modelFlexBeamEAGJ
Model of flexible beam
Information
This block provides an Euler-Bernoulli model of a flexible beam. It is recommended that this model not be used directly. Instead, use DeployStructLib.Parts.Beam and set the "useEAGJ" flag to true.
Copyright © 2018
ATA ENGINEERING, INC.
ALL RIGHTS RESERVED
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Boolean | animation | true | = true, if animation shall be enabled |
| SI.Length | L | Beam length | |
| EAGJ_BeamProperty | EAGJprop | Beam properties in EAGJ format | |
| SI.Mass | mass | if DSLglb.quasiStatic then DSLglb.quasiStaticFactor*EAGJprop.rhoA*L else EAGJprop.rhoA*L | Beam mass |
| Real | qsFacR | if DSLglb.quasiStatic then 1/DSLglb.quasiStaticFactor else 1.0 | Quasi-static factor |
| Real | alpha | EAGJprop.alpha | Rayleigh damping coefficient (mass proportional) |
| Real | beta | EAGJprop.beta | Rayleigh damping coefficient (stiffness proportional) |
| Boolean | steadyState | DSLglb.SteadyState | Initialize to steady state? |
| Boolean | useLumpedMassMatrix | false | =true, use a lumped mass matrix formulation else use a consistent mass matrix formulation |
| Boolean | useGravity | false | =true, use gravity in the simulation (computational speedup if not used) |
| SI.Position[3] | r | {L, 0, 0} | Vector from frame_a to undeformed frame_b resolved in frame_a |
| Real | dim2 | sqrt(12*EAGJprop.EIzz/EAGJprop.EA) | |
| Real | dim3 | sqrt(12*EAGJprop.EIyy/EAGJprop.EA) | |
| Types.RotationSequence | sequence | {1, 2, 3} | Angles are returned to rotate frame_a around axes sequence[1], sequence[2] and finally sequence[3] into frame_b |
| Real | Kff | {{EAGJprop.EA/L, 0, 0, 0, 0, 0}, {0, 12*EAGJprop.EIzz/L^3, 0, 0, 0, -6*EAGJprop.EIzz/L^2}, {0, 0, 12*EAGJprop.EIyy/L^3, 0, 6*EAGJprop.EIyy/L^2, 0}, {0, 0, 0, EAGJprop.GJ/L, 0, 0}, {0, 0, 6*EAGJprop.EIyy/L^2, 0, 4*EAGJprop.EIyy/L, 0}, {0, -6*EAGJprop.EIzz/L^2, 0, 0, 0, 4*EAGJprop.EIzz/L}} | |
| Real | Mff | if useLumpedMassMatrix then {{mass/2, 0, 0, 0, 0, 0}, {0, mass/2, 0, 0, 0, 0}, {0, 0, mass/2, 0, 0, 0}, {0, 0, 0, L*EAGJprop.MOIxx/2, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}} else {{mass/2, 0, 0, 0, 0, 0}, {0, mass*13/35, 0, 0, 0, -mass*11*L/210}, {0, 0, mass*13/35, 0, mass*11*L/210, 0}, {0, 0, 0, L*EAGJprop.MOIxx/2, 0, 0}, {0, 0, mass*11*L/210, 0, mass*L*L/105, 0}, {0, -mass*11*L/210, 0, 0, 0, mass*L*L/105}} | |
| SI.Inertia[3] | Itt_CM | {L*EAGJprop.MOIxx, L*EAGJprop.MOIyy, L*EAGJprop.MOIzz} | Inertia tensor of body box with respect to center of mass, parallel to frame_a |
| SI.Inertia[3] | Itt | Itt_CM + mass*{0, (L/2)^2, (L/2)^2} | Inertia tensor of body box with respect frame_a |
| Animation › if animation = true | |||
| Types.ShapeType | shapeType | "box" | Type of shape |
| Initialization | |||
| SI.Position[3] | r_0_start | {0, 0, 0} | Initial values of position of frame_a |
| SI.Angle[3] | angles_start | {0, 0, 0} | Initial values of angles to rotate frame_a around 'sequence_start' axes into frame_b |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Interfaces.Frame_a | frame_a | Coordinate system fixed to the component with one cut-force and cut-torque | |
| Interfaces.Frame_b | frame_b | Coordinate system fixed to the component with one cut-force and cut-torque |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Types.Color | color | Modelica.Mechanics.MultiBody.Types.Defaults.RodColor | Color of shape |
| Types.SpecularCoefficient | specularCoefficient | world.defaultSpecularCoefficient | Reflection of ambient light (= 0: light is completely absorbed) |
| SI.Position[6] | qf | ||
| Real[6] | dqf | ||
| Real[6] | ddqf | ||
| SI.Velocity[3] | v | ||
| SI.Velocity[3] | v0 | ||
| SI.Acceleration[3] | a | ||
| SI.AngularVelocity[3] | w | ||
| SI.AngularAcceleration[3] | z | ||
| SI.Force[3] | Fb_a | ||
| SI.Torque[3] | Tb_a | ||
| Frames.Orientation | R_rel | Relative orientation object from frame_a to frame_b | |
| Real | QeR | ||
| Real | Qet | ||
| Real | QvR | ||
| Real | Qvt | ||
| Real | Qef | ||
| Real | Qvf | ||
| Real | Qeg | ||
| Real | r_CM | ||
| SI.Acceleration[3] | g_0 | Gravity acceleration resolved in world frame | |
| SI.Position[3] | r_0 | Position vector from origin of world frame to origin of frame_a | |
| SI.Angle[3] | phi | Dummy or 3 angles to rotate world frame into frame_a of body | |
| SI.AngularVelocity[3] | phi_d | = der(phi) |