A scheme is proposed for linking together into a single equation the equations and inequalities that make up a piecewise representation of a non-harmonic, periodic, continuous or discontinuous function. A method using this scheme is proposed in order to obtain, in closed form, the displacement response of linear vibration problems with piecewise-continuous forcing functions. Since the solution is exact, so are the derivatives, i.e. the velocity and acceleration responses. An example is presented.
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