Vibrations of a circular membrane.The axisymmetric case
Solution are described with the help of Bessel functions .

https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane



Bessel'2.sm (29.66 KiB) downloaded 898 time(s).

Tanks Ber7: saved in your named file.

Vibrations of a rectangular membrane
Calculation formulas are taken from the book:S.Timoshenko,
Vibration Problems In Engineering
MemPl.sm (14.03 KiB) downloaded 868 time(s).
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Vibrations of a circular membrane.The general case
Bessel'5.sm (22.49 KiB) downloaded 862 time(s).

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.

triangular plate.sm (12.86 KiB) downloaded 835 time(s).

Thanks Ber7 for that one and the other one few days ago.

Jean

I tried to use the plugin Maxima

PlateMaxima.sm (143.87 KiB) downloaded 868 time(s).

Wrote

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 ?

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 (32.68 KiB) downloaded 815 time(s).

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

Wrote

Vibrations of a rectangular membrane
Calculation formulas are taken from the book:S.Timoshenko,
Vibration Problems In Engineering




MemPl.sm (14.03 KiB) downloaded 868 time(s).

Wrote

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 (75.19 KiB) downloaded 801 time(s).

Wrote

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 (31.26 KiB) downloaded 746 time(s).

Vibrations of a triangular membrane
Calculation formulas are taken from thearticle:
http://ivdon.ru/uploads/article/pdf/IVD_44__1_Chernyshov.pdf_30f490557a.pdf
Vibration triangular membrane.sm (319.69 KiB) downloaded 765 time(s).
File not found.File not found.

Thanks, works fine after doctoring CreateMesh.

Vibrations of a triangular membrane(Maxima)




TriangularMembrane Maxima.sm (279.28 KiB) downloaded 856 time(s).