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Offline Ber7  
#1 Posted : 28 December 2017 23:10:57(UTC)
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Vibrations of a circular membrane.The axisymmetric case
Solution are described with the help of Bessel functions .

https://en.wikipedia.org/wiki/Vi...s_of_a_circular_membrane



Bessel'2.sm (30kb) downloaded 131 time(s).

Edited by user 09 January 2018 23:25:59(UTC)  | Reason: Not specified

thanks 2 users thanked Ber7 for this useful post.
on 29/12/2017(UTC),  on 24/01/2018(UTC)

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Offline Jean Giraud  
#2 Posted : 31 December 2017 19:46:43(UTC)
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Tanks Ber7: saved in your named file.
Offline Ber7  
#3 Posted : 06 January 2018 11:14:01(UTC)
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Vibrations of a rectangular membrane
Calculation formulas are taken from the book:S.Timoshenko,
Vibration Problems In Engineering
MemPl.sm (15kb) downloaded 129 time(s).
0.gif1.gif
2.gif3.gif

Edited by user 19 April 2022 17:38:55(UTC)  | Reason: Not specified

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Offline Ber7  
#4 Posted : 10 January 2018 00:03:52(UTC)
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Vibrations of a circular membrane.The general case
Bessel'5.sm (23kb) downloaded 73 time(s).

2.gif
3.gif
1.gif (666kb) downloaded 1 time(s).

Edited by user 19 April 2022 18:07:50(UTC)  | Reason: Not specified

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Offline Ber7  
#5 Posted : 19 January 2018 18:37:31(UTC)
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Deflection of simply supported equilateral triangular plate
The plate rests on a frame in the form of an equilateral triangle.
The triangular part of the plate is loaded uniformly distributed
load. The equation of the surface of deflections of a triangular plate is taken
from the book of S.P.Timoshenko.Timoshenko S.P., Woinowsky-Krieger S. Theory of plates and shells. New York, NY: McGraw-Hill; 1959.
1.gif
triangular plate.sm (13kb) downloaded 72 time(s).

Edited by user 19 April 2022 18:12:24(UTC)  | Reason: Not specified

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Offline Jean Giraud  
#6 Posted : 19 January 2018 20:47:19(UTC)
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Thanks Ber7 for that one and the other one few days ago.

Jean
Offline Ber7  
#7 Posted : 24 January 2018 22:02:51(UTC)
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I tried to use the plugin Maxima
PlateMaxima (3).png
PlateMaxima.sm (144kb) downloaded 84 time(s).

Edited by user 19 April 2022 18:21:48(UTC)  | Reason: Not specified

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Offline Jean Giraud  
#8 Posted : 26 January 2018 05:52:49(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
I tried to use the plugin Maxima


Thanks Ber7, I love those 3D, though it will never beat Mathcad 8... 11.
On my own, I published several times more than the entire Mathcad Community.
I don't miss them in Smath 6179, why ? purely useless for the Engineer.
They are just for the Gallery [Tom G. would say Peanut Gallery].

We are just waiting for a stable Smath version delivered with Maxima plugin
and more of the possible plugins. Scilab looks far superior to Maxima ?
Offline Ber7  
#9 Posted : 29 January 2018 12:24:36(UTC)
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Deflection of a Circular Plate.Plate contains rigid
inclusion of radius b and loaded at the Center
(Timoshenko,S.and Woinowsky-Krieger, S.,Theory of plates and shells, 1959)



Inclusion.sm (33kb) downloaded 71 time(s).
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Offline loha  
#10 Posted : 27 January 2019 04:30:30(UTC)
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Hello Beer7, is this vibration of a rectangular membrane equivalent to the deflection of a simply supported, uniformly loaded, rectangular plate? (leaving aside the physical parameters like plate thickness, Young's modulus etc.) I am only interested in the curvature on various locations on the surface, not in absolute values (max deflection can be calculated using simple civil engineering formulaes).
Thanks,
Laurent

Originally Posted by: Ber7 Go to Quoted Post
Vibrations of a rectangular membrane
Calculation formulas are taken from the book:S.Timoshenko,
Vibration Problems In Engineering




MemPl.sm (15kb) downloaded 129 time(s).


Offline Jean Giraud  
#11 Posted : 27 January 2019 06:30:46(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
Vibrations of a circular membrane.The axis symmetric case
Solutions are described with the help of Bessel functions .

Thanks Ber7, works great. Beautiful work.
mwbesselj(0,x) is ~ 4 times faster 15 decimals
Hart JZERO 5852 is 23 decimals up to ± 8.

Cheers ... Jean

Bessel JY.sm (76kb) downloaded 53 time(s).
Offline Jean Giraud  
#12 Posted : 27 January 2019 07:55:42(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
Vibrations of a circular membrane.The axis symmetric case
Solutions are described with the help of Bessel functions .

What happened, your previous post is gone with the wind ???
Try this, so much faster !

Bessel mwbesselj Membrane Ber7 [20190126].sm (32kb) downloaded 75 time(s).
Offline Ber7  
#13 Posted : 03 January 2021 11:47:58(UTC)
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Vibrations of a triangular membrane
Calculation formulas are taken from thearticle:
http://ivdon.ru/uploads/...yshov.pdf_30f490557a.pdf
Vibration triangular membrane.sm (320kb) downloaded 38 time(s).
ezgif-4-af2e901b8a.gifezgif-4-11a5949f59.gif
ezgif-4-4b11ff3370.gif

Edited by user 19 April 2022 18:43:47(UTC)  | Reason: Not specified

thanks 1 user thanked Ber7 for this useful post.
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Offline Jean Giraud  
#14 Posted : 03 January 2021 17:28:34(UTC)
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Thanks, works fine after doctoring CreateMesh.
Offline Ber7  
#15 Posted : 03 January 2021 19:23:53(UTC)
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Vibrations of a triangular membrane(Maxima)




TriangularMembrane Maxima.sm (280kb) downloaded 44 time(s).

Edited by user 06 January 2021 12:14:07(UTC)  | Reason: Not specified

thanks 1 user thanked Ber7 for this useful post.
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