In this paper, dynamic behavior of multi-layered viscoelastic nanobeams resting on a viscoelastic medium with a moving nanoparticle is studied. Eringens nonlocal theory is used to model the small scale effects. Layers are coupled by Kelvin-Voigt viscoelastic medium model. Hamilton's principle, eigen-function technique and the Laplace transform method are employed to solve the governing differential equations. Analytical solutions for transverse displacements of double-layered is presented for both viscoelastic nanobeams embedded in a viscoelastic medium and without it while numerical solution is achieved for higher layered nanobeams. The influences of the nonlocal parameter, stiffness and damping parameter of medium, internal damping parameter and number of layers are studied while the nanoparticle passes through. Presented results can be useful in analysing and designing nanocars, nanotruck moving on surfaces, racing nanocars etc.

The differential quadrature method (DQM) has been successfully used in a variety of fields. Similar to the conventional point discrete methods such as the collocation method and finite difference method, however, the DQM has some difficulty in dealing with singular functions like the Dirac-delta function. In this paper, two modifications are introduced to overcome the difficulty encountered in solving differential equations with Dirac-delta functions by using the DQM. The moving point load is work-equivalent to loads applied at all grid points and the governing equation is numerically integrated before it is discretized in terms of the differential quadrature. With these modifications, static behavior and forced vibration of beams under a stationary or a moving point load are successfully analyzed by directly using the DQM. It is demonstrated that the modified DQM can yield very accurate solutions. The compactness and computational efficiency of the DQM are retained in solving the partial differential equations with a time dependent Dirac-delta function.

This paper presents an axisymmetric layerwise finite element formulation for dynamic analysis of laminated structures with embedded viscoelastic material whose constitutive behavior is represented by the Prony-generalized Maxwell series. To account the time dependence of the constitutive relations of linear viscoelastic materials, the incremental formulation in the temporal domain is used. Layerwise finite element has been shown to provide an efficient and accurate tool for the simulation of laminated structure. Most of the previous work on numerical simulation of laminated structures has been limited to elastic material behavior. Thus, the current work focuses on layerwise finite element analysis of laminated structures with embedded viscoelastic material. A computer code based on the presented formulation has been developed to provide the numerical results. The present approach is verified by studying its convergence behavior and comparing the numerical results with those obtained using the ABAQUS software. Finally, and as an application of the presented formulation, the effects of load duration on the dynamic structural responses of multilayered pavements are studied.

This paper considers the effect of the damage caused by transverse stresses due to a low velocity impact loading on composite plates. The dynamic response of a plate is calculated using the modal superposition technique based on the classical plate theory of sandwich plates (stratified) taking into account transverse shear effects. An indentation law, based on the Hertz theory and verified experimentally, governs the behavior of the plate subsequent to impact. The numerical time integration scheme is used to calculate the contact force at any instant by combining the indentation and the dynamic response of the structure. The obtained results show a good correlation between the shock results and their prediction. This method is equally applied to the contact force as well as to the deformation of the plate. The simulation permits a parametric study of the structure dimensions and the material properties on the global behavior of the plate.

This paper extends the recently developed method of reverberation-ray matrix for planar structures to three-dimensional framed structures. The propagation of steady state axial, flexural and torsional waves, as well as the mode conversions through scattering of all three waves at connecting joints are evaluated in the frequency domain. The transient waves in all members are then determined by the Fourier synthesis. The transient responses of a two-storey framed building subject to a step time loading are calculated in detail. Numerical results are obtained for early time as well as moderately long time records. The results are shown to be accurate in arrival times of all three types of waves and in asymptotic values at times.

Une étude théorique du comportement statique et dynamique d'un palier lisse indéformable lubrifié par des huiles additivées en prenant en considération le défaut de mésalignement est présentée. Ces huiles dont le comportement rhéologique est non-newtonien sont modélisées comme des fluides à couple de contrainte. D'après la théorie des milieux continus de V. K. Stokes qui tient compte de la taille des particules, ces fluides se caractérisent par deux constantes physiques qui sont la viscosité dynamique (µ) et une deuxième caractéristique responsable des couples de contrainte dans le fluide (η). Les effets des couples de contrainte sur le comportement statique et dynamique du palier aligné ou mésaligné sont étudiés en définissant un paramètre du couple de contrainte adimensionnel. Les résultats obtenus montrent que la présence des additifs dans le lubrifiant a une influence non négligeable sur les performances statiques et dynamiques ainsi que la stabilité et la réponse dynamique du palier surtout pour les grandes valeurs du paramètre du couple de contrainte, c'est-à-dire dans le cas des polymères de longue chaîne moléculaire. Toutefois, leur influence sur le débit de fuite est négligeable sauf pour les grandes excentricités de fonctionnement.

Dans cet article, on étudie numériquement la propagation des ondes de déformations linéaires dans les ressorts hélicoïdaux dues à un chargement axial. La modélisation mathématique consiste en un système linéaire de deux équations aux dérivées partielles de type hyperbolique représentant les équations de quantité de mouvement du ressort. Les méthodes numériques des caractéristiques et des différences finies de Lax-Wendroff sont utilisées pour la résolution de ce système. Les résultats obtenus ont permis d'examiner la propagation des ondes de déformations et de vitesses axiales et angulaires et d'analyser leurs évolutions en différentes sections du ressort. Pour valider la fiabilité de cette modélisation, les résultats issus de ces deux méthodes ont été confrontés avec succès à la solution analytique du problème étudié. Pour mettre en évidence l'influence des caractéristiques mécaniques du ressort sur l'évolution de ces ondes, différents matériaux ont été considérés. On a constaté que deux ressorts, constitués de deux matériaux différents, peuvent avoir le même comportement dynamique comme ils peuvent avoir un comportement dynamique différent.

The dynamic response of a homogeneous, isotropic and elastic circular plate on an elastic foundation subjected to axisymmetric time dependent loads is investigated both analytically and numerically in thisv paper. First, the Extended Finite Hankel Transform (EFHT) is derived. After applying the technique of the EFHT to the governing equation of the vibrating circular plate, the governing partial differential equation (PDE) is transformed into the governing ordinary differential equation (ODE). Therefore, the analytical solution of the plate problem can be found completely. Once the dynamic response of the plate is solved, the internal forces of the plate, including shear force, bending moment and torsion, can be obtained subsequently. Under the particular case that elastic springs do not exist under the foundation, the dynamic response of the circular plate by the method of EFHT matches exactly with that by the method of modal analysis. By comparing the methods of EFHT, Boundary Element Method (BEM) and Finite Element Method (FEM), the results indicate that the proposed method of EFHT is accurate, systematic and convenient.