Impact of support stiffness on the performance of negative stiffness dampers for vibration control of stay cables

Abstract

Summary Bridge stay cables are susceptible to dynamic excitations due to their low intrinsic damping and lateral stiffness. Installation of transverse passive dampers near the cable‐deck anchorage on a rigid/flexible support is one of the practical measures to mitigate cable vibrations. The limited performance of conventional positive stiffness dampers (PSDs) has led to the emergence of negative stiffness dampers (NSDs). Recent research has found that unlike PSD, NSD would perform more effectively in the presence of a flexible support. In this study, the impact of damper support stiffness on the NSD control performance is investigated. Based on an existing analytical design formula for achieving a target damping ratio, the design of NSD for a given support condition, the design of damper support for a given NSD, and the design of the entire NSD‐support system are addressed. An optimization algorithm is proposed to identify the optimum combination of NSD parameters and damper support stiffness. The NSD design is refined through numerical iterations to minimize the impact of assumptions made in developing the analytical formulation. A numerical example is presented for a 325 m long stay cable equipped with an optimized NSD and subjected to harmonic excitation. The optimized NSD performance is compared with an optimal active linear‐quadratic regulator (LQR) controller. Results show that the presence of flexible support leads to a cost‐efficient NSD with smaller size and lower level of negative stiffness. Moreover, the optimized NSD is shown to be as effective as LQR to suppress cable vibrations.

Stay cable tension estimation of cable‐stayed bridge under limited information on cable properties using artificial neural networks

“…Þ are transformed into distributed parts before writing the finite difference approximations for Equation (21). Dirac delta function can be presented by a cosine approximation, a piecewise cubic function, a linear hat function hat, 37 etc.…”

“…Others have considered restrained boundary conditions at cable ends rather than purely fixed or hinged ends. 11,12 Another point to consider is the lateral attachments like dampers or cross ties attached to cables; stay cables have shown very low inherent damping 13 ; thus, cross ties [14][15][16] or dampers [17][18][19][20][21] are often mounted to cables to suppress wind-induced vibration. The presence of the lateral components has made estimation of cable force even more challenging.…”

Optimized negative stiffness damper with flexible support for stay cables

“…Compared with a rigid support, a flexible support could amplify the equivalent negative stiffness and Coulomb friction of the damper support system remarkably. Javanbakht et al 49 investigated the impact of support stiffness on NSD control performance. The presence of flexible support resulted in an efficient design of NSD that is still as effective as LQR for cable vibration mitigation.…”

Shake table testing of a passive negative stiffness device with curved leaf springs for seismic response mitigation of structures

“…In addition, numerical investigation and optimum design of a negative stiffness damper for vibration control of stay cables have been conducted. [30][31][32] In the present study, a new passive negative stiffness device composed of curved leaf springs is proposed. It utilizes the reversal phenomenon due to elastic snap-through buckling to produce negative restoring force characteristics.…”

“…A displacement‐dependent oil damper, 29 whose damping force passively decreases with increasing displacement, has been proposed, as for past devices that exert a kind of pseudo‐negative stiffness effect. In addition, numerical investigation and optimum design of a negative stiffness damper for vibration control of stay cables have been conducted 30–32 …”