Showing papers in "Archive of Applied Mechanics in 2001"
TL;DR: In this paper, a simple theoretical model for friction in the presence of ultrasonic oscillations is derived theoretically and validated experimentally, and the model is capable of predicting the reduction of the macroscopic friction force as a function of the ultrasonic vibration frequency and amplitude and the macro-scopic sliding velocity.
Abstract: It was often observed that friction forces can be reduced significantly if ultrasonic oscillations are superposed to the macroscopic sliding velocity. This phenomenon can be used to improve machining processes by addition of ultrasonic vibration to tools or workpieces, and forms the basis for many processes of ultrasonic machining. On the other hand, ultrasonic vibrations can be used to generate motion. The thrusting force of ultrasonic motors is provided to the rotor through friction. In the present paper, a simple theoretical model for friction in the presence of ultrasonic oscillations is derived theoretically and validated experimentally. The model is capable of predicting the reduction of the macroscopic friction force as a function of the ultrasonic vibration frequency and amplitude and the macroscopic sliding velocity.
156 citations
TL;DR: In this article, a series of experiments (tension, torsion and combinations of both) was carried out on cylindrical bars made of a carbon-black filled rubber mixture.
Abstract: A characteristic of filled elastomers is their ability to undergo very large deformations without damaging their internal structure. The material behaviour is mainly elastic, however, elastomers show hysteresis effects leading to damping properties, which are quite important as regards their applications in various fields of mechanical engineering. A series of experiments (tension, torsion and combinations of both) was carried out on cylindrical bars made of a carbon-black filled rubber mixture. In addition to a pronounced nonlinear rate-dependence, relaxation and viscosity properties are observed as being influenced by the process histories. The behaviour of elastomeric materials is modelled on the basis of a free energy function and evolution equations for additional internal variables. Incorporating or disregarding the very small rate-independent hysteresis, the constitutive modelling may be classified under viscoplasticity or viscoelasticity. The constitutive equations are formulated for isothermal processes in a thermodynamically consistent manner. Particular attention is focused on nonlinear rate-dependence as well as on process-dependent relaxation properties. Numerical simulations on the basis of identified material parameters show that the proposed constitutive model is able to represent the main elastic and inelastic phenomena.
141 citations
TL;DR: In this paper, a simplified approximate analysis of the overall collapse of the World Trade Center towers is presented, and it is shown that if prolonged heating causes the majority of columns of a single floor to lose their load-carrying capacity, the whole tower is doomed.
Abstract: Simplified approximate analysis of the overall collapse of the World Trade Center towers is presented. It is shown that if prolonged heating causes the majority of columns of a single floor to lose their load-carrying capacity, the whole tower is doomed.
118 citations
TL;DR: In this paper, the authors used integral transforms to obtain the characteristic equation for the oscillator's vibrations and found that such an equation may have a root with a positive real part.
Abstract: Transversal vibrations of a uniformly moving two-mass oscillator on a Timoshenko beam of infinite length supported by a viscoelastic foundation are studied. By using integral transforms, the characteristic equation for the oscillator's vibrations is obtained. It is shown that the equation may have a root with a positive real part. The existence of such a root leads to the exponential increase of the amplitude of the oscillator vibrations, i.e. to instability. The reasons for the instability to occur are discussed. By employing the method of D-decomposition, the instability domains are found in the space of the system parameters.
61 citations
TL;DR: In this article, the authors used principal component analysis (PCA) for structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN).
Abstract: This paper deals with structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a data-reduction technique based on principal component analysis (PCA). The compressed FRFs, represented by their projection onto the most significant principal components, were used as the ANN input variables instead of the raw FRF data. The output is a prediction of the actual state of the specimen, i.e. healthy or damaged. A further advantage of this particular approach is its ability to deal with relatively high measurement noise, which is a common occurrence when dealing with industrial structures. The methodology was applied to detect three different states of a space antenna: reference, slight mass damage and slight stiffness damage. About 600 FRF measurements, each with 1024 spectral points, were included in the analysis. Six 2-hidden layer networks, each with an individually-optimised architecture for a specific FRF reduction level, were used for damage detection. The results showed that it was possible to distinguish between the three states of the antenna with good accuracy, subject to using an adequate number of principal components together with a suitable neural network configuration. It was also found that the quality of the raw FRF data remained a major consideration, though the method was able to filter out some of the measurement noise. The convergence and detection properties of the networks were improved significantly by removing those FRFs associated with measurement errors.
61 citations
TL;DR: In this paper, the Euler-Bernoulli and the Timoshenko beams with material and geometric discontinuities are developed in the space of generalized functions, where the generalized solutions are expressed in terms of a single expression on the entire domain.
Abstract: The bending solutions of the Euler–Bernoulli and the Timoshenko beams with material and geometric discontinuities are developed in the space of generalized functions. Unlike the classical solutions of discontinuous beams, which are expressed in terms of multiple expressions that are valid in different regions of the beam, the generalized solutions are expressed in terms of a single expression on the entire domain. It is shown that the boundary-value problems describing the bending of beams with jump discontinuities on discontinuous elastic foundations have more compact forms in the space of generalized functions than they do in the space of classical functions. Also, fewer continuity conditions need to be satisfied if the problem is formulated in the space of generalized functions. It is demonstrated that using the theory of distributions (i.e. generalized functions) makes finding analytical solutions for this class of problems more efficient compared to the traditional methods, and, in some cases, the theory of distributions can lead to interesting qualitative results. Examples are presented to show the efficiency of using the theory of generalized functions.
44 citations
TL;DR: In this article, a full set of ten effective electrostatic constants is derived, using the method of effective field, for the case of spheroidal piezoelectric inclusions with different properties and of diverse aspect ratios.
Abstract: Piezoelectric transversely isotropic matrix containing spheroidal piezoelectric inclusions with different properties and of, generally, diverse aspect ratios is considered. A full set of ten effective electrostatic constants is derived, using the method of effective field. The case, when the inclusions are circular cylinders (fibers) is analyzed in detail. The results are compared with those of several earlier works. They constitute the theoretical framework for the design of piezocomposites with prescribed overall properties.
39 citations
TL;DR: In this article, the influence of the soil stratification on the free field vibrations generated by the passage of a vehicle on an uneven road is investigated, where the road is modelled as a beam of infinite length, while the boundary element method based on the Green's functions for a horizontally layered linear elastic halfspace is used for the soil.
Abstract: This paper deals with the influence of the soil stratification on the free field vibrations generated by the passage of a vehicle on an uneven road. A two-stage solution procedure is applied for the numerical prediction of the free field traffic-induced vibrations. First, a 2D vehicle model is used for the calculation of the axle loads from the longitudinal road profile. Next, the free field response is calculated with the dynamic Betti-Rayleigh reciprocity theorem, using a transfer function between the road and the receiver. The dynamic road-soil interaction problem is solved with a substructure method. The road is modelled as a beam of infinite length, while the boundary element method, based on the Green's functions for a horizontally layered linear elastic halfspace is used for the soil. The influence of the soil stratification is demonstrated by a numerical example where the free field vibrations during the passage of a vehicle on a traffic plateau are calculated. Three different cases are considered for the layering of the soil: a homogeneous halfspace, a layer built in at its base and a layer on a halfspace. Special emphasis goes to the dynamic interaction between the road and the soil. It is demonstrated that the stratification of the soil has a considerable influence on both the peak particle velocity and the frequency content of the free field vibrations.
36 citations
TL;DR: In this paper, the reflection of a plane wave at an incrementally traction-free boundary of a half-space composed of nearly incompressible elastic material is considered, and two distinct cases exist, these being dependent on the underlying primary deformation.
Abstract: In this paper, the reflection of a plane wave at an incrementally traction-free boundary of a half-space composed of nearly incompressible elastic material is considered. It is shown that two distinct cases exist, these being dependent on the underlying primary deformation. In the first case, the appropriate slowness sections are each approximately elliptical, and the corresponding reflection phenomena closely mirrors that associated with the corresponding linear isotropic theory. Specifically, an angular range of direction of incident wave exists, for which both a quasi-longitudinal and quasi-shear wave are reflected, the former being replaced by a surface wave outside this angular range. In the second case, the outer slowness section is re-enrant and, in addition to the scenarios previously mentioned, it is possible for two quasi-shear waves to be reflected. Numerical illustrations of reflection coefficients are presented in respect of a modified Varga material and the case of increasing bulk modulus is investigated.
34 citations
TL;DR: In this paper, a model of thermo-mechanical behavior of viscoelastic elastomers under large strain is presented with a generalisation to large strain of the Poynting-Thomson rheological model.
Abstract: This paper presents a model of thermo-mechanical behaviour of viscoelastic elastomers under large strain. A formulation is proposed with a generalisation to large strain of the Poynting–Thomson rheological model. A finite element formulation is then exposed taking the incompressibility constraint for mechanical equilibrium into account. On the thermomechanical coupling aspect, an algorithm of time discretisation is proposed with two time scales corresponding respectively to mechanical and thermal behaviours. Finally, an application for the simulation of a double-shearing test is presented with an analysis of parameters' influence and a comparison between numerical and experimental results.
33 citations
TL;DR: In this article, an efficient two-dimensional approach to piezoelectric plates is presented in the framework of linear theory of PDEs, where boundary conditions at the plate faces are placed on the boundary conditions and the approximation of the through-the-thickness variations accounts for the shear effects and a refinement of the electric potential.
Abstract: The paper presents an efficient two-dimensional approach to piezoelectric plates in the framework of linear theory of piezoelectricity. The approximation of the through-the-thickness variations accounts for the shear effects and a refinement of the electric potential. Using a variational formalism, electromechanically coupled plate equations are obtained for the generalized stress resultants as well as for the generalized electric inductions. The latter are deduced from the conservative electric charge equation, which plays a crucial role in the present model. Emphasis is placed on the boundary conditions at the plate faces. The model is used to examine some problems for cylindrical bending of a single simply supported plate. Number of situations are examined for a piezoelectric plate subject to (i) an applied electric potential, (ii) a surface density of force, and (iii) a surface density of electric charge. The through-thickness distributions of electromechanical quantities (displacements, stresses, electric potential and displacement) are obtained, and compared with results provided by finite element simulations and by a simplified plate model without shear effects. A good agreement is observed between the results coming from the present plate model and finite element computations, which ascertains the effectiveness of the proposed approach to piezoelectric plates.
TL;DR: In this article, solid and shell-type finite elements available for plasticity and creep analysis are applied to the creep-damage prediction of a thinwalled pipe bend under uniform internal pressure.
Abstract: Solid- and shell-type finite elements available for plasticity and creep analysis are applied to the creep-damage prediction of a thinwalled pipe bend under uniform internal pressure. Conventional creep-damage material model with scalar damage parameter is used. Based on the comparative numerical study, performed using solid and shell elements, the applicability frame of the shell concept is discussed. Particularly, if a dependence on the stress state is included in the material model, the cross-section assumptions of the first-order shear deformation theory should be refined. The possibilities to modify the through-thickness approximations are demonstrated on the beam equations. The first-order shear-deformation beam theory is discussed in detail. It is shown that if the damage evolution significantly differs for tensile and compressive stresses, the classical parabolic transverse shear-stress distribution and the shear-correction coefficient have to be modified within time-step simulations.
TL;DR: In this paper, the mechanical behavior of different ZrO2/NiCr 80 20 compositions is analyzed and compared with experimental findings, and a newly introduced parameter (matricity) describes the mutual circumvention of the phases and is found to strongly control the stress level of the composite.
Abstract: In this contribution, the mechanical behaviour of different ZrO2/NiCr 80 20 compositions is analysed and compared with experimental findings. The microwave-sintered material is found to possess a slightly dominant ceramic matrix for intermediate volume fractions. Its thermal expansion coefficient deviates from the rule of mixture. The modulus and the stress strain behaviour can be simulated by a numerical homogenization procedure, and the influence of residual stresses is found to be negligible. A newly introduced parameter (matricity) describes the mutual circumvention of the phases and is found to strongly control the stress level of the composite, globally as well as locally. Finally, a graded component and a metal/ceramic bi-material are compared for thermal as well as mechanical loading.
TL;DR: In this article, a viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed, which includes the influence of prestrain on the relaxation function.
Abstract: A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed. The model is derived through linearization of Simo's nonlinear viscoelastic constitutive model and reference configuration transformation. Most importantly, in this model, static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. Natural statically pre-deformed state is served as reference configuration. The proposed constitutive equation is extended to a generalized viscoelastic constitutive equation that includes widely used Morman's model as a special case using objective stress increment. The proposed constitutive model is tested for dynamic behavior of rubber specimens with different carbon black content. It is concluded from the test that the assumption that the effects of static deformation can be separated from time effects, which is the basis of Morman's model, is only applicable to unfilled rubber. The viscoelastic constitutive equation for filled rubber must include, therefore, the influence of the static deformation on the time effects. The suggested constitutive equation with static deformation correction factor shows good agreement with test values.
TL;DR: In this paper, the deformation law for small elasto-plastic strains is presented as a system of nonlinear differential and algebraic equations (DAE) consisting of the stress-strain relation, evolution equations for the internal variables and the yield condition.
Abstract: The presented method to identify material parameters for inelastic deformation laws is based on the numerical analysis of inhomogeneous stress and strain fields received from suitable experiments. Tensile and bending tests were carried out to obtain elastic and hardening parameters. The deformation law for small elasto-plastic strains is presented as a system of nonlinear differential and algebraic equations (DAE) consisting of the stress–strain relation, evolution equations for the internal variables and the yield condition. Different rules for the evolution equations of isotropic, kinematic and distorsional hardening are proposed. The DAE are discretized using an implicit Euler method, and the resulting system of nonlinear algebraic equations is solved using the Newton method. Deterministic optimization procedures are preferred to identify material parameters from a least-squares functional of numerical and measured comparative quantities. The gradient of the objective function was calculated using a semianalytical sensitivity analysis. Due to measurement errors, the optimal sets of material parameters are non unique. The approximate estimation of confidence regions and the calculation of correlation coefficients is presented. The results of several optimization processes for material parameters of elasto-plastic deformation laws show a good agreement between measured and calculated values, but they show also problems which may occur if systematic errors will not be recognized and deleted.
TL;DR: In this paper, the interaction between two semi-elliptical co-planar surface cracks is considered when Poisson's ratio ν = 0.3, and the problem is formulated as a system of singular integral equations, based on the idea of the body force method.
Abstract: In this study, the interaction between two semi-elliptical co-planar surface cracks is considered when Poisson's ratio ν = 0.3. The problem is formulated as a system of singular integral equations, based on the idea of the body force method. In the numerical calculation, the unknown density of body force density is approximated by the product of a fundamental density function and a polynomial. The results show that the present method yields smooth variations of stress intensity factors along the crack front very accurately, for various geometrical conditions. When the size of crack 1 is larger than the size of crack 2, the maximum stress intensity factor appears at a certain point, β1=177∘, of crack 1. Along the outside of crack 1, that is at β1=0∼90∘, the interaction can be negligible even if the two cracks are very close. The interaction can be negligible when the two cracks are spaced in such a manner that their two closest points are separated by a distance exceeding the small crack's major diameter. The variations of stress intensity factor of a semi-elliptical crack are tabulated and charted.
TL;DR: In this article, the authors considered the cracks as permeable thin slits, and assumed that both the normal component of electric displacement and the tangential component of the electric field are continuous across these slits.
Abstract: The anti-plane problem of N collinear interfacial cracks between dissimilar transversely isotropic piezoelectric media, which are subjected to piecewise uniform out-of-plane mechanical loading combined with in-plane electric loading at infinity, and also a line loading at an arbitrary point, is addressed by using the complex function method. In comparison with other relevant works, the present study has two features: one is that the analysis is based on the permeable crack model, i.e. the cracks are considered as permeable thin slits, and, thus, both the normal component of electric displacement and the tangential component of electric field are assumed to be continuous across these slits. The other feature is that explicit closed-form solutions are given not only in piezoelectric media, but also inside cracks when the media are subjected to the most general loading. It is shown that the singularities of electric displacement and electric field in the media are always dependent on that of stress for the general case of loading, and all the singularities of field variables are independent of the applied uniform electric loads at infinity. For the interfacial cracks the electric field is square-root singular at the crack tips and shows jumps across the interface, while the normal component of the electric field is linearly variable inside the crack, but the tangential component is square-root singular. However, for a homogeneous medium with collinear cracks, the electric field is always nonsingular in the medium while the electric displacement exhibits square-root singularity. Moreover, in this case, the electric field inside any crack is equal to a constant when uniform loads are applied at infinity.
TL;DR: In this paper, the authors considered a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material).
Abstract: We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient, as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated.
TL;DR: In this paper, the authors present a strategy for assessing the quality of finite elements in space and for applying an adaptive mesh-refinement for this special engineering problem, characterized by a spectral assessment, comparing a certain set of eigenvalues of the actual discretization with those of a very fine and rather exact numerical model.
Abstract: Extensive studies, [1], concerning the longitudinal behavior of long railway bridges due to braking forces have been done by measurements in situ, [2], and by statical, [3, 4], as well as dynamical simulations. Thereby, the only consistent numerical realization with respect to the measured data was the dynamical one. However, the consecutive discretizations in space and time with time-dependent system matrices are extremely time consuming due to the moving loads and varying stiffness of the ballast under, and in front of, the moving train. Therefore, every effort should be made to optimize the discretization in the space domain. This paper presents a strategy for assessing the quality of finite elements in space and for applying an adaptive mesh-refinement for this special engineering problem. The method is characterized by a spectral assessment, comparing a certain set of eigenvalues of the actual discretization with those of a very fine and rather exact numerical model. The error estimator introduced in this paper controls a whole set of global eigenvalues with corresponding natural vibration modes in order to assess certain types of shape functions. Thus, the procedure estimates local modifications on the one hand and p-properties on the other by means of global indication.
TL;DR: In this paper, the electrohydrodynamic Kelvin-Helmholtz instability of the interface between two uniform superposed viscoelastic (B´ model) dielectric fluids streaming through a porous medium is investigated.
Abstract: The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed viscoelastic (B´ model) dielectric fluids streaming through a porous medium is investigated. The considered system is influenced by applied electric fields acting normally to the interface between the two media, at which there are no surface charges present. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially unstable configuration, or streaming only for the potentially stable configuration, as long as perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists instability for a certain wavenumber range. The instability of this system can be enhanced (increased) by normal electric fields. In the presence of surface tension, it is found also that the normal electric fields have destabilizing effects, and that the surface tension is able to suppress the Kelvin–Helmholtz instability for small wavelength perturbations, and the medium porosity reduces the stability range given in terms of the velocities difference and the electric fields effect. Finally, it is shown that the presence of surface tension enhances the stabilizing effect played by the fluid velocities, and that the kinematic viscoelasticity has a stabilizing as well as a destabilizing effect on the considered system under certain conditions. Graphics have been plotted by giving numerical values to the parameters, to depict the stability characteristics.
TL;DR: In this paper, a new damage indicator suitable for a large variety of structural damage and deterioration processes has been proposed and applied to a reinforced concrete plate and a large cooling tower shell.
Abstract: In the present-day solid mechanics research damage is treated predominantly on material point level, in constitutive laws, wherein it is formulated for further treatment in boundary value problems of continuum damage mechanics. Damage of a particular structure, on the other hand, is primarily observed on a structural level. Damage effects on structural safety and residual lifetime are most likely recognized here. Accumulation of structural damage over a certain limit is usually considered as a primary source of structural failure. The scope of the present paper is damage on structural level. Thus, it investigates first in which process variables of a nonlinear structural response damage can be identified best. It further elucidates recognizable properties of damage phenomena on structural level, and then introduces a new damage indicator suitable for a large variety of structural damage and deterioration processes. The paper illuminates the benefits and limits of the proposed description. Finally, it demonstrates the applicability of this new damage indicator by means of two examples: a reinforced concrete plate and a large cooling tower shell.
TL;DR: In this article, a steady-state solution for a vehicle moving on a tangent track with constant velocity is presented for a train-track model with linearity and periodicity with respect to the track length direction.
Abstract: An algorithm is presented which can be used for the investigation of a large variety of train-track models. These models only have to fulfil the requirements of linearity and periodicity with respect to the track length direction. A steady-state solution is obtained for a vehicle moving on a tangent track with constant velocity. The algorithm itself can be split into three modules: one for the whole train-track system, one for the track, and one for a single rail support. These modules and their interfaces are described in detail. The article demonstrates the applicability of the algorithm by means of four examples. The first example shows the influence of the sleeper elasticity on the sleeper motion. The second one illustrates the effect of an advanced subsoil model on the wheel/rail contact force. Subsequently, as a further example, the compliance frequency-response functions of a ballasted track and a rigid track are compared. The last example deals with the sleeper passing excitation. Here, it is shown that even in the case of resonance, the wheel/rail contact-force fluctuations remain below ten percent of the static value.
TL;DR: In this paper, an integral transform technique is employed to reduce the problem under consideration to dual integral equations, the intensity factors of the stress and the electric displacement and the energy release rate as well as the crack sliding displacement and electric voltage across the crack surfaces are obtained in explicit form for the case of concentrated forces and free charges at the crack surface and at the boundary.
Abstract: The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary. The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems.
TL;DR: In this article, a theoretical analysis of the control of transient thermoelastic displacement is developed for a two-layered composite rectangular plate constructed of an isotropic elastic and a piezoelectric layer due to nonuniform heat supply.
Abstract: In this study, the theoretical analysis of the control of transient thermoelastic displacement is developed for a two-layered composite rectangular plate constructed of an isotropic elastic and a piezoelectric layer due to nonuniform heat supply. The transient three-dimensional temperature in a two-layered composite rectangular plate is analyzed by the methods of Laplace and finite cosine transformations. Exact solutions for isotropic elastic and piezoelectric plates of crystal class mm2 are used in the theoretical analysis. A three-dimensional transient piezothermoelastic solution is developed for a simple-supported combined plate. The analysis yields an appropriate electric potential which when applied to the piezoelectric plate, suppresses the induced thermoelastic displacement in the thickness direction at the midpoint on the free surface of the isotropic plate. As an example, numerical calculations are carried out for an isotropic rectangular plate made of steel, bonded to a piezoelectric plate of cadmium selenide. Some numerical results are shown for temperature change, displacement and stress in transient state, when the transient thermoelastic displacement are controlled.
TL;DR: In this article, the properties of a passive vibration absorber with dry friction significantly differ from those of the classical linear absorber and the exceptional phenomenon is the possibility of suppressing all excited modes, influenced to a small extent by a special shape of the friction characteristic, but mainly by an appropriately adjusted threshold of the static friction.
Abstract: The properties of a passive vibration absorber with dry friction significantly differ from those of the classical linear absorber. The exceptional phenomenon is the possibility of suppressing all excited modes. This effect is influenced to a small extent by a special shape of the friction characteristic, but mainly by an appropriately adjusted threshold of the static friction. The theoretical predictions are confirmed by experimental investigations.
TL;DR: In this article, a hypersingular integral equation formulation of the problem is obtained by an appropriate use of Green's integral theorem followed by utilization of the boundary condition on the plate.
Abstract: The problem of water wave scattering by an inclined thin plate submerged in water of uniform finite depth is investigated here under the assumption of irrotational motion and linear theory. A hypersingular integral equation formulation of the problem is obtained by an appropriate use of Green's integral theorem followed by utilization of the boundary condition on the plate. This hypersingular integral equation involves the discontinuity in the potential function across the plate, which is approximated by a finite series involving Chebyshev polynomials. The coefficients of this finite series are obtained numerically by collocation method. The quantities of physical interest, namely the reflection and transmission coefficients, force and moment acting on the plate per unit width, are then obtained numerically for different values of various parameters, and are depicted graphically against the wavenumber. Effects of finite-depth water, angle of inclination of the plate with the vertical over the deep water and vertical plate results for these quantities are shown. It is observed that the deep-water results effectively hold good if the depth of the mid-point of the submerged plate below the free surface is of the order of one-tenth of the depth of the bottom.
TL;DR: In this paper, an interface crack problem is investigated under various assumptions on an interface between two elastic materials, where the interface is modeled by an additional third structure (thin elastic wedge of differing elastic properties) matching the bonded materials, or by introducing special boundary conditions on the crack line ahead.
Abstract: An interface crack problem is investigated under various assumptions on an interface between two elastic materials. The interface is modeled by an additional third structure (thin elastic wedge of differing elastic properties) matching the bonded materials, or by introducing special boundary conditions on the crack line ahead. The main emphasis of the paper is placed on a comparison of the asymptotic expansion of the elastic solutions near the crack tip obtained for the different models. In particular, the behaviour of the stress singularity exponent and the generalized SIF are discussed. Numerical examples are presented.
TL;DR: In this paper, the in-plane problem of an anisotropic plate or laminate with a circular hole and an elliptical hole reinforcement is considered, and a closed-form solution is derived for all resultant inplane stresses and deformations within and around the hole reinforcement.
Abstract: Within the scope of linear elasticity, the in-plane problem of an anisotropic plate or laminate with a circular hole and an elliptical hole reinforcement is considered. Arbitrary anisotropic elastic stiffnesses are allowed for the base plate and the reinforcement material, and for the reinforcement there is no restriction for its elliptical shape and size. The analysis of the problem is performed by the complex potential method with appropriately chosen series representations inside and outside the reinforcement region. The derived closed-form solution provides all resultant in-plane stresses and deformations within and around the hole reinforcement with little computational effort and at high accuracy. The determined solution allows a proper and effective assessment of hole reinforcements for many technical applications.
TL;DR: In this article, a new Eulerian rate-type isotropic-hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate.
Abstract: Recently, a new Eulerian rate-type isotropic-hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all isotropic hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The simple shear response of this model has been studied and shown to be reasonable for both the shear and normal stress components. The objective of this work is to further study the large deformation response of this model, in particular, the second-order effects, including the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. An analytical perturbation solution is derived, and numerical results are presented by means of the Runge–Kutta method. It is shown that the prediction of this model for the shear stress is in good accord with experimental data, but the predicted axial length change is negligibly small and much less than experimental data. This suggests that the strain-induced anisotropy may be the main cause of the Swift effect.
TL;DR: In this article, a slightly generalised fluid-structure interaction problem is examined, and a closed-form solution is constructed to be compared with the thin-layer approach of [4].
Abstract: Based on the previous analysis, [4], a slightly generalised fluid-structure interaction problem is examined. A closed-form solution is constructed to be compared with the `thin-layer' approach of [4]. It is shown that the `thin-layer' results are a rough approximation which are significantly improved by the results of the method presented here for a large gap length.