Dynamic Characteristics of SDOF Structure with Maxwell Element

Dynamic characteristics are analytically investigated for a single degree of freedom structure with a Maxwell element (SSME). Eigenvalues are obtained analytically and approximated by a perturbation method. Then, cases are sorted by a stiffness ratio $\lambda$ : the ratio of a structural spring to an auxiliary spring. For a small $\lambda$ , the optimal damping ${\varphi }_c$ provides the maximum damping ratio. For a large $\lambda$ , the lower and upper critical dampings ${\varphi }_a$ and ${\varphi }_b$ provide duplex eigenvalues. These values are approximated by simple terms. To reduce transient response, $\lambda$ should be large, and $\varphi$ should be around ${\varphi }_c$ , ${\varphi }_a$ , and ${\varphi }_b$ , which provide the SSME with large damping. For a stationary excitation, the optimal damping ${\varphi }_d$ is introduced to produce the minimum peak deformation. In fact, ${\varphi }_d$ is larger than ${\varphi }_c$ and ${\varphi }_b$ , and provides larger stiffness and a smaller damping ratio. For a seismic excitation, some cases with ${\varphi }_d$ might reduce deformation more than those with ${\varphi }_c$ and ${\varphi }_b$ , but must support larger stress in the Maxwell element. Thus, $\varphi$ should be based on design constraints.