E. Chicurel-uziel, Exact, single equation, closed-form solution of vibrating systems with piecewise linear springs, J SOUND VIB, 245(2), 2001, pp. 285-301
A method is proposed to obtain in a single equation the exact, closed-form
displacement response of both free undamped vibrations and the steady state
of forced damped vibrations of systems with piecewise linear springs, with
continuous or discontinuous force-deflection relations. Since the displace
ment equations are exact the velocity and acceleration responses are obtain
ed by differentiation. The solutions are complete, they apply for any value
of time from zero to infinity. The method is designed to be handled in a c
omputer either in conjunction with a Symbolic Mathematics package, like Mat
hematica or Maple, or without it. However, for certain relatively simple pr
oblems the phase-plane solution may be obtained even in a hand-held calcula
tor. Two examples are presented. (C) 2001 Academic Press.