.. _V5.01.104:

**v5.01.104** SDND104 - Calculation of the wear power of a friction mass under harmonic seismic excitation
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**Summary:**

We consider a mass in frictional contact with a rigid plane on which a vibratory movement of the harmonic type is imposed. Friction is modelled by Coulomb's law. The calculation of the mass response is of a non-linear transient type. The wear power resulting from the sliding phases between the mass and the rigid plane is calculated. Since the calculation of wear power is only developed in *Aster* for modal calculations, the analysis is conducted on the modal (trivial) basis of the system. In order to avoid numerical problems resulting from the nullity of the single rigid body mode of the mass, a very slightly stiff spring is introduced, binding the mass to a point integral to the vibrating rigid plane.

The reference solution is a quasianalytic calculation of the transient response, whose numerical estimates are programmed with Maple.

The unique *Aster* modeling selected tests the explicit constant step integration algorithms of Euler (order 1), Devogeleare (order 4) and the variable step algorithms ADAPT_ORDRE2 (order 2) and RUNGE_KUTTA (orders 54 and 32) developed in the operator dedicated to vibratory dynamics, for different amplitudes of the harmonic acceleration of seismic excitation of the rigid support plane. According to this amplitude, the mass response regime is of the adherent type at all times (stick), successively adherent and slippery (stick-slip), or always slippery with the reversal of the sliding direction (slip-slip).

It is noted that in the case of a sufficiently low amplitude of excitation (first regime, permanent adherence), the wear power is strictly zero.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    R_sultats_de_la_mod_lisation_A
    Synth_se_des_r_sultats