Benchmark solution ===================== Calculation method used for the reference solution -------------------------------------------------------- .. _1291536073: .. _1291535993: .. _1291535740: .. _1183277437: .. _1183275405: .. _1183275350: .. _1183275244: .. _1183275091: The reference results were obtained both experimentally [:ref:`1 <1>`] and with the code HERCULE [:ref:`2 <2>`]. The finite element model used is identical to that used for modeling A performed with*Code_Aster*. +-----------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------+ | |Mesh: | + .. image:: images/1000000000000207000001594C43CE9088988969.png + :math:`1019` + | :width: 3.3945in | | + :height: 2.1602in + + | | :math:`\mathrm{N6}-\mathrm{N17}` | + + + | | | +-----------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------+ .. _11832774011: .. _11832773321: The geometric dimensions used in calculations with HERCULE are very slightly different from those shown in ยง1.1: * :math:`L=\mathrm{692.50}\mathrm{mm}`; :math:`l=\mathrm{438.50}\mathrm{mm}`; :math:`H=\mathrm{473.25}\mathrm{mm}` Benchmark results ---------------------- * Natural frequencies * Move to the points forming the corners of the table, * Support reactions to anchorages, * Internal forces at the "corners". +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |**Identification**|Reference [] **experimental** |Reference [] **Hercule** |**Effective mass** (% of total mass) | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |Fashion |Frequency (:math:`\mathrm{Hz}`)|Frequency (:math:`\mathrm{Hz}`)|:math:`X` |:math:`Y`|:math:`Z`| +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |1 |110.0 |110.857 |94.2 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |2 |117.0 |115.471 |0.0 |0.0 |94.4 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |3 |134.0 |135.936 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |4 |214.0 |213.541 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |5 |416.0 |417.332 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |6 | |434.813 |0.0 |24.1 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |7 | |464.097 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |8 |553.0 |557.262 |0.0 |0.0 |0.3 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |9 |821.0 |821.746 |0.0 |18.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |10 | |847.071 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |11 |927.0 |978.174 |1.6 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |12 | |991.842 |0.0 |2.2 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |13 | |1021.669 |1.8 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |14 | |1040.240 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |15 | |1056.948 |0.0 |0.0 |0.2 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |16 | |1088.861 |0.0 |18.8 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |17 | |1093.157 |1.2 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ |18 | |1107.870 |0.0 |0.0 |0.0 | +------------------+-------------------------------+-------------------------------+------------------------------------+---------+---------+ +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |**Identification** |**Values obtained with combination** | + +------------------------------------+-----------------------------------------------+ | |quadratic directions of excitations |Of NEWMARK of the directions of the excitations| +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |Displacement: | | | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{N17}` :math:`\mathrm{DX}(m)` |3.4246E-04 |3.4265E-04 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{DY}(m)` |4.3562E-06 |4.8392E-06 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{DZ}(m)` |3.0321E-04 |3.0324E-04 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{DRX}(\mathrm{rad})` |3.7031E-04 |3.7612E-04 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{DRY}(\mathrm{rad})` |4.7665E-05 |5.2602E-05 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{DRZ}(\mathrm{rad})` |5.1104E-04 |5.2310E-04 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |Reactions: | | | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{N25}` :math:`\mathrm{FX}(N)` |1.2536E+03 |1.2790E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FY}(N)` |1.2473E+03 |1.3868E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FZ}(N)` |1.2196E+03 |1.2441E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MX}(\mathrm{N.m})` |3.2474E+02 |3.2789E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MY}(\mathrm{N.m})` |4.1310E+00 |4.5579E+00 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MZ}(\mathrm{N.m})` |3.4846E+02 |3.5199E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |Efforts: | | | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`1019` :math:`\mathrm{N17}` :math:`\mathrm{FX}(N)`|1.1312E+03 |1.1486E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FY}(N)` |1.2431E+03 |1.3793E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FZ}(N)` |1.0982E+03 |1.1141E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MX}(\mathrm{N.m})` |2.2833E+02 |2.2982E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MY}(\mathrm{N.m})` |4.1301E+00 |4.5580E+00 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MZ}(\mathrm{N.m})` |2.2068E+02 |2.2537E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`1009` :math:`\mathrm{N17}` :math:`\mathrm{FX}(N)`|1.8813E+02 |2.0079E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FY}(N)` |1.0419E+03 |1.0650E+03 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FZ}(N)` |1.3175E+02 |1.4833E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MX}(\mathrm{N.m})` |2.2833E+02 |2.2975E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MY}(\mathrm{N.m})` |2.9165E+01 |3.2490E+01 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MZ}(\mathrm{N.m})` |1.6408E-01 |1.6400E-01 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`1008` :math:`\mathrm{N17}` :math:`\mathrm{FX}(N)`|2.9587E+02 |3.3579E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FY}(N)` |6.3879E+02 |6.7526E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{FZ}(N)` |2.6539E+02 |2.7947E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MX}(\mathrm{N.m})` |1.8400E-01 |1.8500E-01 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MY}(\mathrm{N.m})` |3.2361E+01 |3.5570E+01 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ |:math:`\mathrm{MZ}(\mathrm{N.m})` |2.2068E+02 |2.2535E+02 | +--------------------------------------------------------+------------------------------------+-----------------------------------------------+ notes * The movements of corners :math:`(\mathrm{N9},\mathrm{N12},\mathrm{N17},\mathrm{N20})` are the same, * The reactions to the :math:`(\mathrm{N25},\mathrm{N26},\mathrm{N27},\mathrm{N28})` supporters are the same, * Generalized efforts are expressed in the global benchmark. Bibliographical references --------------------------- 1. NEUBERT V.H. and EZELL W. H.: Dynamic behavior of a foundation like structure. ASME Colloquium on Mechanical Impedance Methods for Mechanical Vibrations, pp. 77-86, 1958. 2. HERCULE: finite element calculation code for building structures developed by SOCOTEC.