Location: BondGraph Basic @ 2e6e3a63b664 / BG Tutorial Mechanical Systems / Oscillating beam with spring and damper.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2020-04-15 21:55:56+12:00
- Desc:
- removed old files.
- Permanent Source URI:
- https://models.fieldml.org/workspace/43b/rawfile/2e6e3a63b664e945f1c3b2d893b61a3674c4b84d/BG Tutorial Mechanical Systems/Oscillating beam with spring and damper.cellml
<?xml version='1.0'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- Your code goes here-->
<units name="rad_per_s">
<unit units="radian"/>
<unit exponent="-1" units="second"/>
</units>
<units name="m4">
<unit exponent="4" units="metre"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="m_per_s">
<unit units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="Jm">
<unit units="joule"/>
<unit units="metre"/>
</units>
<units name="J_per_m">
<unit units="joule"/>
<unit exponent="-1" units="metre"/>
</units>
<units name="J_per_m2">
<unit units="joule"/>
<unit exponent="-2" units="metre"/>
</units>
<units name="J_per_m3">
<unit units="joule"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="Js_per_m2">
<unit units="joule"/>
<unit units="second"/>
<unit exponent="-2" units="metre"/>
</units>
<component name="main">
<!-- Unknown is omega-->
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="1" name="t_ref" units="second"/>
<variable initial_value="0" name="x" units="metre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x</ci>
</apply>
<cn cellml:units="m_per_s">1</cn>
</apply>
</math>
<variable initial_value="0" name="theta" units="radian"/>
<variable name="omega" units="rad_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>omega</ci>
<apply>
<times/>
<cn cellml:units="rad_per_s">0.1</cn>
<apply>
<cos/>
<apply>
<divide/>
<ci>t</ci>
<ci>t_ref</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>theta</ci>
</apply>
<ci>omega</ci>
</apply>
</math>
<!-- Beam geometry-->
<variable initial_value="1" name="l_AB" units="metre"/>
<variable name="l_AB_error" units="metre"/>
<variable initial_value="0.2" name="x_A_1" units="metre"/>
<variable initial_value="0.2" name="x_A_2" units="metre"/>
<variable initial_value="1.2" name="x_B_1" units="metre"/>
<variable initial_value="0.2" name="x_B_2" units="metre"/>
<variable name="v_B_1" units="m_per_s"/>
<variable name="v_B_2" units="m_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_B_1</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>l_AB</ci>
</apply>
<apply>
<sin/>
<ci>theta</ci>
</apply>
<ci>omega</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_B_2</ci>
<apply>
<times/>
<ci>l_AB</ci>
<apply>
<cos/>
<ci>theta</ci>
</apply>
<ci>omega</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_B_1</ci>
</apply>
<ci>v_B_1</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_B_2</ci>
</apply>
<ci>v_B_2</ci>
</apply>
<apply>
<eq/>
<ci>l_AB_error</ci>
<apply>
<minus/>
<ci>l_AB</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<minus/>
<ci>x_B_1</ci>
<ci>x_A_1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>x_B_2</ci>
<ci>x_A_2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Spring-damper geometry-->
<variable initial_value="1.2" name="x_C_1" units="metre"/>
<variable initial_value="1.2" name="x_C_2" units="metre"/>
<variable initial_value="1" name="l_BC" units="metre"/>
<variable name="l_BC_error" units="metre"/>
<variable name="v_BC" units="m_per_s"/>
<variable name="beta" units="radian"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_BC</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>x_B_1</ci>
<ci>x_C_1</ci>
</apply>
<ci>v_B_1</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>x_B_2</ci>
<ci>x_C_2</ci>
</apply>
<ci>v_B_2</ci>
</apply>
</apply>
<ci>l_BC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>l_BC</ci>
</apply>
<ci>v_BC</ci>
</apply>
<apply>
<eq/>
<ci>l_BC_error</ci>
<apply>
<minus/>
<ci>l_BC</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<power/>
<apply>
<minus/>
<ci>x_B_1</ci>
<ci>x_C_1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>x_B_2</ci>
<ci>x_C_2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<arctan/>
<apply>
<divide/>
<apply>
<minus/>
<ci>x_B_1</ci>
<ci>x_C_1</ci>
</apply>
<apply>
<minus/>
<ci>x_B_2</ci>
<ci>x_C_2</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Spring-damper equations-->
<variable initial_value="1" name="E_1" units="J_per_m2"/>
<variable initial_value="1" name="R_1" units="Js_per_m2"/>
<variable name="f_C_e" units="J_per_m"/>
<variable name="f_C_r" units="J_per_m"/>
<variable initial_value="1" name="l_BC_0" units="metre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_C_e</ci>
<apply>
<times/>
<ci>E_1</ci>
<apply>
<minus/>
<ci>l_BC</ci>
<ci>l_BC_0</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_C_r</ci>
<apply>
<times/>
<ci>R_1</ci>
<ci>v_BC</ci>
</apply>
</apply>
</math>
<!-- Beam equations -->
<variable initial_value="1" name="b" units="metre"/>
<variable initial_value="1" name="h" units="metre"/>
<variable name="I" units="m4"/>
<variable initial_value="1" name="E" units="J_per_m3"/>
<variable name="EI" units="Jm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>b</ci>
<apply>
<power/>
<ci>h</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">12</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>EI</ci>
<apply>
<times/>
<ci>E</ci>
<ci>I</ci>
</apply>
</apply>
</math>
<variable initial_value="1" name="n" units="dimensionless"/>
<variable name="f_A_n" units="J_per_m"/>
<variable name="f_B_n" units="J_per_m"/>
<variable initial_value="1" name="a_n" units="metre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_A_n</ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>n</ci>
<pi/>
</apply>
<ci>l_AB</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<ci>EI</ci>
<ci>a_n</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>f_B_n</ci>
<apply>
<times/>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<ci>n</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>n</ci>
<pi/>
</apply>
<ci>l_AB</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>EI</ci>
<ci>a_n</ci>
</apply>
</apply>
</math>
<!-- BG equations-->
<variable name="u_A_x1" units="J_per_m"/>
<variable name="u_A_x2" units="J_per_m"/>
<variable name="u_B_x1" units="J_per_m"/>
<variable name="u_B_x2" units="J_per_m"/>
<variable name="u_C_x1" units="J_per_m"/>
<variable name="u_C_x2" units="J_per_m"/>
<variable name="u_tot_x1" units="J_per_m"/>
<variable name="u_tot_x2" units="J_per_m"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_A_x1</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>f_A_n</ci>
</apply>
<apply>
<sin/>
<ci>theta</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_A_x2</ci>
<apply>
<times/>
<ci>f_A_n</ci>
<apply>
<cos/>
<ci>theta</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_x1</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>f_B_n</ci>
</apply>
<apply>
<sin/>
<ci>theta</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>f_C_e</ci>
<ci>f_C_r</ci>
</apply>
<apply>
<sin/>
<ci>beta</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_B_x2</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>f_B_n</ci>
<apply>
<cos/>
<ci>theta</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>f_C_e</ci>
<ci>f_C_r</ci>
</apply>
<apply>
<cos/>
<ci>beta</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_C_x1</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>f_C_e</ci>
<ci>f_C_r</ci>
</apply>
<apply>
<sin/>
<ci>beta</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_C_x2</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>f_C_e</ci>
<ci>f_C_r</ci>
</apply>
<apply>
<cos/>
<ci>beta</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_tot_x1</ci>
<apply>
<plus/>
<ci>u_A_x1</ci>
<ci>u_B_x1</ci>
<ci>u_C_x1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_tot_x2</ci>
<apply>
<plus/>
<ci>u_A_x2</ci>
<ci>u_B_x2</ci>
<ci>u_C_x2</ci>
</apply>
</apply>
</math>
</component>
</model>