dyna2¶

Compute the dynamic solution to a set of uncoupled second-order differential equations.

Syntax:

X = dyna2(w2, xi, f, g, dt)

Description:

dyna2 computes the solution to the set

\[\ddot{x}_i + 2 \xi_i \omega_i \dot{x}_i + \omega^{2}_i x_i = f_i g(t), \qquad i=1,\ldots,m\]

of differential equations, where \(g(t)\) is a piecewise linear time function.

The vectors w2, xi, and f contain the squared circular frequencies \(\omega_i^2\), the damping ratios \(\xi_i\), and the applied forces \(f_i\), respectively.

The vector g defines the load function in terms of straight line segments between equally spaced points in time. This function may have been formed by the command gfunc.

The dynamic solution is computed at equal time increments defined by dt. Including the initial zero vector as the first column vector, the result is stored in the \(m \times n\) matrix X, where \(n-1\) is the number of time steps.

See also:

gfunc