Targeted energy transfers in vibro-impact oscillators for seismic mitigation

In the field of seismic protection of structures, it is crucial to be able to diminish ‘as much as possible’ and dissipate ‘as fast as possible’ the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency – energy plots (FEPs) of branches of periodic orbits of underlying Conservative systems.     

Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading

The displacement-based finite element method dominates current practice for material nonlinear analysis of structures. However, there are several characteristics that may limit the effectiveness of this approach. In particular, for elastoplastic analysis, the displacement method relies upon a step-by-step incremental approach stemming from flow theory and also requires significant mesh refinement to resolve behavior in plastic zones. This leads to computational inefficiencies that, in turn, encourage the reconsideration of force-based approaches for elastoplastic problems.One of these force algorithms that has been recently developed is the large increment method. The main advantage of the flexibility-based large increment method (LIM) over the displacement method is that it separates the global equilibrium and compatibility equations from the local constitutive relations. Consequently, LIM can reach the solution in one large increment or in a few large steps, thus, avoiding the development of cumulative errors. This paper discusses the extension of the large increment methodology for the nonlinear analysis of plane frame structures controlled by an elastic, perfectly plastic material model. The discussion focuses on the power of LIM to handle these nonlinear problems, especially when plastic hinges form in the frame and ultimately as the structure approaches the collapse stage. Illustrative planar frame examples are presented and the results are compared with those obtained from a standard displacement method.     

A Trigger of Coupled Singularities

By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number eight in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined.     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Dynamic analysis of geometrically nonlinear robot manipulators

In this paper, a method for the dynamic analysis of geometrically nonlinear elastic robot manipulators is presented. Robot arm elasticity is introduced using a finite element method which allows for the gross arm rotations. A shape function which accounts for the combined effects of rotary inertia and shear deformation is employed to describe the arm deformation relative to a selected component reference. Geometric elastic nonlinearities are introduced into the formulation by retaining the quadratic terms in the strain-displacement relationships. This has lead to a new stiffness matrix that depends on the rotary inertia and shear deformation and which has to be iteratively updated during the dynamic simulation. Mechanical joints are introduced into the formulation using a set of nonlinear algebraic constraint equations. A set of independent coordinates is identified over each subinterval and is employed to define the system state equations. In order to exemplify the analysis, a two-armed robot manipulator is solved. In this example, the effect of introducing geometric elastic nonlinearities and inertia nonlinearities on the robot arm kinematics, deformations, joint reaction forces and end-effector trajectory are investigated.     

Dynamic theory for smectic A liquid crystals

A dynamic continuum theory is presented for smectic A liquid crystals in which the usual director n and unit layer normal a do not always necessarily coincide. Most previous dynamic continuum theories equate n with a; the theory developed in this article allows n and a to differ in non-equilibrium situations, work that has been motivated by the recent investigations by Auernhammer et al. (Rheol. Acta 39, 215–222, 2000; Phys. Rev. E 66, 061707, 2002) and Soddemann et al. (Eur. Phys. J. E 13, 141–151, 2004). The usual Oseen constraint () for smectics is not imposed upon the unit normal a. Permeation is also included. After a summary of the complete dynamic equations, an application is given via an example which shows that planar aligned layers of smectic A subjected to an arbitrary periodic disturbance are linearly stable.      

Stability of noisy nonlinear auto-parametric systems

The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ɛ and dissipation ɛ² the exponent grows in proportion with ɛ^2/3.     

Model equations for the Eiffel Tower profile: historical perspective and new results

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, “in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind”. An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).     

Precise control for vibration of rigid–flexible mechanical arm

In the present paper, based on the nonlinear dynamic equation of spacial flexible mechanical arm with dual-link bar, the method of linear quadratic control is used to eliminate the remain vibration of mechanical arm. In the process of computation, the traditional differential algorithm is replaced by the time integration method. Because of taking the more precise time-intervals in the given time-interval and avoiding a lot of computational difficulties, the method of this paper has the characteristics of high precision and unconditional stable. For a typical structure, the precise control law is obtained and the advantages of the algorithm in this paper are shown.