Generalized pseudo-excitation method and its application for vibration control of wind/seismic resistant buildings

Abstract

This dissertation presents a generalized pseudo-excitation method for random vibration analysis of buildings with supplemental discrete control devices and its application to various types of vibration control problems of wind/seismic resistant buildings. The generalized pseudo-excitation method is actually a combination of the complex modal superposition method and the pseudo-excitation method. The proposed method can naturally retain all cross-correlation terms between closely spaced modes of vibration in structural response and accurately handle the non-orthogonal structural damping due to the installation of discrete control devices. The method also provides a convenient way of determining internal force response of a building. The principle and algorithm of the generalized pseudo-excitation method is first applied to a wind-excited tall building with active tendon devices and a wind-excited tall building with a light appendage at its top. The numerical examples show-that for the tall building with a light appendage under alongwind excitation, the classical random-vibration-based modal superposition method (the SRSS method) may underestimate or overestimate the building response. The installation of active tendon devices may alter the natural frequencies and increase the modal damping ratio of the building so significantly that the building is no longer lightly damped or possesses the orthogonal damping property. To pursue the application of modern control algorithm and the closed form solution for wind-excited tall buildings with active control devices, the cross-spectral density matrix of alongwind excitation on a tall building is factorized. The generalized pseudo-excitation method is then applied to find the closed form solution for wind-induced response of the building implemented by active control devices with Linear Quadratic Gaussian (LQG) controllers. The effectiveness of active control devices with LQG controllers in reducing wind-induced vibration of tall buildings is investigated. The advantages and disadvantages of this approach are discussed in the dissertation. The generalized pseudo-excitation method is then extended to investigate modal properties and seismic response of steel frames with connection dampers. The connection dampers are modeled as rotational springs and rotational dampers in parallel. The dissertation derives the mass, stiffness, and damping matrices for the beam element with connection dampers using a combination of the finite element method and the direct stiffness method. After the equations of motion of the system are established, the complex modal analysis is carried out to determine the modal properties of steel frames with connection dampers and the generalized pseudo-excitation method is used to determine seismic response. The parametric studies on the example frame with and without connection dampers show that there is an optimal damper damping coefficient for a given mode of vibration and a given fixity factor of the frame. With the optimal damper damping coefficient, the modal damping ratio of the frame can be significantly increased and the seismic response, including lateral displacement, shear force, and bending moment, can be considerably reduced to the level smaller than those of the frame with rigid connections. The generalized pseudo-excitation method is finally extended and applied to vibration control of adjacent buildings under earthquake. The viscoelastic dampers, the fluid dampers, and the active tendon devices are respectively used to link the adjacent buildings together for control of seismic response. The viscoelastic dampers are passive energy dissipation devices, mathematically represented by the Voigt model. The fluid dampers that operate on the principle of fluid flow through orifices specially shaped are also passive energy dissipation devices but they are defined by the Maxwell model. The active tendons with damper-structure interaction but without active control algorithm and the active control devices with LQG controllers are also investigated respectively. The dissertation derives the equations of motion for earthquake-excited adjacent buildings connected by the viscoelastic dampers, the fluid dampers, and the active tendon devices, respectively. The dissertation also derives the closed form solution for seismic response of adjacent buildings with LQG controllers. The dynamic characteristics of the control device-adjacent building system are determined through the complex modal analysis. The generalized pseudo-excitation method is used to find the seismic response of the system. Extensive parametric studies are performed to assess the effectiveness of control devices and to identify the beneficial control parameters using the generalized pseudo-excitation method. It is found that if control parameters are selected properly, the modal damping ratios of the adjacent buildings can be significantly enhanced and the seismic responses can be considerably reduced. It is also found that if active control force is limited to a certain level, the effectiveness of passive control devices is almost the same as that of active control devices. Toward the real application of vibration control of adjacent buildings, dynamic characteristic and harmonic response of adjacent buildings connected by fluid dampers are also experimentally investigated using model buildings and fluid damper. Two building models are constructed as two three-story shear buildings of different natural frequencies. Model fluid damper connecting the two buildings is designed as linear viscous damper of which damping coefficient can be adjusted. The two buildings without fluid dampers connected are first tested to obtain their individual dynamic characteristics and response to harmonic excitation. The tests are then carried out to determine modal damping ratios of the adjacent buildings connected by the fluid damper, from which optimal damper damping coefficient and location for achieving the maximum modal damping ratio are found. The measured modal damping ratios and harmonic responses of the building-fluid damper system are finally compared with those from the individual buildings. The comparison shows that the fluid damper of proper parameter can significantly increase the modal damping ratio and tremendously reduce the dynamic response of both buildings.