B modeling ============== Characteristics of modeling and meshes ---------------------------------------------------- Digital mesh: The digital mesh is done directly in ASTER format. It has 4 knots and 3 discreet stitches. .. image:: images/10000000000001A10000006D6E7C040BE011C30F.png :width: 3.2327in :height: 0.8583in .. _RefImage_10000000000001A10000006D6E7C040BE011C30F.png: Experimental mesh: The measurement mesh includes only 2 point elements and 2 nodes: .. image:: images/100000000000019600000069235D71002B0543DA.png :width: 3.1472in :height: 0.8272in .. _RefImage_100000000000019600000069235D71002B0543DA.png: Characteristics of the measurements --------------------------- The experimental measurements provided are: * At node :math:`\mathrm{N3}`: The data are axial displacements, multiplied by :math:`–1/\sqrt{2}`, and applied in the :math:`-x` direction. The local orientation specified in the command file is :math:`(45.0.0.)` The time sampling is constant: the initial time is :math:`0s`, the time step is :math:`{10}^{-3}s`, and the number of moments is 1001 (i.e. up to a final time of :math:`1s`). * At node :math:`\mathrm{N2}`: The data is the axial displacements, applied in the :math:`X` direction. The time sampling is variable: all the moments are indicated from :math:`0s` to :math:`1s`, in steps of :math:`{10}^{-3}s` (1001 moments in total). The values are derived from the analytical calculation carried out with Maple. Characteristics of the modal base ---------------------------------- The only two modes are stored in a mode_meca concept, created by the DEFI_BASE_MODALE command. The interface, of the Craig-Bampton type, is placed on the following degree of freedom in movement :math:`x` of the node :math:`\mathrm{N2}` (corresponding to the mass :math:`\mathrm{m1}`). The modal base therefore contains a dynamic mode (with :math:`\mathrm{N2}` locked) and a static mode. Tested values --------------- +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |**Identification** |**Reference**|**Aster_code**|**difference**| +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.1 s|1.745 10—4 |1.745 10—4 |0.01% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.3 s|6.797 10—4 |6.797 10—4 |0.01% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |DEPL_X |At node :math:`\mathrm{N2}`|at*t* = 0.5 s|—1.217 10—3 |—1.217 10—3 |0.01% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |(:math:`m`) |(mass 1) |at*t* = 0.7 s|5.214 10—4 |5.214 10—4 |— 0.01% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.9 s|9.031 10—4 |9.031 10—4 |0.00% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.1 s|9.154 10—6 |9.154 10—6 |0.00% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.3 s|6.414 10—4 |6.414 10—4 |0.00% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |DEPL_X |At node :math:`\mathrm{N3}`|at*t* = 0.5 s|—8.636 10—4 |—8.636 10—4 |0.00% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |(:math:`m`) |(mass 2) |at*t* = 0.7 s|—1.107 10—4 |—1.107 10—4 |0.03% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.9 s|1.633 10—3 |1.633 10—3 |0.02% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.1 s|4.586 10—3 |4.616 10—3 |0.65% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.3 s|—7.598 10—3 |—7.663 10—3 |0.85% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |VITE_X |At node :math:`\mathrm{N2}`|at*t* = 0.5 s|—1.581 10—4 |—8,000 10—5 |7.81 10—5m/s | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |(:math:`m/s`) |(mass 1) |at*t* = 0.7 s|9.382 10—3 |9.354 10—3 |— 0.30% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.9 s|—7.481 10—3 |—7.537 10—3 |0.75% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.1 s|4.328 10—4 |4.405 10—4 |1.79% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.3 s|3.671 10—3 |3.640 10—3 |— 0.84% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |VITE_X |At node :math:`\mathrm{N3}`|at*t* = 0.5 s|—1.539 10—2 |—1.536 10—2 |— 0.20% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |(:math:`m/s`) |(mass 2) |at*t* = 0.7 s|2.453 10—2 |2.457 10—2 |0.15% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.9 s|—1.899 10—2 |—1.912 10—2 |0.68% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.1 s|6.112 10—2 |6.100 10—2 |— 0.20% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.3 s|—1.306 10—1 |—1.300 10—1 |— 0.46% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |ACCE_X |At node :math:`\mathrm{N2}`|at*t* = 0.5 s|1.571 10—1 |1.600 10—1 |1.85% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |(:math:`m/{s}^{2}`)|(mass 1) |at*t* = 0.7 s|—5.657 10—2 |—5.800 10—2 |2.53% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.9 s|—1.124 10—1 |—1.130 10—1 |0.53% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.1 s|1.562 10—2 |1.618 10—2 |3.58% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.3 s|—6.031 10—2 |—6.223 10—2 |3.18% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |ACCE_X |At node :math:`\mathrm{N3}`|at*t* = 0.5 s|5.102 10—2 |5.374 10—2 |5.33% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ |(:math:`m/{s}^{2}`)|(mass 2) |at*t* = 0.7 s|7.428 10—2 |7.043 10—2 |— 5.19% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ | | |at*t* = 0.9 s|—2.364 10—1 |—2.263 10—1 |— 4.28% | +-------------------+---------------------------+-------------+-------------+--------------+--------------+ **Note:** *The speed at the node* :math:`\mathrm{N2}` *at instant* :math:`t=0.5s` *being relatively close to zero, the comparison is carried out for this case in absolute value.*