2904ea33-6bb5-4166-aab4-6b3078cc3f6d 29 4 5 decimal

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Vibrations of a rectangular membrane

Calculation formulas are taken from the book:S.Timoshenko,Vibration Problems In Engineering, 2nd Edition ,Read Books, 2008

a 2 :

b 1.5 :

Dimensions and coefficient of membrane tension c 1 :

Amplitude A 0.5 :

m n T 4 π * c m a / (2^n b / (2^+ (* sqrt / eval : (Periods of oscillations of standing waves ≡ m n tmax 60 m n T * 11 T / eval : (Number of animation frames ≡ γ 0.8232 - 0.4194 - 0.3827 0.5677 0.6187 - 0.543 0.009 0.6643 0.7474 33 mat : u v m n t F u 0.5 - v A m π * u * a / sin * n π * v * b / sin * 2 π * t * m n tmax / cos * 1 + 31 mat : m n t W u v m n t F 0 a 0 b 1212 CreateMesh γ * 10 * eval : m n τ 0 m n tmax range : 61 line

τ1 11 τ :

τ2 21 τ :

τ3 12 τ :

τ4 22 τ :

Mode (1,1)

1 1 t W 2 1 sys

Mode(2,1).Nodal line y=b/2

2 1 t W 2 1 sys

Mode(1,2).Nodal line x=a/2

1 2 t W 2 1 sys

M(2,2).Nodlin x=a/2,y=b/2

2 2 t W 2 1 sys