Archive of Applied Mechanics

Afagh, F. F.; Lin, B.

doi: 10.1007/s004190050200pmid: N/A

Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates.

Paquin, A.; Sabar, H.; Berveiller, M.

doi: 10.1007/s004190050201pmid: N/A

Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem requires a complete mechanical formulation, including the static equilibrium property concerning the known field σ, in addition to the classical field equations concerning the unknown fields ɛ˙ and σ˙. The formulation leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous elastoviscoplastic medium with elastic moduli C and viscoplastic moduli B.

Betelú, S.; Diez, J.; Gratton, R.

doi: 10.1007/s004190050202pmid: N/A

We study the time-evolution of periodical ripples of a viscous liquid at the plane free surface under the action of a distant pure straining flow. We neglect inertial forces (Stokes flow) and include surface tension effects. The solutions for a contracting surface and constant strain rate show that the ripples may develop near-cusps during a stage of the evolution, though later the free surface inevitably asymptotically tends to a smooth plane with vanishing ripples due to the action of capillarity. We obtain the condition for cusp formation in this intermediate stage in terms of the initial capillary number and aspect ratio. If the capillary number is kept constant, the surface tends to shrink through a succession of self-similar trochoidal shapes, whose aspect ratio is given by the capillary number.

Cheng, G.; Liu, Y. Z.

doi: 10.1007/s004190050203pmid: N/A

In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions, and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered, and a stability diagram in terms of system parameters is presented.

Grundmann, H.; Lieb, M.; Trommer, E.

doi: 10.1007/s004190050204pmid: N/A

The dynamic behaviour of a railway system is influenced by the interaction of its three subsystems: the vehicles, the rail construction itself and the subsoil. In this paper, the subsoil is considered as a linear-elastic layered half-space. Integral transformations are used for the analysis of this system: Fourier transformation for the time/frequency domain and for the space/wavenumber domains with respect to the horizontal coordinates. One arrives at an ordinary differential equation for the vertical direction, by which different layers or continuously changing elastic properties can be taken into account in an efficient manner. The efficiency of the transformation technique depends substantially on the effort necessary for the inverse transformation. A substantial reduction of data can be achieved in an error-controlled procedure if a wavelet transformation is applied as an additional transformation. The calculations are illustrated by solutions of several examples of moving time-dependent loads, particularly of a train model with four vehicles idealized by moving forces, time depending as if they were passing a rigid surface with a given roughness.

Zheng, Z.-C.; Ren, G.; Cheng, Y.-M.

doi: 10.1007/s004190050205pmid: N/A

The aeroelastic response analysis of a coupled rotor/fuselage system is approached by iterative solution of the blade aeroelastic response in the non-inertial reference frame fixed on the hub, and the periodic response of the fuselage in the inertial reference frame. A model of the coupled system hinged with the flap and lag hinges, the pitching bearing which may not coincide with the hinges, and the sweeping-blade configuration is established. The moderate-deflection beam theory and the two-dimensional quasi-steady aerodynamic model are employed to model the aeroelastic blade, all the kinetic and inertial factors are taken into account in a unified manner. A five-nodes, 15-DOFs pre-twisted nonuniform beam element is developed for the discretization of the blade, three rigid-body-motion DOFs are introduced for the motion of the hinges and the bearing. The Hamilton's principle is employed to evaluate the equation of motion of the blade. The derived nonlinear ordinary differential equations with time-dependent periodic coefficients are solved by a modified quasi-linearization method, which is developed for the higher DOF periodic system. The resulting periodic forces and moments exerted on the fuselage by all the blades are evaluated every time, when the converged nonlinear periodic response of the blade is obtained under the consideration of the equilibrium of the blades. The fuselage structure is simplified to be a beam structure, the governing equation is established in the inertial reference frame and a two-nodes beam element is used to discretize the flexible fuselage. The periodic response of the fuselage is solved by a simple shooting method. The iteration of the rotor/fuselage response is continued, until the aeroelastic responses of the blade and the fuselage converge simultaneously. Both the hovering and the forward flight states can be considered. The results of a computed numerical example by the developed program are presented to verify in practice the economy of the modeling as well as the reliability and efficiency of the corresponding solving methods.