Coupled_vibration_solved_python_part_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7917f54e",
   "metadata": {},
   "source": [
    "### <font color=\"red\">DESIGN ANALYSIS - COUPLED VIBRATION<font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11a71d47",
   "metadata": {},
   "source": [
    "This is an open-research conducted on Design analysis, which is key features and core study in Mechnical engineering. All material used during research are free of cost and open-source softwares, such as Jupyter Notebook, Pandas, Numpy, Math Python in-built libraries and Previous publish journals (most of them are professional industrial or univeristy websites)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2c57d5c",
   "metadata": {},
   "source": [
    "#### Hemant Thapa"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93390f51",
   "metadata": {},
   "source": [
    "Linkedin: https://www.linkedin.com/in/thapahemant/\n",
    "\n",
    "Email: hemantthapa1998@gmail.com"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73af91d4",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68aba132",
   "metadata": {},
   "source": [
    "#### 1. Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "62b5336c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math \n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "979d121e",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ddeeda1",
   "metadata": {},
   "source": [
    "The Figure shows a schematic diagram of a motor vechile. The mass of the vehicle\n",
    "is 1250 kg and its moment of inertia about its axis through its centre of mass G perpendicular to the section is 2000kgm^2. The equivalent stiffness of the tyres and springs of the front suspension is 40kN/m and that of the rear suspension is 60kN/m.\n",
    "\n",
    "The C of G of the engine is 0.2m from the front suspension as shown, and when the engine idles at 500 rev/min. it produces an unbalanced vertical perodic force of the form 100.cos(wt) newtons, where 'w' is the engine speed in rad/sec. Determine the amplitude of the vibrations of the front and rear of the vehicle."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "31436015",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44fe7ed4",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d77c89a7",
   "metadata": {},
   "source": [
    "#### 2. Given: \n",
    "\n",
    "1. Mass: 1250 Kg\n",
    "2. Distance between front axle and C.G. (a): 1m\n",
    "3. Distance between rear axle and C.G. (b): 1.5m\n",
    "4. Front spring stifness (k1 or kf): 40000 N/m\n",
    "5. Rear Spring stifness (k2 or kr): 60000 N/m\n",
    "6. Moment of Interia (M): 2000 Kgm^2\n",
    "7. Engine Revolution per min: 500 rev/min\n",
    "8. Center of gravity of engine from front suspension (ce): 0.2m"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7821d747",
   "metadata": {},
   "source": [
    "#### <font color=\"red\">INPUT :<font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "49bac9c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INPUT:\n",
      "\n",
      "Mass of the system (Kgm^2)1250\n",
      "a - Distance from centre of mass, G to front (m): 1\n",
      "b - Distance from centre of mass, G to rear (m): 1.5\n",
      "ce - Center of gravity of the engine (m): 0.2\n",
      "k1 - Stiffness of the front suspension (kN/m): 40000\n",
      "k2 - Stiffness of the rear suspension (kN/m): 60000\n",
      "I - Moment of Intertia (Kgm^2): 2000\n",
      "N - Number of revolution per min: 500\n"
     ]
    }
   ],
   "source": [
    "print(\"INPUT:\")\n",
    "mass = float(input(\"\\nMass of the system (Kgm^2)\"))\n",
    "a = float(input(\"a - Distance from centre of mass, G to front (m): \"))\n",
    "b = float(input(\"b - Distance from centre of mass, G to rear (m): \"))\n",
    "ce = float(input(\"ce - Center of gravity of the engine (m): \"))\n",
    "k1 = float(input(\"k1 - Stiffness of the front suspension (kN/m): \"))\n",
    "k2 = float(input(\"k2 - Stiffness of the rear suspension (kN/m): \"))\n",
    "I = float(input(\"I - Moment of Intertia (Kgm^2): \"))\n",
    "N = float(input(\"N - Number of revolution per min: \"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "674502f4",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08857230",
   "metadata": {},
   "source": [
    "####  3. Angular frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a95539cd",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Angular frequency (W): 52.3599 rad/sec\n"
     ]
    }
   ],
   "source": [
    "w = (2*math.pi*N)/60 #60sec, pi = 22/7\n",
    "print(f\"\\nAngular frequency (W): {round(w,4)} rad/sec\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b00826",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "346f8943",
   "metadata": {},
   "source": [
    "#### 4. Peak periodic force (Amplitude)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3434209",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perodic force (P): 100 N\n"
     ]
    }
   ],
   "source": [
    "#peak value of periodic force = 100 cos(wt) N\n",
    "p = 100\n",
    "print(f\"Perodic force (P): {p} N\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f872511",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0068357f",
   "metadata": {},
   "source": [
    "#### 5. Torque about center of gravity "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dc14e32f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Torque (T): 80.0 Nm\n"
     ]
    }
   ],
   "source": [
    "t = 100*(a-ce)\n",
    "print(f\"Torque (T): {t} Nm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bde244cc",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eea943cc",
   "metadata": {},
   "source": [
    "#### 6. Solving A, C, E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "444f6795",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A: -3326945.97 C: -50000.0 E: -5308113.56\n"
     ]
    }
   ],
   "source": [
    "A = k1+k2-mass*(w**2)\n",
    "C = k1*a-k2*b\n",
    "E = (k1*a**2)+(k2*b**2)-(I*w**2)\n",
    "print(f\"A: {round(A,2)}\",f\"C: {C}\",f\"E: {round(E,2)}\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "75c92558",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3326945.9726004708, -50000.0, -5308113.556160754)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def equation(k1, k2, mass, w, a, b, I):\n",
    "    A = k1+k2-mass*(w**2)\n",
    "    C = k1*a-k2*b\n",
    "    E = (k1*a**2)+(k2*b**2)-(I*w**2)\n",
    "    return A, C, E\n",
    "equation(k1, k2, mass, w, a, b, I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a52597c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A: -3326945.97 C: -50000.0 E: -5308113.56\n"
     ]
    }
   ],
   "source": [
    "print(f\"A: {round(A,2)}\",f\"C: {C}\",f\"E: {round(E,2)}\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "623b778d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>C</th>\n",
       "      <th>E</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.326946e+06</td>\n",
       "      <td>-50000.0</td>\n",
       "      <td>-5.308114e+06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              A        C             E\n",
       "0 -3.326946e+06 -50000.0 -5.308114e+06"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dic_ACE = {\"A\":A, \"C\":C, \"E\":E}\n",
    "df_ACE = pd.DataFrame([dic_ACE])\n",
    "df_ACE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9f7b941",
   "metadata": {},
   "source": [
    "#### <font color=\"red\">OUTPUT :<font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "841ad811",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Angular frequency (W): 52.3599 rad/sec\n",
      "Perodic force (P): 100 N\n",
      "Torque (T): 80.0 Nm\n",
      "A: -3326945.97\n",
      "C: -50000.0\n",
      "E: -5308113.56\n"
     ]
    }
   ],
   "source": [
    "print(f\"\\nAngular frequency (W): {round(w,4)} rad/sec\")\n",
    "print(f\"Perodic force (P): {p} N\")\n",
    "print(f\"Torque (T): {t} Nm\")\n",
    "print(f\"A: {round(A,2)}\")\n",
    "print(f\"C: {C}\")\n",
    "print(f\"E: {round(E,2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80e7c879",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c473e1ca",
   "metadata": {},
   "source": [
    "#### 7. The linear algebra that illustrates a system of equations. Consider AX=B, where we need to solve for X"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "f5138baa",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fd3e10b",
   "metadata": {},
   "source": [
    "The dynamic matrix equation ignoring damping effect is written as"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "2d859076",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d7e523e",
   "metadata": {},
   "source": [
    "[alpha][X] = [beta] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d72fc635",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Y: -2.9835317191106952e-05 m\n",
      "value of Theta:-1.4790232595782672e-05 radian\n"
     ]
    }
   ],
   "source": [
    "alpha = np.array([[A, C],[C,E]])\n",
    "beta = np.array([p, t])\n",
    "X = np.linalg.solve(alpha, beta)\n",
    "L = list(X)\n",
    "L[0], L[1]\n",
    "Y = L[0] \n",
    "Theta = L[1]\n",
    "print(f\"Value of Y: {Y} m\")\n",
    "print(f\"value of Theta:{Theta} radian\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2ee9b8fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Y (m)</th>\n",
       "      <th>Theta (radians)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.00003</td>\n",
       "      <td>-0.000015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Y (m)  Theta (radians)\n",
       "0 -0.00003        -0.000015"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dic_solved_x = {\"Y (m)\":Y, \"Theta (radians)\":Theta}\n",
    "df_solved_x = pd.DataFrame([dic_solved_x])\n",
    "df_solved_x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5e41a60",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e64eb695",
   "metadata": {},
   "source": [
    "#### 8. Amplitudes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1f286d5",
   "metadata": {},
   "source": [
    "The amplitude of the vertical vibrations at the front and rear end of vehicle "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "087ddba4",
   "metadata": {},
   "outputs": [],
   "source": [
    "yf = Y + a*(Theta) #Amplitude of the vertical vibration at the front end\n",
    "yr = Y - b*(Theta) #Amplitude of the vertical vibration at the rear end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "142f0332",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "value substituting on above equation for vertical vibration\n",
      "Y:-2.9835317191106952e-05 m, a:1.0 m, b:1.5 m, Theta:-1.4790232595782672e-05 radians\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nvalue substituting on above equation for vertical vibration\")\n",
    "print(f\"Y:{Y} m, a:{a} m, b:{b} m, Theta:{Theta} radians\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "178a2409",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "yf: -4.4625549786889626e-05 m, yr :-7.649968297432945e-06 m\n"
     ]
    }
   ],
   "source": [
    "print(f\"\\nyf: {yf} m, yr :{yr} m\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c60beee2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>yf</th>\n",
       "      <th>yr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.000045</td>\n",
       "      <td>-0.000008</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         yf        yr\n",
       "0 -0.000045 -0.000008"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dic_amp = {\"yf\":yf, \"yr\":yr}\n",
    "df_amp = pd.DataFrame([dic_amp])\n",
    "df_amp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d304cef4",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91e18934",
   "metadata": {},
   "source": [
    "Reference:\n",
    "\n",
    "https://integratedmlai.com\n",
    "\n",
    "https://nrsyed.com\n"
   ]
  }
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