Cantilever Beam Matlab Code - Dynamic Analysis

The theoretical foundation for this analysis lies in the Euler-Bernoulli beam theory. The partial differential equation governing the transverse vibration ( w(x,t) ) of a uniform beam is ( EI \frac\partial^4 w\partial x^4 + \rho A \frac\partial^2 w\partial t^2 = f(x,t) ), where ( EI ) is the flexural rigidity, ( \rho ) is density, and ( A ) is the cross-sectional area. For a cantilever beam, the boundary conditions are zero displacement and zero slope at the fixed end (( x=0 )), and zero bending moment and zero shear force at the free end (( x=L )). Solving this equation analytically yields an infinite set of natural frequencies and mode shapes. However, real-world engineering requires a finite, computable solution, which is where MATLAB's numerical capabilities become invaluable.

Once you master the basic code, consider these enhancements: Dynamic Analysis Cantilever Beam Matlab Code

| What to change | Where in code | |----------------|----------------| | Material (aluminum, composite) | E and rho | | Beam dimensions | L , b , h | | Number of elements | ne (increase for accuracy) | | Damping level | zeta factor | | External force | Inside the time loop: add to F_eff | | Initial condition | u0_red(tip_disp_idx) or any node | | Time step | dt (must be small enough for highest mode) | The theoretical foundation for this analysis lies in

The dynamic behavior of a uniform cantilever beam is typically modeled using the . This theory assumes the beam is "slender" (length much greater than thickness) and that cross-sections remain plane and perpendicular to the neutral axis during bending. Solving this equation analytically yields an infinite set

% Update a = a + delta_a; v = v_pred + dt*gamma*delta_a; u = u_pred + dt^2*beta_nm*delta_a;