2 | Mechanical Modeling

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

  1. Create EOM for 1DOF systems using Lagrange’s equations

    • Find equivalent mass-, spring- and damping coefficients

  2. Use beam tables to find equivalent spring constant of continuous beam

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.

Including Spring Elements

Lagrange’s Equation for undamped system:

Deformable Elements

Including Damper Elements

Lagrange’s Equation for damped system:

CodE