A re?evaluation of overshooting in time integration schemes: The neglected effect of physical damping in the starting procedure

An important property of implicit time integration algorithms for structural dynamics is their tendency to “overshoot” the exact solution in first few steps computed response due high-frequency components initial excitations. The typical analysis technique overshooting involves study asymptotic algorithm's step limiting high frequency case. This article finds that prior much engineering literature incomplete it neglects effect physical damping. With damping included, first-order enter into several well-known which were previously thought exhibit zero-order displacement. Newmark method, Wilson- ? Bazzi- ? HHT- ? WBZ- and three parameter optimal/generalized- method are analyzed, as well generalized single-step single-solve (GSSSS) framework encompasses all schemes other new optimal designs based upon issues under consideration. additional component eliminated novel amended GSSSS V0 family (which noteworthy cannot be derived by conventional means), while numerically dissipative U0 (encompassing traditional methods such among algorithm designs) shown irremediable from enters second response, a wholly finding. Numerical verifications performed SDOF MDOF structures with without damping, practical recommendations given problems on basis design selection various conditions.