音響設計学概説

３．振動と音

３．１　振動の基礎理論

３．１．１　１自由度系の振動

• m = 1 [kg], k = 40 [N/m], x⁰ = 0.1 [m]

• m = 1 [kg], c = 0.5 [N s/m], k = 40 [N/m], x⁰ = 0.1 [m]　　　(減衰が弱い状態)
• m = 0.2 [kg], c = 0.5 [N s/m], k = 40 [N/m], x⁰ = 0.1 [m]　　　(減衰が弱い状態)
• m = 1 [kg], c = 12 [N s/m], k = 40 [N/m], x⁰ = 0.1 [m]　　　(臨界制動の状態)
• m = 1 [kg], c = 20 [N s/m], k = 40 [N/m], x⁰ = 0.1 [m]　　　(減衰が強い状態)

• m = 1 [kg], k = 40 [N/m], f = 1 [Hz]
• m = 1 [kg], k = 40 [N/m], f = 2 [Hz]
• m = 1 [kg], c = 0.5 [N s/m], k = 40 [N/m], f = 2 [Hz]
• Tacoma Narrows Bridge Disaster

３．１．２　多自由度系の振動

• m₁ = 1 [kg], k₁ = 40 [N/m]
  m₂ = 1 [kg], k₂ = 40 [N/m], x₂⁰ = 0.1 [m]
• m₁ = 1 [kg], k₁ = 40 [N/m]
  m₂ = 0.2 [kg], k₂ = 40 [N/m], x₂⁰ = 0.1 [m]
• m₁ = 1 [kg], c₁ = 0.5 [N s/m], k₁ = 40 [N/m]
  m₂ = 1 [kg], c₂ = 0.5 [N s/m], k₂ = 40 [N/m], x₂⁰ = 0.1 [m]
• m₁ = 1 [kg], c₁ = 0.5 [N s/m], k₁ = 40 [N/m]
  m₂ = 0.2 [kg], c₂ = 0.5 [N s/m], k₂ = 40 [N/m], x₂⁰ = 0.1 [m]
• m₁ = 1 [kg], k₁ = 40 [N/m]
  m₂ = 1 [kg], k₂ = 40 [N/m]
  m₃ = 1 [kg], k₃ = 40 [N/m]
  m₄ = 1 [kg], k₄ = 40 [N/m]
  m₅ = 1 [kg], k₅ = 40 [N/m], x₅⁰ = 0.1 [m]
• m₁ = 1 [kg], c₁ = 0.5 [N s/m], k₁ = 40 [N/m]
  m₂ = 1 [kg], c₂ = 0.5 [N s/m], k₂ = 40 [N/m]
  m₃ = 1 [kg], c₃ = 0.5 [N s/m], k₃ = 40 [N/m]
  m₄ = 1 [kg], c₄ = 0.5 [N s/m], k₄ = 40 [N/m]
  m₅ = 1 [kg], c₅ = 0.5 [N s/m], k₅ = 40 [N/m], x₅⁰ = 0.1 [m]

３．２　発音体の振動

３．２．１　弦の振動

• r = 0.001 [kg/m], c = 200 [1/s], P = 100 [N], L = 1 [m], a = 0.5 [m], y₀ = 0.1 [m]
• r = 0.001 [kg/m], c = 200 [1/s], P = 100 [N], L = 1 [m], a = 0.25 [m], y₀ = 0.1 [m]
• r = 0.001 [kg/m], c = 500 [1/s], P = 100 [N], L = 1 [m], a = 0.25 [m], y₀ = 0.1 [m]
• r = 0.001 [kg/m], c = 200 [1/s], P = 100 [N], L = 1 [m], a = 0.143 [m], y₀ = 0.1 [m]

• r = 0.001 [kg/m], c = 1500 [1/s], P = 100 [N], f = 250 [Hz], L = 1 [m], a = 0.25 [m]
• r = 0.001 [kg/m], c = 1500 [1/s], P = 100 [N], f = 500 [Hz], L = 1 [m], a = 0.25 [m]
• r = 0.001 [kg/m], c = 1500 [1/s], P = 100 [N], f = 1000 [Hz], L = 1 [m], a = 0.25 [m]
• r = 0.001 [kg/m], c = 1500 [1/s], P = 100 [N], f = 158 [Hz], L = 1 [m], a = 0.25 [m]

• r = 0.001 [kg/m], c = 200 [1/s], P = 100 [N], L = 1 [m], a = 0.25 [m]

３．２．２　膜の振動

• r = 0.001 [kg/m²], c = 200 [1/s], P = 100 [N], L_x = 1.2 [m], L_y = 1.0 [m], s_x = 0.25 [m], s_y = 0.25 [m]

３．３　音から音場へ

３．３．１　固体の振動によって生ずる音場の解析法

• a = 0.17 [m], f = 1000 [Hz]

• a = 0.17 [m], f = 1000 [Hz]

３．３．２　障害物による散乱音場の解析法

• a = 0.17 [m], f = 1000 [Hz]
• a = 0.17 [m], Hanning pulse

• a = 0.17 [m], z₀ = 1.667 [m], f = 1000 [Hz]
• a = 0.17 [m], z₀ = 1.667 [m], Hanning pulse

３．３．３　音場の数値解析

• L_x = 1.439 [m], L_y = 1.186 [m], s_x = 0.3 [m], s_y = 0.593 [m]
  2 [fps], Stratton's impulse function
  6 [fps], Stratton's impulse function
  2 [fps], Unit impulse function
  6 [fps], Unit impulse function

• L_x = 1.439 [m], L_y = 1.186 [m], d_y = 0.25[m], s_x = 0.3 [m], s_y = 0.593 [m]
  2 [fps]
  6 [fps]

• L_x = 1.439 [m], L_y = 1.186 [m], d_y = 0.08[m], s_x = 0.3 [m], s_y = 0.593 [m]
  2 [fps]
  6 [fps]

• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m]
  r_x = 5.7 [m], r_y = 0.3 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m]
  r_x = 5.7 [m], r_y = 1.5 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m]
  r_x = 3 [m], r_y = 2.7 [m]

• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 5.7 [m], r_y = 0.3 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 5.7 [m], r_y = 1.5 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 3 [m], r_y = 2.7 [m]

• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 5.7 [m], r_y = 0.3 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 5.7 [m], r_y = 1.5 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 3 [m], r_y = 2.7 [m]

• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 5.7 [m], r_y = 0.3 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 5.7 [m], r_y = 1.5 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], h = 1 [m], d = 0.2 [m]
  r_x = 3 [m], r_y = 2.7 [m]

• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], r_1,2,3,4 = 0.3549 [kg/m²], r₅ = 0.073 [kg/m²]
  r_x = 5.7 [m], r_y = 0.3 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], r_1,2,3,4 = 0.3549 [kg/m²], r₅ = 0.073 [kg/m²]
  r_x = 5.7 [m], r_y = 1.5 [m]
• L_x = 6 [m], L_y = 3 [m], s_x = 1 [m], s_y = 0.3 [m], r_1,2,3,4 = 0.3549 [kg/m²], r₅ = 0.073 [kg/m²]
  r_x = 3 [m], r_y = 2.7 [m]

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