2 | Mechanical Modeling

By the end of this section, you should be able to

Create EOM for 1DOF systems using Lagrange’s equations
- Find equivalent mass-, spring- and damping coefficients
Use beam tables to find equivalent spring constant of continuous beam

Mechanical Modeling Using Lagrange Equations

Including Spring Elements

Deformable Elements

Including Damper Elements

CodE

Mechanical Modeling Using Lagrange Equations

In standard form for a linear system, the EOM/ODE should have dependent variables (with constant coefficients) on the LHS and explicit functions of time (and constants without a dependent variable) on the RHS. If constants are time-dependent (e.g., mass changing with time) then the system becomes non-linear. We will consider a system free/autonomous when it is homogenous, i.e., the RHS is zero when in standard form. A system will be forced when it is non-homogeneous, i.e., having a non-zero RHS when in standard form.