modular beam coupled with a transmission electrical line when the coupling is obtained by piezoelectric actuators which act as bars in the module and as capacitances in the electrical line.The truss module length is assumed negligible with respect to the considered wave lengths. The transmission electrical line is assumed continuously distributed along the truss beam.Applying the method of virtual power as expounded in  we formulate a continuum model for PEM truss beams and we prove that there exists a critical value for the transmission electrical impedance in the neighborhood of which the electromechanical modal coupling is maximum and the possible electrical dissipation of mechanical energy is relevant.
The subject of the consideration is the contribution of a regular honeycomb core to the effective in-plane stiffnesses of a sandwich structure. Due to the coupling of the core displacements with those of the sandwich face sheets, the stiffness contribution of the core is not proportional to its total thickness, as could be expected. The corresponding thickness effect is investigated by means of an appropriate closed-form approach. In doing so, the total elastic core strain energy is calculated based on an adequately chosen displacement representation. Further on, the resultant effective stiffnesses are derived as a function of the total core thickness. A comparative computation of the effective stiffnesses by finite element analysis gives good agreement.
A new device to damp mechanical waves in modular truss beams has been proposed in . It is based on the electro-mechanical coupling of the truss beam with an electrical transmission line by a line distribution of PZT actuators. It has been proved in  that extensional and torsional waves can be damped using a standard second-order transmission line, and that such a line is not suitable to damp bending waves. In the present paper, we propose to couple the beam with a fourth-order transmission line, obtained from the standard one by adding a voltage-driven current generator, thus electrically paralleling the structure of the bending wave equation. As a detailed description of the system would require huge numerical programming, to test qualitatively the efficiency of the proposed electro-mechanical coupling we consider a coarse continuum model of PiezoElectro-Mechanical (PEM) beams, using an identification procedure based on the principle of virtual power . We define the critical value for line impedance maximizing the electro-mechanical energy exchange for every wave frequency, thus proving that the electric damping of bending waves by distributed PZT control is technically feasible.
For a two-dimensional piezoelectric plate, the thermoelectroelastic Green's functions for bimaterials subjected to a temperature discontinuity are presented by way of Stroh formalism. The study shows that the thermoelectroelastic Green's functions for bimaterials are composed of a particular solution and a corrective solution. All the solutions have their singularities, located at the point applied by the dislocation, as well as some image singularities, located at both the lower and the upper half-plane. Using the proposed thermoelectroelastic Green's functions, the problem of a crack of arbitrary orientation near a bimaterial interface between dissimilar thermopiezoelectric material is analysed, and a system of singular integral equations for the unknown temperature discontinuity, defined on the crack faces, is obtained. The stress and electric displacement (SED) intensity factors and strain energy density factor can be, then, evaluated by a numerical solution at the singular integral equations. As a consequence, the direction of crack growth can be estimated by way of strain energy density theory. Numerical results for the fracture angle are obtained to illustrate the application of the proposed formulation.
Comparative analysis has been carried out for three nonlocal fracture criteria (NLFC) in application to plane problems: the average stress fracture criterion (ASFC), the minimum stress fracture criterion (MSFC) and the fictitious crack fracture criterion (FCFC). Each of them may be considered as an equality for a particular form of the general nonlocal strength functional. The criteria contain two material parameters: a characteristic length and the tensile strength (ASFC and MSFC) or the critical stress intensity factor (FCFC).The criteria have been used for a strength description of a plate containing a smooth stress concentrator (circular hole) or a singular stress concentrator (central straight crack). It has been ascertained that ASFC and FCFC lead to identical results for the symmetrically loaded central straight crack. ASFC and MSFC may be successfully used for the description of strength of bodies with smooth as well as singular concentrators, while FCFC gives incorrect predictions for large smooth concentrators and for some other cases. A comparison of the predicted and experimental data has shown that ASFC is preferable in most cases; nevertheless, there exists a systematic deviation of experimental points from the criterion predictions.
The problem of a two-dimensional piezoelectric material with an elliptic cavity under a uniform heat flow is discussed, based on the modified Stroh formalism for the piezothermoelastic problem. The exact electric boundary conditions at the rim of the hole are introduced in the analysis. Expressions for the elastic and electric variables induced within and outside the cavity are derived in closed form. Hoop stress around the hole and electric fields in the hole are obtained. The limit situation when the hole is reduced to a slit crack is discussed, and the intensity factors for the problem are obtained.
A gradient-enhanced smeared crack model and bond-slip interface elements are utilized in finite element simulations of reinforced concrete. The crack model is rooted in an enhanced plasticity theory. It uses the Rankine failure surface dependent on an equivalent inelastic strain measure as well as on its Laplacian. As a result, finitely sized fracture process zones and realistic crack spacings are obtained. A reinforced concrete bar in uniaxial tension is analyzed to demonstrate the regularizing influence of the internal length parameter in the model and to evaluate the influence of the model parameters on the energy dissipation in multiple cracks. A comparison of numerical simulations with experimental results for a beam without shear reinforcement in four-point bending concludes the analysis.
The basic theory of nonlocal elasticity is stated with emphasis on the difference between the nonlocal theory and classical continuum mechanics. The concept of Nonlocal Interface Residual (NIR) is introduced in nonlocal theory. With the concept of NIR and the nonlocal constitutive equation, we calculate nonlocal stresses due to an edge dislocation on the interface of bi-materials. The nonlocal stress distribution along an interface is quite different from the classical one. Instead of the singularity in the dislocation core, nonlocal stress gives a finite value in the core. A maximum of the stress is also found near the dislocation core.
A fully saturated two-phase solid or structure subjected to variable, in particular cyclic, external actions is described as a nonhardening poroelastoplastic material with piecewise linearized yield loci. With reference to a multifield finite element model, sufficient and necessary conditions for shakedown are established by the static Melan's approach. Shakedown analysis by linear programming is briefly discussed.
In this contribution, attention is focused on the problem of a moving load on a Timoshenko beam-half plane system. Both the subcritical and the supercritical state will be analysed via a FE-simulation. The character of the response is explained by the analytical derivation and the elaboration of the eigen-value problem that follows from the characteristic wave equations together with the boundary conditions. It will be demonstrated that also transcritical states can occur. The total number of critical states and the values of the corresponding critical velocities are determined by the beam-half plane stiffness properties as well as the contact conditions.
In this paper a hierarchical approach using several mechanical models with different complexities and modeling depths to describe a single engineering system is presented. The mechanical models are derived from (but not limited to) multibody dynamics. The computer power available and improvements in theoretical understanding allow today not only to perform analyses but also to attack the problem of multimodel synthesis. Therefore, hierarchical modeling is used as a basis to analyze simultaneously models with different complexities and different excitations, and to optimize the performance with the most appropriate model for an investigated mechanical effect.Since only one single engineering system is investigated, its different models must be coupled by shared parameters, and the different criteria have to be combined with multicriteria optimization algorithms in order to obtain a single feasible design. An example taken from vehicle dynamics demonstrates the application of the approach.
The article presents a fast numerical algorithm for calculating the response of a halfspace under any surface loads. Under certain conditions there exists an analytical solution to the problem in the Fourier domain. To get the desired response, a numerical inverse Fourier transform of this analytic solution has to be made. By using a wavelet decomposition, the proposed algorithm can reduce the calculation time significantly, thus allowing the computation of complex problems. As an example, the response of the beam-halfspace coupled system under moving load is presented.
We study the stability of thin films of fluids subject to gravity along inclined planes, obeying a power-law constitutive relation of the Ostwald-de Waele type. A first analysis, in which the inertia terms are ignored, shows such flow to be stable against small, linear perturbations; a second analysis, in which the inertia terms are included, proves that there are stable and unstable regimes that are separated by a critical Ostwald-de Waele number O. Numerical computations for selected values of O demonstrate the decay and growth rate behavior of some finite amplitude disturbances.
The stress singularity around the bond edge of a cylindrical joint with two dissimilar materials is analysed using the Love stress function approach. The order of the stress singularity is proved to be the same as that under plane strain deformation. Emphasis is placed on the asymptotic description of the stress field because, in axisymmetric deformation problems, the singular-stress term alone cannot correctly describe the stress field near the singular point, even under mechanical loading at a very small range. An asymptotic description consisting of one singular-stress term and one constant stress term is presented. The constant stress term depends on the r-direction displacement of the singular point, in which it differs from the plane deformation problem's solution.
Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This fact has been shown to be valid for certain mechanisms, composites with voids and frameworks and has recently been verified for microstructures optimally designed by the homogenization approach. For microstructures composed of beams, it has been postulated that nonconvex shapes (with reentrant corners) are responsible for this effect. In this paper, it is numerically shown that mainly the shape, but also the ratio of shear-to-bending rigidity of the beams do influence the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids, or for composites with irregular shapes of inclusions, even if the constituents are quite usual materials, provided that their porosity is strongly manifested. Elements of the numerical homogenization theory and first attempts towards an optimal design theory are presented in this paper and applied for a numerical investigation of such types of materials.