Pseudo-excitation Method Research Articles

VIBRATION ANALYSIS OF TWO BUILDINGS LINKED BY MAXWELL MODEL-DEFINED FLUID DAMPERS

Fluid dampers that operate on the principle of fluid flow through orifices specially shaped and defined by the Maxwell model have found more and more applications in vibration mitigation of buildings and structures. This paper thus presents an accurate and effective procedure for determining dynamic characteristics and seismic response of adjacent buildings linked by fluid dampers. Dynamic characteristics of damper-linked adjacent buildings are obtained by solving the eigenvalue problem for real non-symmetric matrices. Random seismic response of adjacent buildings linked by dampers is determined by a combination of the state-space method and the pseudo-excitation method. Based on a derived formula, a computer program is written and extensive parametric studies are performed to assess the effectiveness of the fluid damper and to identify beneficial damper relaxation time and damping coefficient at zero frequency. It is shown that using the Maxwell model-defined fluid dampers of proper parameters to link adjacent buildings can increase the modal damping ratios and reduce the seismic responses of adjacent buildings significantly. It is also shown that the behaviour of the adjacent buildings linked by the Maxwell model-defined fluid dampers could be the same as that connected by the Voigt model-defined viscoelastic dampers.

Fully coupled buffeting analysis of Tsing Ma suspension bridge

A fully coupled buffeting analysis of the Tsing Ma suspension bridge in Hong Kong is carried out in this paper. The features of the bridge, its natural frequencies and mode shapes from finite element analysis are first presented. Followed is an introduction to the formulation for fully coupled buffeting analysis of cable-supported bridges, which is featured mainly by a combination of finite element approach and pseudo-excitation method in the frequency domain. The buffeting response of bridge deck is then computed and compared with that from the conventional method. After the comparison, the effects from aeroelastic forces, multimodes and intermodes of vibration on deck response are examined. Finally, the buffeting response of the whole bridge is investigated with aerodynamic forces on not only bridge deck but also bridge towers and main cables. The results show that aeroelastic forces significantly affect the torsional response of the deck. The multimode responses are larger than single-mode responses in the vertical and torsional motions of the deck. The significant intermode responses may exist between the vibration modes of similar mode shapes or similar modal components. The buffeting of towers and main cables affects the lateral vibration of bridge deck and, in turn, the vibration of the bridge deck impacts the buffeting of the bridge towers and main cables.

FULLY COUPLED BUFFETING ANALYSIS OF LONG-SPAN CABLE-SUPPORTED BRIDGES: FORMULATION

A formulation for fully coupled buffeting analysis of long-span cable-supported bridges is presented, in which dynamic coupling between modes of vibration, dynamic forces on bridge deck and towers and cables, and varying wind speed and structural properties along the bridge deck and towers and cables can be taken into consideration. This formulation adopts a finite element approach and a pseudo-excitation method. Aeroelastic forces on the bridge deck are changed into nodal forces to form aeroelastic damping and stiffness matrices while aerodynamic forces on the bridge deck, towers and cables are converted into nodal forces to obtain a loading vector. After the system equation of motion is assembled, the pseudo-excitation method is applied and the formulation is programmed so that a personal computer can be used to execute the buffeting analysis of the system of hundreds of degrees of freedom in 1 or 2 h. The results from the case study of a long suspension bridge using the proposed formulation and program are also selectively presented in this paper.

Pseudo-excitation method for vibration analysis of wind-excited structures

The pseudo-excitation method, in which random excitations are mathematically represented by a series of harmonic loads, is developed for vibration analysis of wind-excited large civil engineering structures of closely spaced natural frequencies or equipped with discrete damping devices. By using this method, all cross-correlation terms between normal modes in a structural response can be retained naturally, and the non-orthogonal structural damping or stiffness properties can be handled accurately. The principle and algorithm of the pseudo-excitation method are introduced in this paper for structures with and without control devices. The accuracy of the method is validated through the comparison with the transfer matrix method. Two example buildings are presented to demonstrate the advantages of the suggested method.

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.

Buffeting analysis of long span bridges: a new algorithm

This paper presents a new algorithm for buffeting analysis of long span bridges, featured mainly by a complete finite element approach and a pseudo-excitation method. Aeroelastic forces on a bridge deck are first converted into nodal forces to form element aeroelastic damping and stiffness matrices. Aerodynamic forces are then converted into nodal forces to obtain an element loading vector. After the system equation of motion is assembled, the pseudo-excitation method is finally applied to determine the buffeting response, which naturally includes inter-mode and multi-mode contributions. The accuracy of the new algorithm is examined by comparison with the Scanlan's method through an example bridge deck. The potential advantages of the algorithm are also pointed out.

Localization investigation of stationary random wave transmission along damped ordered substructural chains

Based on the symplectic eigensolution and the pseudo-excitation method, the localization of structural chains subjected to stationary random point excitation is investigated. The stiffness, mass and the hysteretic damping distributions are all continuously variable. The cause of the displacement and internal force localization is explained in terms of the symplectic eigenvalues and eigenvectors of a typical substructure of the structural chain. When duplicate symplectic eigenvalues occur, the degeneration of the stopband as well as the corresponding degeneration of the mode localization phenomenon are discussed.

PROPAGATION OF NON-STATIONARY RANDOM WAVES ALONG SUBSTRUCTURAL CHAINS

Propagation of non-stationary random waves along hysteretically damped repetitive structures is investigated numerically, by extending recently developed theory. It is proved that symplectic mathematics combined with the pseudo-excitation method gives efficient solutions not only for stationary random excitations, but also for non-stationary random excitations. The numerically computed time-dependent variance curves of the displacement and internal force responses at different stations of a substructural chain are given as an example.

A high precision direct integration scheme for non-stationary random seismic responses of non-classically damped structures

For non-classically damped structures subjected to evolutionary random seismic excitations, the non-stationary random responses are computed by means of a high precision direct (HPD) integration scheme combined with the pseudo excitation method. Only real modes are used, so that the reduced equations of motion remain coupled for such non-classically damped structures. In the given examples, the efficiency of this method is compared with that of the Newmark method.

Propagation of stationary random waves along substructural chains

Stationary random waves travelling along hysteretically damped repetitive structures are investigated numerically by means of symplectic algebra. Power spectral densities and variances of various responses are computed conveniently by virtue of the “pseudo-excitation method”.

Pseudo-excitation algorithm for nonstationary random seismic responses

A simple and accurate algorithm for nonstationary responses of structures subjected to evolutionary random seismic excitation is presented as an extension of the pseudo-excitation method for stationary random seismic responses. The analyses of various time-dependent auto- or cross-power spectral density (PSD) functions have simple and unified formulae. For some important envelope functions, time-dependent PSD functions can be calculated by means of simple frequency-domain analyses.