Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments

Abstract

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

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

“…These kinds of equations have been studied in [2,5] investigating the behaviour of regular nonlinearities.…”

“…Then multiple scales are introduced in derivatives with fast time ߬ 0 = ߬ and ߬ ݆ = ߝ ݆ ߬ for j=1, 2,.. slow time scales. As exposed in [2,5,6,7] there is a nonlinear relation between ܰ 1 and ܰ 2 if we consider ߬ 0 → ∞, i.e. to analyse fixed points of the system.…”

“…If initial condition is such as N 1 < (N 2-, N 1+ ) the system will directly reach the stable branch on the left until static equilibrium. It has been exposed in [5,6,7,9] that the first behaviour when the dynamic of the system bifurcates is more efficient for vibration control. As a result the invariant manifold and its local maximum (ܰ 2− , ܰ 1+ ) can be used for design purpose.…”

A novel energy sink with piecewise linear stiffness

“…To overcome the shortcoming of coil springs, various nonlinear elements are proposed, the most common are the cubic stiffness nonlinear elements made up of two transverse springs [9][10][11][12][13] or strings [14][15][16], and the cubic restoring forces can be achieved by selfgeometric nonlinearity when the springs stretch in tension. Besides, some NESs are formed by permanent magnets or electromagnet, as the magnetic forces are strongly nonlinearity [17][18][19][20][21].…”

Dynamics of a forced 2 dof piece-wise linear system by consideration of the weight

“…It has been proved that a system can be passively controlled by endowing nonlinear innate of coupled cubic systems, namely nonlinear energy sink (NES) to the main one [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There has been some attempts to consider the nonsmooth NES systems instead of cubic ones.…”