Exact solutions for dynamic response of a periodic spring and mass structure

This paper derives exact analytical solutions for the dynamic response of a periodic structure for which the unit cell consists of one mass and one spring. The solutions cover arbitrary initial conditions and both polynomial and harmonic external forces. They involve Bessel, Lommel, Weber and hypergeometric functions.

► Exact solutions for the dynamic response of a special periodic structure are derived.
► Arbitrary initial conditions and both polynomial and harmonic external forces treated.
► The solutions involve Bessel, Lommel, Weber and hypergeometric functions.