2025-01-15 13:46:04 +08:00
{
"nodes":[
{"id":"9461f7dd96103316","type":"text","text":"Kane方法","x":-120,"y":-280,"width":250,"height":50},
{"id":"0c8534c8ba68c9a6","type":"text","text":"**广义**主动力","x":-280,"y":-140,"width":250,"height":50},
{"id":"5eaa425c204bf600","type":"text","text":"**广义**惯性力","x":40,"y":-140,"width":250,"height":50},
{"id":"e398416e55019686","type":"text","text":"运动学","x":-210,"y":220,"width":250,"height":60},
2025-01-16 15:27:27 +08:00
{"id":"38d3d1a313c094ee","type":"text","text":"广义坐标","x":-280,"y":340,"width":250,"height":60},
2025-01-24 09:55:07 +08:00
{"id":"8ec17237cebe7433","type":"text","text":"广义速率","x":60,"y":340,"width":250,"height":60},
{"id":"7351d2bbb065d539","type":"text","text":"动力学 ","x":-210,"y":110,"width":250,"height":60},
2025-04-11 10:37:09 +08:00
{"id":"da500b2b12ed0901","type":"text","text":"填充augmat矩阵","x":290,"y":-30,"width":250,"height":60},
{"id":"20ce8d75f0f35588","type":"text","text":"解出来q_dot ---u","x":580,"y":-30,"width":250,"height":60},
2026-01-08 15:16:18 +08:00
{"id":"6094c53caf966263","type":"text","text":"由F + F* 的形式转换到 [C(q,t)]，
2025-04-11 10:37:09 +08:00
{"id":"c20eeff7484d8a39","type":"text","text":"叠加法","x":-275,"y":560,"width":250,"height":60},
{"id":"a729b7930412f0b1","type":"text","text":"需要保持边界条件一致","x":60,"y":560,"width":250,"height":60},
{"id":"d405163cb9ecd804","type":"text","text":"叶片多段拆分，小段做模态叠加？","x":60,"y":670,"width":250,"height":60},
2025-05-09 09:23:51 +08:00
{"id":"4a08e20366911d68","type":"text","text":"v1pt_theory","x":290,"y":140,"width":250,"height":60},
{"id":"6e5a6a3cdd47bd52","type":"text","text":"v2pt_theory","x":290,"y":207,"width":250,"height":60},
2025-06-10 13:47:31 +08:00
{"id":"4bfacdf3ddedbdec","type":"text","text":"柔性体 / 连续体","x":-340,"y":960,"width":250,"height":60},
{"id":"ae48e80ccd92bffa","type":"text","text":"连续体振动","x":60,"y":960,"width":250,"height":60},
{"id":"ed5a265dc4b72aaa","type":"text","text":"连续体动力学","x":420,"y":960,"width":250,"height":60},
{"id":"fc13b731983ac384","type":"text","text":"浮动坐标系","x":-340,"y":1181,"width":250,"height":60},
2026-01-08 15:16:18 +08:00
{"id":"df8e8a93ea4af203","type":"text","text":"叶片","x":984,"y":-235,"width":250,"height":60},
{"id":"7dc483819d8b527b","type":"text","text":"轮毂","x":1280,"y":-235,"width":250,"height":60},
{"id":"c02c22667637367f","type":"text","text":"机舱","x":1580,"y":-235,"width":250,"height":60},
{"id":"623ac90ce5bad160","type":"text","text":"塔架","x":1580,"y":-60,"width":250,"height":60},
{"id":"0324f23e7dc78d68","type":"text","text":"机舱","x":1580,"y":55,"width":250,"height":60},
{"id":"ba5c15a27611709c","type":"text","text":"偏航轴承","x":1580,"y":-150,"width":250,"height":60},
{"id":"6c3a6982a53e7df9","type":"text","text":"刚体部件：","x":984,"y":177,"width":250,"height":60},
{"id":"f3c36900dd3ed9d1","type":"text","text":"刚体的广义主动力、惯性力公式","x":1280,"y":177,"width":250,"height":60},
{"id":"b624e8c6302b9a1c","type":"text","text":"叶片、塔架","x":984,"y":310,"width":250,"height":60},
{"id":"1054909d642ce071","type":"text","text":"广义惯性力：质点广义惯性力公式 积分","x":1280,"y":310,"width":250,"height":60},
{"id":"1e1a1a0d67920443","type":"text","text":"广义主动力：
{"id":"092cf6719d47d01d","type":"text","text":"弹性恢复力、阻尼、重力、气动力","x":1280,"y":530,"width":250,"height":60},
{"id":"32b762bd2a4b0d66","type":"text","text":"传动链、偏航","x":984,"y":640,"width":250,"height":60},
2026-01-08 16:58:12 +08:00
{"id":"14a4450243ca9953","type":"text","text":"原理呢？","x":1620,"y":530,"width":250,"height":60},
{"id":"5ed3765756616b02","type":"text","text":"叶片","x":-936,"y":1420,"width":250,"height":60},
{"id":"9a7256948b4e439c","type":"text","text":"轮毂","x":-640,"y":1420,"width":250,"height":60},
{"id":"db5161e16a8e2c3f","type":"text","text":"机舱","x":-340,"y":1420,"width":250,"height":60},
{"id":"95eb99b9b0299f2f","type":"text","text":"塔架","x":-340,"y":1595,"width":250,"height":60},
{"id":"a2e90c49290ecb52","type":"text","text":"偏航轴承","x":-340,"y":1505,"width":250,"height":60},
{"id":"cccd4482e817fca4","type":"text","text":"$$\n{k'}_{ij}^{B1F} = \\sqrt{FlStTunr^{B1}(i) \\, FlStTunr^{B1}(j)} \\int_{0}^{BldFlexL} EI^{B1F}(r) \\frac{d^2 \\phi_i^{B1F}(r)}{dr^2} \\frac{d^2 \\phi_j^{B1F}(r)}{dr^2} dr \\quad (i, j = 1, 2) \\tag{9}\n$$","x":-180,"y":1855,"width":980,"height":130},
{"id":"722e4b9c310e6d2a","type":"text","text":"$$\nEI^{B1F}(r) = AdjFlSt^{B1} \\cdot FlpStff^{B1}(r) \\tag{10}\n$$","x":-180,"y":2050,"width":980,"height":80},
{"id":"50e241bef2144ea1","type":"text","text":"$$\n\\frac{d^2 \\phi_i^{B1F}(r)}{dr^2} \\frac{d^2 \\phi_j^{B1F}(r)}{dr^2}\n$$","x":200,"y":2190,"width":220,"height":120},
2026-01-09 16:17:19 +08:00
{"id":"f65edb48b74e18d7","type":"text","text":"叶片广义挥舞刚度","x":-540,"y":1904,"width":250,"height":32,"color":"2"},
2026-01-08 16:58:12 +08:00
{"id":"e0d016f4bb106554","type":"text","text":"- 需要叶片挥舞刚度","x":-540,"y":2072,"width":250,"height":36},
{"id":"a9889437875a9263","type":"text","text":"- 模态形状二阶导","x":-540,"y":2232,"width":250,"height":36},
{"id":"da8b0f86919e99d9","type":"text","text":"$$\n\\left[ \\frac{d^2 \\phi_{1}^{B1E}(r)}{dr^2} \\right]^2\n$$","x":10,"y":2710,"width":220,"height":120},
{"id":"6454ea0b5f37aafa","type":"text","text":"- 模态形状二阶导","x":-540,"y":2752,"width":250,"height":36},
{"id":"36c9ab3fd7a0a402","type":"text","text":"- 需要叶片挥舞刚度","x":-540,"y":2592,"width":250,"height":36},
2026-01-09 16:17:19 +08:00
{"id":"ab5c75b7401fb031","type":"text","text":"叶片广义摆振刚度","x":-540,"y":2424,"width":250,"height":32,"color":"2"},
2026-01-08 16:58:12 +08:00
{"id":"da00f9548457388f","type":"text","text":"$$\n{k'}_{11}^{B1E} = \\int_{0}^{BldFlexL} EI^{B1E}(r) \\left[ \\frac{d^2 \\phi_{1}^{B1E}(r)}{dr^2} \\right]^2 dr \\tag{11}\n$$","x":-180,"y":2380,"width":600,"height":120},
{"id":"a20bd9b934093730","type":"text","text":"$$\nEI^{B1E}(r) = AdjEdSt^{B1} \\cdot EdgStff^{B1}(r) \\tag{12}\n$$","x":-180,"y":2570,"width":560,"height":80},
{"id":"c477cd2a76cd46fb","x":-540,"y":3101,"width":250,"height":60,"type":"text","text":"- 模态形状一阶导"},
2026-01-09 16:17:19 +08:00
{"id":"2ee598faf0603188","x":-540,"y":2921,"width":250,"height":83,"color":"2","type":"text","text":"离心刚化效应引起的刚度项"},
{"id":"dcd9236bd7c84bd4","type":"text","text":"叶片质量属性","x":-540,"y":3356,"width":250,"height":32,"color":"2"},
2026-01-08 16:58:12 +08:00
{"id":"ebc5c6d7451acc3b","type":"text","text":"- 叶片质量","x":-540,"y":3454,"width":250,"height":36},
{"id":"a49465d6a6a3c3c2","type":"text","text":"- 叶片一阶矩","x":-540,"y":3534,"width":250,"height":36},
{"id":"11e198e842aadec4","type":"text","text":"- 叶片质心","x":-540,"y":3853,"width":250,"height":36},
{"id":"7f6f9185b340d930","type":"text","text":"- 风轮质量","x":-540,"y":3954,"width":250,"height":36},
{"id":"5a48574ff6eeda7e","type":"text","text":"- 风轮惯性","x":-540,"y":4054,"width":250,"height":36},
{"id":"987e81ef1f1995b3","type":"text","text":"- 叶片二阶矩","x":-540,"y":3614,"width":250,"height":36},
{"id":"c4978e46cf739ba4","x":-180,"y":2885,"width":820,"height":346,"type":"text","text":"```rust\nelmnt_stff = f_mom_abv_nd[[k, j]] * p.dr_nodes[j] * p.rot_speed.powi(2);\n\nshape1 = shp_array(p.r_nodes_norm[j], p.bld_flex_l, &p.bld_fl1_sh.slice(s![.., k]).to_owned(), 1);\n\nshape2 = shp_array(p.r_nodes_norm[j], p.bld_flex_l, &p.bld_fl2_sh.slice(s![.., k]).to_owned(), 1);\n\nk_bf_cent[[k, 0, 0]] += elmnt_stff * shape1 * shape1;\n\nk_bf_cent[[k, 1, 1]] += elmnt_stff * shape2 * shape2;\n\nshape = shp_array(p.r_nodes_norm[j], p.bld_flex_l, &p.bld_edg_sh.slice(s![.., k]).to_owned(), 1);\n\nk_be_cent[[k, 0, 0]] += elmnt_stff * shape * shape;\n```"},
{"id":"c29809ca3c70881b","type":"text","text":" ```fortran\n p%BldMass (K) = p%TipMass(K)\n p%FirstMom (K) = p%TipMass(K)*p%BldFlexL\n p%SecondMom(K) = p%TipMass(K)*p%BldFlexL*p%BldFlexL\n ...\n p%BElmntMass(J,K) = p%MassB(K,J)*p%DRNodes(J)\n ...\n p%BldMass (K) = p%BldMass (K) + p%BElmntMass(J,K)\n p%FirstMom (K) = p%FirstMom (K) + p%BElmntMass(J,K)*p%RNodes(J)\n p%SecondMom(K) = p%SecondMom(K) + p%BElmntMass(J,K)*p%RNodes(J)*p%RNodes(J)\n \n ```","x":-180,"y":3320,"width":789,"height":460},
{"id":"253044dc6cebe206","type":"text","text":"```rust\np.bld_cg[k] = p.first_mom[k] / p.bld_mass[k];\n\np.rot_mass += p.bld_mass[k];\n\np.rot_iner += (p.second_mom[k] + p.bld_mass[k] * p.hub_rad * (2.0 * p.bld_cg[k] + p.hub_rad)) * p.cos_pre_c[k].powi(2);\n```\n","x":-156,"y":3853,"width":796,"height":237},
{"id":"9a824939bad661d2","x":-2120,"y":2252,"width":250,"height":36,"type":"text","text":"- 摆振广义质量"},
{"id":"8fa04043b651b57e","x":-2120,"y":2394,"width":250,"height":36,"type":"text","text":"- 模态形状0阶导"},
2026-01-09 16:17:19 +08:00
{"id":"34fed438f96dfa4c","x":-2120,"y":2540,"width":250,"height":60,"color":"2","type":"text","text":"固有频率"},
2026-01-08 16:58:12 +08:00
{"id":"9005abbfdd8f3246","x":-2120,"y":2660,"width":250,"height":60,"type":"text","text":"挥舞固有频率"},
{"id":"8944328366cdad0c","x":-2120,"y":2780,"width":250,"height":69,"type":"text","text":"考虑叶尖质量、离心刚化"},
{"id":"a96110788e264552","x":-2120,"y":3180,"width":250,"height":60,"type":"text","text":"摆振固有频率"},
{"id":"6f03c475fcf16a01","type":"text","text":"考虑叶尖质量、离心刚化","x":-2120,"y":3320,"width":250,"height":69},
2026-01-09 16:17:19 +08:00
{"id":"f1cd43613a1fdfa5","type":"text","text":"广义质量","x":-2120,"y":1996,"width":250,"height":32,"color":"2"},
2026-01-08 16:58:12 +08:00
{"id":"5b82d2f5eb26eefc","type":"text","text":"- 挥舞广义质量","x":-2120,"y":2094,"width":250,"height":36},
{"id":"5d4daed7f83a3fa5","x":-2938,"y":2057,"width":640,"height":110,"type":"text","text":"$$\nm_{ij}^{\\prime B1F} = \\int_{0}^{BldFlexL} \\mu^{B1}(r) \\phi_i^{B1F}(r) \\phi_j^{B1F}(r) \\, dr \\quad (i, j = 1, 2) \\tag{16}\n$$"},
{"id":"44300ab8ae0139cc","x":-2618,"y":2630,"width":320,"height":120,"type":"text","text":"$$\nf_i^{\\prime B1F} = \\frac{1}{2\\pi} \\sqrt{\\frac{k_{ii}^{\\prime B1F}}{m_{ii}^{\\prime B1F}}} \\tag{14}\n$$"},
{"id":"0bc6d2d448f012fd","x":-3014,"y":2780,"width":716,"height":315,"type":"text","text":"```rust\n// Natural blade I-flap frequency w/o centrifugal stiffening nor
{"id":"5047212eb42c9e69","type":"text","text":"$$\nf_i^{\\prime B1E} = \\frac{1}{2\\pi} \\sqrt{\\frac{k_{ii}^{\\prime B1E}}{m_{ii}^{\\prime B1E}}} \\tag{15}\n$$","x":-2618,"y":3150,"width":320,"height":120},
{"id":"f5ccbef2e5e250b9","type":"text","text":"```rust\n// Natural blade 1-edge frequency w/o centrifugal stiffening nor
2026-01-09 16:17:19 +08:00
{"id":"b5bee6a3e7c29d31","type":"text","text":"**叶片广义参数计算**","x":-1440,"y":2916,"width":250,"height":93,"color":"1"},
{"id":"d89b6477389b9a45","x":-2774,"y":2196,"width":476,"height":112,"type":"text","text":"$$\nm_{11}^{\\prime B1E} = \\int_{0}^{BldFlexL} \\mu^{B1}(r) \\left[ \\phi_1^{B1E}(r) \\right]^2 dr \\tag{17}\n$$"},
{"id":"d1cb8d99b00c07c8","x":-3022,"y":3699,"width":724,"height":203,"type":"text","text":"$$\n\\left. F_r \\right|_{DampB1} =\n\\begin{cases}\n-\\frac{\\zeta_1^{B1F} {k'}_{11}^{B1F}}{\\pi f^{\\prime B 1 F}_1} \\dot{q}_{B1F1} - \\frac{\\zeta_2^{B1F} {k'}_{12}^{B1F}}{\\pi f^{\\prime B 1 F}_2} \\dot{q}_{B1F2} & \\text{for } r = B1F1 \\\\\n-\\frac{\\zeta_1^{B1E} {k'}_{11}^{B1E}}{\\pi f^{\\prime B 1 E}_1} \\dot{q}_{B1E1} & \\text{for } r = B1E1 \\\\\n-\\frac{\\zeta_1^{B1F} {k'}_{21}^{B1F}}{\\pi f^{\\prime B 1 F}_1} \\dot{q}_{B1F1} - \\frac{\\zeta_2^{B1F} {k'}_{22}^{B1F}}{\\pi f^{\\prime B 1 F}_2} \\dot{q}_{B1F2} & \\text{for } r = B1F2 \\\\\n0 & \\text{otherwise}\n\\end{cases} \\tag{13}\n$$"},
{"id":"204d6c2f3ec03ac0","x":-2120,"y":3771,"width":250,"height":60,"color":"2","type":"text","text":"广义阻尼"},
{"id":"1684e3f8b6f17829","type":"text","text":"挥舞和摆振方向结构阻尼比","x":-2120,"y":3980,"width":250,"height":69},
{"id":"b1dddd3ed142c348","x":-2600,"y":3973,"width":302,"height":84,"type":"text","text":"$\\zeta_{i}^{BIF} = BldFlDmp^{B1}(i)/100$\n$\\zeta_{i}^{BIE} = BldEdDmp^{B1}(i)/100$"},
{"id":"c328cec51da1530b","x":-2963,"y":4080,"width":665,"height":230,"type":"text","text":" ```fortran\n\tp%CBF(K,I,L) = ( 0.01*p%BldFDamp(K,L) )*p%KBF(K,I,L)/( Pi*p%FreqBF(K,L,1) )\n\tp%CBE(K,1,1) = ( 0.01*p%BldEDamp(K,1) )*p%KBE(K,1,1)/( Pi*p%FreqBE(K,1,1) )\n ``` "},
{"id":"169bd99d304f6f85","x":-2120,"y":4165,"width":250,"height":60,"type":"text","text":"广义阻尼系数"},
{"id":"cd865939df274ef7","x":-3291,"y":4420,"width":993,"height":623,"type":"text","text":" ```fortran\n ! Calculate the 2nd derivatives of the twisted shape functions:\n Shape = SHP( p%RNodesNorm(J), p%BldFlexL, p%BldFl1Sh(:,K), 2, ErrStat, ErrMsg )\n p%TwistedSF(K,1,1,J,2) = Shape*p%CThetaS(K,J)\n ...\n ! Integrate to find the 1st derivatives of the twisted shape functions:\n TwstdSF ( I,L, 1) = p%TwistedSF(K,I,L,J,2)*0.5*p%DRNodes(J)\n p%TwistedSF (K,I,L,J,1) = TwstdSF ( I,L, 1)\n ...\n ! Integrate to find the twisted shape functions themselves (i.e., their zeroeth derivative):\n TwstdSF ( I,L, 0) = p%TwistedSF(K,I,L,J,1)*0.5*p%DRNodes(J)\n p%TwistedSF (K,I,L,J,0) = TwstdSF ( I,L, 0)\n ...\n ! Integrate to find the blade axial reduction shape functions:\n AxRdBld ( I,L ) = 0.5*p%DRNodes(J)*( &\n p%TwistedSF(K,1,I,L,1)*p%TwistedSF(K,1,L,J,1) &\n + p%TwistedSF(K,2,I,L,1)*p%TwistedSF(K,2,L,J,1) )\n p%AxRedBld (K,I,L,J) = AxRdBld(I,L)\n ```"},
{"id":"43c52f1d3f4f4337","x":-2120,"y":4580,"width":250,"height":60,"color":"4","type":"text","text":"扭转形状函数和轴向缩短系数"}
2025-01-15 13:46:04 +08:00
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2025-01-24 09:55:07 +08:00
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2026-01-09 16:17:19 +08:00
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2025-01-15 13:46:04 +08:00
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