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Milestone 1: Implement frequency-dependent density and bulk modulus #9

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bangerth opened this issue May 14, 2021 · 2 comments
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@bangerth
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For example, for air:

%         frequency(Hz)                     density(kg/m3)    bulk modulus(Pa)              
                        10                  1.205728          142090.344491053
          60.2010050251256                  1.205728          142090.344491053
          110.402010050251                  1.205728          142090.344491053
          160.603015075377                  1.205728          142090.344491053
          210.804020100503                  1.205728          142090.344491053
          261.005025125628                  1.205728          142090.344491053
          311.206030150754                  1.205728          142090.344491053
          361.407035175879                  1.205728          142090.344491053
          411.608040201005                  1.205728          142090.344491053
          461.809045226131                  1.205728          142090.344491053
          512.010050251256                  1.205728          142090.344491053
          562.211055276382                  1.205728          142090.344491053
          612.412060301507                  1.205728          142090.344491053
          662.613065326633                  1.205728          142090.344491053
          712.814070351759                  1.205728          142090.344491053
          763.015075376884                  1.205728          142090.344491053
           813.21608040201                  1.205728          142090.344491053
          863.417085427136                  1.205728          142090.344491053
          913.618090452261                  1.205728          142090.344491053
          963.819095477387                  1.205728          142090.344491053
          1014.02010050251                  1.205728          142090.344491053
          1064.22110552764                  1.205728          142090.344491053
          1114.42211055276                  1.205728          142090.344491053
          1164.62311557789                  1.205728          142090.344491053
          1214.82412060302                  1.205728          142090.344491053
          1265.02512562814                  1.205728          142090.344491053
          1315.22613065327                  1.205728          142090.344491053
          1365.42713567839                  1.205728          142090.344491053
          1415.62814070352                  1.205728          142090.344491053
          1465.82914572864                  1.205728          142090.344491053
          1516.03015075377                  1.205728          142090.344491053
          1566.23115577889                  1.205728          142090.344491053
          1616.43216080402                  1.205728          142090.344491053
          1666.63316582915                  1.205728          142090.344491053
          1716.83417085427                  1.205728          142090.344491053
           1767.0351758794                  1.205728          142090.344491053
          1817.23618090452                  1.205728          142090.344491053
          1867.43718592965                  1.205728          142090.344491053
          1917.63819095477                  1.205728          142090.344491053
           1967.8391959799                  1.205728          142090.344491053
          2018.04020100503                  1.205728          142090.344491053
          2068.24120603015                  1.205728          142090.344491053
          2118.44221105528                  1.205728          142090.344491053
           2168.6432160804                  1.205728          142090.344491053
          2218.84422110553                  1.205728          142090.344491053
          2269.04522613065                  1.205728          142090.344491053
          2319.24623115578                  1.205728          142090.344491053
           2369.4472361809                  1.205728          142090.344491053
          2419.64824120603                  1.205728          142090.344491053
          2469.84924623116                  1.205728          142090.344491053
          2520.05025125628                  1.205728          142090.344491053
          2570.25125628141                  1.205728          142090.344491053
          2620.45226130653                  1.205728          142090.344491053
          2670.65326633166                  1.205728          142090.344491053
          2720.85427135678                  1.205728          142090.344491053
          2771.05527638191                  1.205728          142090.344491053
          2821.25628140704                  1.205728          142090.344491053
          2871.45728643216                  1.205728          142090.344491053
          2921.65829145729                  1.205728          142090.344491053
          2971.85929648241                  1.205728          142090.344491053
          3022.06030150754                  1.205728          142090.344491053
          3072.26130653266                  1.205728          142090.344491053
          3122.46231155779                  1.205728          142090.344491053
          3172.66331658291                  1.205728          142090.344491053
          3222.86432160804                  1.205728          142090.344491053
          3273.06532663317                  1.205728          142090.344491053
          3323.26633165829                  1.205728          142090.344491053
          3373.46733668342                  1.205728          142090.344491053
          3423.66834170854                  1.205728          142090.344491053
          3473.86934673367                  1.205728          142090.344491053
          3524.07035175879                  1.205728          142090.344491053
          3574.27135678392                  1.205728          142090.344491053
          3624.47236180905                  1.205728          142090.344491053
          3674.67336683417                  1.205728          142090.344491053
           3724.8743718593                  1.205728          142090.344491053
          3775.07537688442                  1.205728          142090.344491053
          3825.27638190955                  1.205728          142090.344491053
          3875.47738693467                  1.205728          142090.344491053
           3925.6783919598                  1.205728          142090.344491053
          3975.87939698492                  1.205728          142090.344491053
          4026.08040201005                  1.205728          142090.344491053
          4076.28140703518                  1.205728          142090.344491053
           4126.4824120603                  1.205728          142090.344491053
          4176.68341708543                  1.205728          142090.344491053
          4226.88442211055                  1.205728          142090.344491053
          4277.08542713568                  1.205728          142090.344491053
           4327.2864321608                  1.205728          142090.344491053
          4377.48743718593                  1.205728          142090.344491053
          4427.68844221106                  1.205728          142090.344491053
          4477.88944723618                  1.205728          142090.344491053
          4528.09045226131                  1.205728          142090.344491053
          4578.29145728643                  1.205728          142090.344491053
          4628.49246231156                  1.205728          142090.344491053
          4678.69346733668                  1.205728          142090.344491053
          4728.89447236181                  1.205728          142090.344491053
          4779.09547738693                  1.205728          142090.344491053
          4829.29648241206                  1.205728          142090.344491053
          4879.49748743719                  1.205728          142090.344491053
          4929.69849246231                  1.205728          142090.344491053
          4979.89949748744                  1.205728          142090.344491053
          5030.10050251256                  1.205728          142090.344491053
          5080.30150753769                  1.205728          142090.344491053
          5130.50251256281                  1.205728          142090.344491053
          5180.70351758794                  1.205728          142090.344491053
          5230.90452261307                  1.205728          142090.344491053
          5281.10552763819                  1.205728          142090.344491053
          5331.30653266332                  1.205728          142090.344491053
          5381.50753768844                  1.205728          142090.344491053
          5431.70854271357                  1.205728          142090.344491053
          5481.90954773869                  1.205728          142090.344491053
          5532.11055276382                  1.205728          142090.344491053
          5582.31155778894                  1.205728          142090.344491053
          5632.51256281407                  1.205728          142090.344491053
           5682.7135678392                  1.205728          142090.344491053
          5732.91457286432                  1.205728          142090.344491053
          5783.11557788945                  1.205728          142090.344491053
          5833.31658291457                  1.205728          142090.344491053
           5883.5175879397                  1.205728          142090.344491053
          5933.71859296482                  1.205728          142090.344491053
          5983.91959798995                  1.205728          142090.344491053
          6034.12060301508                  1.205728          142090.344491053
           6084.3216080402                  1.205728          142090.344491053
          6134.52261306533                  1.205728          142090.344491053
          6184.72361809045                  1.205728          142090.344491053
          6234.92462311558                  1.205728          142090.344491053
           6285.1256281407                  1.205728          142090.344491053
          6335.32663316583                  1.205728          142090.344491053
          6385.52763819095                  1.205728          142090.344491053
          6435.72864321608                  1.205728          142090.344491053
          6485.92964824121                  1.205728          142090.344491053
          6536.13065326633                  1.205728          142090.344491053
          6586.33165829146                  1.205728          142090.344491053
          6636.53266331658                  1.205728          142090.344491053
          6686.73366834171                  1.205728          142090.344491053
          6736.93467336683                  1.205728          142090.344491053
          6787.13567839196                  1.205728          142090.344491053
          6837.33668341709                  1.205728          142090.344491053
          6887.53768844221                  1.205728          142090.344491053
          6937.73869346734                  1.205728          142090.344491053
          6987.93969849246                  1.205728          142090.344491053
          7038.14070351759                  1.205728          142090.344491053
          7088.34170854271                  1.205728          142090.344491053
          7138.54271356784                  1.205728          142090.344491053
          7188.74371859296                  1.205728          142090.344491053
          7238.94472361809                  1.205728          142090.344491053
          7289.14572864322                  1.205728          142090.344491053
          7339.34673366834                  1.205728          142090.344491053
          7389.54773869347                  1.205728          142090.344491053
          7439.74874371859                  1.205728          142090.344491053
          7489.94974874372                  1.205728          142090.344491053
          7540.15075376884                  1.205728          142090.344491053
          7590.35175879397                  1.205728          142090.344491053
           7640.5527638191                  1.205728          142090.344491053
          7690.75376884422                  1.205728          142090.344491053
          7740.95477386935                  1.205728          142090.344491053
          7791.15577889447                  1.205728          142090.344491053
           7841.3567839196                  1.205728          142090.344491053
          7891.55778894472                  1.205728          142090.344491053
          7941.75879396985                  1.205728          142090.344491053
          7991.95979899498                  1.205728          142090.344491053
           8042.1608040201                  1.205728          142090.344491053
          8092.36180904523                  1.205728          142090.344491053
          8142.56281407035                  1.205728          142090.344491053
          8192.76381909548                  1.205728          142090.344491053
           8242.9648241206                  1.205728          142090.344491053
          8293.16582914573                  1.205728          142090.344491053
          8343.36683417085                  1.205728          142090.344491053
          8393.56783919598                  1.205728          142090.344491053
          8443.76884422111                  1.205728          142090.344491053
          8493.96984924623                  1.205728          142090.344491053
          8544.17085427136                  1.205728          142090.344491053
          8594.37185929648                  1.205728          142090.344491053
          8644.57286432161                  1.205728          142090.344491053
          8694.77386934673                  1.205728          142090.344491053
          8744.97487437186                  1.205728          142090.344491053
          8795.17587939699                  1.205728          142090.344491053
          8845.37688442211                  1.205728          142090.344491053
          8895.57788944724                  1.205728          142090.344491053
          8945.77889447236                  1.205728          142090.344491053
          8995.97989949749                  1.205728          142090.344491053
          9046.18090452261                  1.205728          142090.344491053
          9096.38190954774                  1.205728          142090.344491053
          9146.58291457286                  1.205728          142090.344491053
          9196.78391959799                  1.205728          142090.344491053
          9246.98492462312                  1.205728          142090.344491053
          9297.18592964824                  1.205728          142090.344491053
          9347.38693467337                  1.205728          142090.344491053
          9397.58793969849                  1.205728          142090.344491053
          9447.78894472362                  1.205728          142090.344491053
          9497.98994974874                  1.205728          142090.344491053
          9548.19095477387                  1.205728          142090.344491053
            9598.391959799                  1.205728          142090.344491053
          9648.59296482412                  1.205728          142090.344491053
          9698.79396984925                  1.205728          142090.344491053
          9748.99497487437                  1.205728          142090.344491053
           9799.1959798995                  1.205728          142090.344491053
          9849.39698492462                  1.205728          142090.344491053
          9899.59798994975                  1.205728          142090.344491053
          9949.79899497487                  1.205728          142090.344491053
                     10000                  1.205728          142090.344491053

and for a porous metarial:

%frequency(Hz)    density(kg/m3)          bulk modulus(Pa)              
10            1.7507    +i*-251.40     112615.491+i*119.669
60.201        1.7507    +i*-41.763     112631.842+i*720.021
110.402       1.7507    +i*-22.776     112671.498+i*1318.65
160.603       1.7506    +i*-15.66      112734.259+i*1914.15
210.804       1.7505    +i*-11.934     112819.809+i*2505.12
261.005       1.7504    +i*-9.6422     112927.724+i*3090.22
311.206       1.7502    +i*-8.0903     113057.471+i*3668.13
361.407       1.75      +i*-6.97       113208.422+i*4237.61
411.608       1.7498    +i*-6.1235     113379.853+i*4797.49
461.809       1.7496    +i*-5.4615     113570.962+i*5346.66
512.0101      1.7493    +i*-4.9296     113780.870+i*5884.10
562.2111      1.7491    +i*-4.493      114008.635+i*6408.88
612.4121      1.7487    +i*-4.1283     114253.261+i*6920.16
662.6131      1.7484    +i*-3.8192     114513.708+i*7417.19
712.8141      1.7481    +i*-3.5538     114788.905+i*7899.32
763.0151      1.7477    +i*-3.3236     115077.755+i*8366.00
813.2161      1.7473    +i*-3.1221     115379.149+i*8816.76
863.4171      1.7468    +i*-2.9441     115691.971+i*9251.25
913.6181      1.7464    +i*-2.786      116015.112+i*9669.18
963.8191      1.7459    +i*-2.6445     116347.473+i*10070.3
1014.0201     1.7454    +i*-2.5171     116687.976+i*10454.7
1064.2211     1.7449    +i*-2.4019     117035.568+i*10822.1
1114.4221     1.7443    +i*-2.2973     117389.226+i*11172.7
1164.6231     1.7437    +i*-2.2018     117747.966+i*11506.7
1214.8241     1.7432    +i*-2.1144     118110.842+i*11824.0
1265.0251     1.7425    +i*-2.034      118476.952+i*12125.1
1315.2261     1.7419    +i*-1.9598     118845.440+i*12410.1
1365.4271     1.7412    +i*-1.8913     119215.500+i*12679.4
1415.6281     1.7406    +i*-1.8277     119586.372+i*12933.3
1465.8291     1.7399    +i*-1.7685     119957.347+i*13172.3
1516.0302     1.7392    +i*-1.7134     120327.767+i*13396.7
1566.2312     1.7384    +i*-1.6619     120697.022+i*13607.0
1616.4322     1.7377    +i*-1.6137     121064.551+i*13803.7
1666.6332     1.7369    +i*-1.5685     121429.842+i*13987.3
1716.8342     1.7361    +i*-1.526      121792.427+i*14158.1
1767.0352     1.7353    +i*-1.4859     122151.885+i*14316.7
1817.2362     1.7345    +i*-1.4482     122507.835+i*14463.7
1867.4372     1.7336    +i*-1.4126     122859.939+i*14599.4
1917.6382     1.7328    +i*-1.3789     123207.898+i*14724.4
1967.8392     1.7319    +i*-1.3469     123551.447+i*14839.2
2018.0402     1.731     +i*-1.3166     123890.358+i*14944.2
2068.2412     1.7301    +i*-1.2879     124224.435+i*15040.0
2118.4422     1.7292    +i*-1.2605     124553.510+i*15126.9
2168.6432     1.7283    +i*-1.2345     124877.445+i*15205.4
2218.8442     1.7273    +i*-1.2097     125196.127+i*15275.9
2269.0452     1.7264    +i*-1.186      125509.466+i*15338.9
2319.2462     1.7254    +i*-1.1635     125817.397+i*15394.8
2369.4472     1.7244    +i*-1.1419     126119.870+i*15444.0
2419.6482     1.7234    +i*-1.1212     126416.859+i*15486.8
2469.8492     1.7224    +i*-1.1014     126708.349+i*15523.7
2520.0503     1.7214    +i*-1.0824     126994.343+i*15554.9
2570.2513     1.7204    +i*-1.0643     127274.858+i*15580.7
2620.4523     1.7194    +i*-1.0468     127549.922+i*15601.6
2670.6533     1.7183    +i*-1.03       127819.573+i*15617.9
2720.8543     1.7173    +i*-1.0139     128083.859+i*15629.7
2771.0553     1.7162    +i*-0.9983     128342.838+i*15637.4
2821.2563     1.7152    +i*-0.9834     128596.573+i*15641.3
2871.4573     1.7141    +i*-0.9690     128845.135+i*15641.6
2921.6583     1.713     +i*-0.9551     129088.599+i*15638.6
2971.8593     1.7119    +i*-0.9417     129327.048+i*15632.4
3022.0603     1.7108    +i*-0.9288     129560.564+i*15623.3
3072.2613     1.7097    +i*-0.9163     129789.237+i*15611.4
3122.4623     1.7086    +i*-0.9042     130013.157+i*15597.1
3172.6633     1.7075    +i*-0.8925     130232.416+i*15580.4
3222.8643     1.7064    +i*-0.8813     130447.11 +i*15561.5
3273.0653     1.7053    +i*-0.8703     130657.333+i*15540.7
3323.2663     1.7042    +i*-0.8597     130863.183+i*15518.0
3373.4673     1.7031    +i*-0.8495     131064.755+i*15493.5
3423.6683     1.702     +i*-0.8395     131262.148+i*15467.5
3473.8693     1.7008    +i*-0.8299     131455.457+i*15440.0
3524.0704     1.6997    +i*-0.8205     131644.779+i*15411.3
3574.2714     1.6986    +i*-0.8114     131830.209+i*15381.2
3624.4724     1.6974    +i*-0.8026     132011.842+i*15350.1
3674.6734     1.6963    +i*-0.7940     132189.771+i*15318.0
3724.8744     1.6952    +i*-0.7856     132364.090+i*15284.9
3775.0754     1.694     +i*-0.7775     132534.888+i*15251.0
3825.2764     1.6929    +i*-0.7696     132702.256+i*15216.4
3875.4774     1.6918    +i*-0.7619     132866.281+i*15181.0
3925.6784     1.6906    +i*-0.7544     133027.051+i*15145.1
3975.8794     1.6895    +i*-0.7471     133184.649+i*15108.6
4026.0804     1.6884    +i*-0.7400     133339.159+i*15071.7
4076.2814     1.6872    +i*-0.7331     133490.662+i*15034.3
4126.4824     1.6861    +i*-0.7263     133639.237+i*14996.6
4176.6834     1.685     +i*-0.7197     133784.963+i*14958.5
4226.8844     1.6838    +i*-0.7133     133927.914+i*14920.2
4277.0854     1.6827    +i*-0.7070     134068.166+i*14881.7
4327.2864     1.6816    +i*-0.7009     134205.789+i*14843.0
4377.4874     1.6805    +i*-0.6949     134340.855+i*14804.1
4427.6884     1.6793    +i*-0.6890     134473.431+i*14765.2
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9748.995      1.5875    +i*-0.4008     141756.700+i*11703.7
9799.196      1.5869    +i*-0.3995     141795.243+i*11684.4
9849.397      1.5863    +i*-0.3981     141833.509+i*11665.2
9899.598      1.5857    +i*-0.3968     141871.502+i*11646.1
9949.799      1.5851    +i*-0.3955     141909.226+i*11627.1
10000         1.5845    +i*-0.3942     141946.684+i*11608.3
@bangerth
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But, better settle on a 5-column format.

@bangerth
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Fixed by 99a5a61 and previous commits.

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