In this paper, we study a Targeted Energy Transfer (TET) problem between a p degreesof-freedom (dof) linear master structure and several coupled parallel slave Nonlinear Energy Sink (NES) systems. In detail, each lth dof l = 1, 2, . . . , p contains n l parallel NES; so the linear structure has (n 1 + n 2 + · · · + n l + · · · + n p ) NES. We are interested to study analytically the TET phenomenon during the first mode of the compound system. To this end, complexification, averaging, and multiple scales methods are used.The system is studied under 1:1 resonance for the transient regime and under harmonic excitation. The influence of the system parameters is observed through dimensionless variables. An analytical criterion is defined to tune NES parameters which lead to an efficient TET for the transient and the forced regimes. It will be demonstrated that analytical results are in good agreement with numerical ones. This paper will be followed by a companion paper which mainly deals with the governing equations for compound nonlinear systems with trees of NES devices at each dof; then experimental results of a four storey structure with two parallel NES at the top floor which are tuned by the mentioned technique in the current paper will be demonstrated and commented upon.

International audienceIn this paper governing equations of general multi degrees of freedom (dof) systems with trees of parallel Nonlinear Energy Sink (NES) devices at each dof are derived. Then these equations are summarized for a 4 dof structure with two parallel NES at the 4th dof in order to control the first mode of the system. A prototype four storey structure with two parallel NES at the top floor is studied experimentally. The NES of the mentioned system is designed by endowing the suggested method in the Part I of this paper. A couple of experimental tests are carried out on the structure at the DGCB laboratory of the ENTPE, France. The aim is to control the first mode of the compound nonlinear system by demonstrating the efficiency of the parallel NES systems on the intended task

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The paper is composed of three main parts: the first part presents a two degrees of freedom coupled oscillators with rheology. One of the oscillators is intended to be the main structure and the second one is a nonlinear energy sink. The rheology of the system is represented via a set of internal variables that are governed by either differential inclusions or differential equations or direct algebraic relations between system variables. A step by step methodology is explained to trace system behaviors around a 1 : 1 resonance at different time scales. Invariant of the system at fast time scale is detected while possible periodic and strongly modulated regimes around its invariant are traced at slow time scales. The second part of the paper considers a set of several degrees of freedom main oscillators which are coupled to several nonlinear energy sinks. The overall system can house several rheologies. Explained methodology of the first part is expanded to this general case for tracing system responses at different time scales around 1 : 1 resonances. The third part of the paper presents two practical examples: The proposed methodology is used to detect invariants of systems and their equilibrium and singular points. This methodology provides some tools for designing equilibrium and singular points, i.e. periodic and strongly modulated regimes which lead to the design of nonlinear energy sinks for passively controlling and/or energy harvesting of the main oscillators.

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<p>The article describes recent cases of tendon ruptures by corrosion and investigations carried out on some bridges. Several causes related to HDPE ducts have been identified as damages during handling, degradation during threading and tensioning of strands, defective connection of the duct to the anchor body, damage during construction or operation, low quality of HDPE material, etc.</p><p>A warning note on existing structures with external prestressing has been updated by Cerema in November 2018. It describes the diagnosis methodology based on detailed inspection, destructive and non-destructive techniques. New non-destructive investigation techniques such as guided- wave ultrasonic technique and magnetic leakage field test using permanent magnets and induction coils are presented. Innovative methods of local repair of the ducts are presented. Different protective devices are analyzed with regards of safety of workers in the case of a sudden failure of tendon.</p>

International audienceIn this paper the targeted energy transfer (TET) phenomenon between a linear multi- DOF master structure and several slave parallel nonlinear energy sink (NES) devices during a 1:1 resonance capture is investigated. An analytical method is proposed for tuning optimal NES parameters, which leads to efficient TETs. Then, the procedure is intentionally narrowed for a 4DOF master structure with two parallel NESs at the last DOF in order to grasp optimum NES parameters of a prototype structure that is built and tested at the Civil Engineering and Building Department Laboratory of the ENTPE. The aim is to control the first mode of the compound nonlinear prototype system by demonstrating the efficiency of designed parallel NESs by the suggested method