fcce4e80-a14e-4bed-bb9a-31c5d30b506f 77 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Vibrations of a circular membrane.The general case

contour radius a 1 :

wave speed c 1 :

Approximation of the Bessel function J0(x) by trigonometric functions x P.0 19128 x 2^* / - 367532768 x 4^* / + 24012454194304 x 6^* / - 130439058752147483648 x 8^* / + : x Q.0 18 x * / - 751024 x 3^* / + 59535262144 x 5^* / - 5797291533554432 x 7^* / + : x J.0maxX 2 π x * / sqrt x π 4 / - cos x P.0 * x π 4 / - sin x Q.0 * - (* (: x J.0minX 1 x 2 / (2^- 122^/ x 2 / (4^(* + 162^/ x 2 / (6^(* - : Approximation of the Bessel function J0(x),J1(x) x J.0 x J.0minX x 2 ≤ (x 2 - ≥ (& (* x J.0maxX x 2 > ((* + x - J.0maxX x 2 - ≤ (* + : x J1 x J.0minX x diff - maple x 2 ≤ (* x J.0maxX x diff - (x 2 > (* + : 71 line

График функции J0(x),J1(x)

x J.0 x J1 2 1 sys

J1Zeros 3.8315 7.0156 10.1735 31 mat : (Zeros of the Bessel J1(x) funktion ≡ k λ1 1 a 2^/ J1Zeros k el (2^* eval : (Frequency and periods of oscillations of standing waves ≡ k T1 2 π * a * c J1Zeros k el * / eval : k t1max 60 k T1 * 1 T1 / 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 k t Fc u v cos * u v sin * k λ1 sqrt u * J1 v cos * 2 π * t * k t1max / cos * 31 mat : k t wc u v k t Fc 106 -^a 02 π * 1120 CreateMesh γ * 9 * eval : u v G v sin v cos u 31 mat : Cil u v G 0 0.015 π 2 / - 32 / π * 120 CreateMesh γ * 9 * eval : k τ 0 k t1max range : 101 line

τ11 1 τ :

τ12 2 τ :

τ13 3 τ :

Mode(1,1) JZeros1= 3.83171

Cil 1 t wc 2 1 sys

Mode(1,2) JZeros1 =7.01559

Cil 2 t wc 2 1 sys

Mode(1,3) JZeros1 = 10.1735

Cil 3 t wc 2 1 sys