Parametric studies on inelastic response spectra for systems with bilinear spring resistance and kinematic strain-hardening, low-to-moderate viscous damping, and standing on firm soil, indicate that aseismic design of such systems based on the associated elasto-plastic spectra is not always conservative, in particular, for systems in the intermediate frequency range. By contrast, present understanding of the effect of viscous damping on inelastic spectra is thoroughly verified. In addition, mathematical expressions for a tripartite model of design spectra for inelastic systems are presented and tested for a ground motion record representative of a major destructive earthquake. These formulas provide generally conservative estimates of parameters of response for undamped systems, as compared with both numerically generated spectra and spectral upper bounds previously reported in the literature; however, for damped systems, the inelastic design spectra provide safe envelopes for most of the frequency range, but often make unconservative predictions over a small portion of the intermediate frequency range.
Analytical model for viscous damping and the spring force for perforated planar microstructures acting at both audible and ultrasonic frequencies
