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The behavior of many engineering systems is governed by the second order differential equation £/(/) +F[£/(r)] =<?(')> (1) where G(t) is a specified oscillatory function of time t, a dot denotes differentiation with respect to t, F(U) is a nonlinear restoring function representing the system hysteresis, as shown in Fig. 1, and U(0) = U(0) = 0. In a recent paper [1], it has been shown that /= F(u) < (l/a)g, (2) where / = sup|.F(I/)|, " = sup|t/(?)|, g = sup|G(/)|, and 0 < a < 1 is given by A a = ~rr> Afu where A is the area of the hysteresis loop.

Response bounds for hysteretic second order systems