scholarly journals Seismic Response Analysis of Continuous Multispan Bridges with Partial Isolation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
E. Tubaldi ◽  
A. Dall’Asta ◽  
L. Dezi
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Approximate Solutions ◽  
Transverse Motion ◽  
Response Analysis ◽  
Superposition Method ◽  
Complex Mode ◽  
Mode Superposition ◽  
Mode Superposition Method ◽  
Isolated Bridges

Partially isolated bridges are a particular class of bridges in which isolation bearings are placed only between the piers top and the deck whereas seismic stoppers restrain the transverse motion of the deck at the abutments. This paper proposes an analytical formulation for the seismic analysis of these bridges, modelled as beams with intermediate viscoelastic restraints whose properties describe the pier-isolator behaviour. Different techniques are developed for solving the seismic problem. The first technique employs the complex mode superposition method and provides an exact benchmark solution to the problem at hand. The two other simplified techniques are based on an approximation of the displacement field and are useful for preliminary assessment and design purposes. A realistic bridge is considered as case study and its seismic response under a set of ground motion records is analyzed. First, the complex mode superposition method is applied to study the characteristic features of the dynamic and seismic response of the system. A parametric analysis is carried out to evaluate the influence of support stiffness and damping on the seismic performance. Then, a comparison is made between the exact solution and the approximate solutions in order to evaluate the accuracy and suitability of the simplified analysis techniques for evaluating the seismic response of partially isolated bridges.

Efficient Mode Superposition Method for Seismic Analysis of Nonlinear Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S264-S272 ◽  
Author(s):  
Roberto Villaverde ◽  
Melad M. Hanna
Keyword(s):  
Nonlinear Systems ◽  
Comparative Study ◽  
Integration Method ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Superposition Method ◽  
Direct Integration ◽  
Mode Superposition ◽  
Mode Superposition Method ◽  
Direct Integration Method

A step-by-step integration method is proposed to compute within the framework of the conventional mode superposition technique the response of bilinear hysteretic structures subjected to earthquake ground motions. The method is computationally efficient because only a few modes need to be considered to obtain an accurate estimate of such a response, and because it does not require the use of excessively small time steps to avoid problems of accuracy or stability. It is developed on the basis that the nonlinear terms in the equations of motion for nonlinear systems may be considered as additional external forces, and on the fact that by doing so such equations of motion can be interpreted as the equations of motion of an equivalent linear system, excited by a modified ground motion. These linear equations are then subjected to a conventional modal decomposition and transformed, as with linear systems, into a set of independent differential equations, each representing the system’s response in one of its modes of vibration. To increase the efficiency of the method and properly account for the participation of higher modes, these independent equations are solved using Nigam-Jennings technique in conjunction with the so-called mode-acceleration method. In addition, an iterative scheme is introduced to avoid an inefficient recalculation of the system’s eigenvectors and eigenvalues every time there is a change in the stiffness of one of its elements. The accuracy and efficiency of the method is verified by means of a comparative study with solutions obtained with a conventional direct integration method. In this comparative study, with only a few modes considered, the proposed method accurately predicts the seismic response of three two-dimensional frame structures, but requiring only, on the average, about 43 per cent of the computer time spent when using the direct integration method.

Complex mode superposition method of nonproportionally damped linear systems with hysteretic damping

2020 ◽  
pp. 107754632094346
Author(s):  
Panxu Sun ◽  
Hong Yang ◽  
Yunjun Deng
Keyword(s):  
Linear System ◽  
Time Domain ◽  
Superposition Method ◽  
Viscous Damping ◽  
Complex Mode ◽  
Mode Superposition ◽  
Damping Matrix ◽  
Mode Superposition Method ◽  
Hysteretic Damping ◽  
Damping Model

The vibration response of a damped linear system is always calculated based on the mode superposition method. However, the construction of the damping matrix is difficult for the conventional mode superposition methods based on the viscous damping model, and this problem is much more serious for nonproportionally damped linear systems. The damping matrix based on the hysteretic damping model is easy to construct and unique, which is determined only by the structural stiffness and material loss factor. The time-domain motion equation of a multi-degree-of-freedom nonproportionally damped linear system is easily constructed based on the hysteretic damping model. According to the characteristics of external excitation, the general solution of the corresponding homogeneous equation and special solution of the corresponding nonhomogeneous equation can be solved. By the aid of the easiness of the damping matrix, a complex mode superposition method based on the hysteretic damping model is proposed for the nonproportionally damped linear system. Based on the proposed method, a user subroutine in ANSYS and MATLAB is developed to calculate vibration responses in time-domain dynamic analyses. A shaking table test of a cantilever plate composed of host and damping layers is conducted to validate the proposed method. The method proposed in this article is unconditionally convergent, and its convergence is independent of the time step of time-domain analyses. Compared with the common complex mode superposition method based on the viscous damping model, the simulation results of the proposed method are closer to the test results, and its accuracy and efficiency are higher. In addition, the calculation results of the proposed method are unique, which is irrelevant to the choice of vibration modes.

scholarly journals Seismic Response Analysis of Multi-Story Steel Frames Using BRB and SCB Hybrid Bracing System

2019 ◽  
Vol 10 (1) ◽  
pp. 284 ◽  
Author(s):  
Rong Chen ◽  
Canxing Qiu ◽  
Dongxue Hao
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Steel Frames ◽  
Residual Deformation ◽  
High Energy ◽  
Response Analysis ◽  
Building Structures ◽  
Seismic Capacity ◽  
Story Drift ◽  
Bracing System

Multi-story steel frames are popular building structures. For those with insufficient seismic resistance, their seismic capacity can be improved by installing buckling-restrained braces (BRBs), which is known for high energy dissipation capacity, and the corresponding frame is denoted as BRB frame (BRBF). However, BRBFs are frequently criticized because of excessive residual deformations after earthquakes, which impede the post-event repairing work and immediate occupancy. Meanwhile, self-centering braces (SCBs), which were invented with a particular purpose of eliminating residual deformation for the protected structures, underwent fast development in recent years. However, the damping capability of SCBs is relatively small because their hysteresis is characterized by a flag shape. Therefore, this paper aims to combine these two different braces to form a hybrid bracing system. A total of four combinations are proposed to seek an optimal solution. The multi-story steel frames installed with BRBs, SCBs, and combined braces are numerically investigated through nonlinear static and dynamic analyses. Interested seismic response parameters refer to the maximum story drift ratios, maximum floor accelerations, and residual story drift ratios. The seismic analysis results indicate that the frames using the combined bracing system are able to take the advantages of BRBs and SCBs.

scholarly journals Modeling Traveling Waves Using Mode Superposition

2010 ◽  
Author(s):  
Vivek Jaiswal ◽  
Aditi Sheshadri ◽  
J. Kim Vandiver
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Force Model ◽  
Superposition Method ◽  
Mode Superposition ◽  
Response Characteristics ◽  
Excitation Region ◽  
Mode Superposition Method ◽  
Excitation Force ◽  
Measured Response

Analysis of the data from two Vortex-Induced Vibration (VIV) experiments conducted in the Gulf Stream on a 500-foot-long, 1.43 inches diameter, flexible, tension dominated riser model revealed that the response is predominantly characterized by the presence of traveling waves. It was also observed that the location of the VIV excitation region (power-in) affects the characteristics of the response. The conventional method of modeling the excitation force as a standing wave was found inadequate to predict the location of the peak measured response accurately, especially in the cases where the excitation region is close to a boundary (the ends of the riser model). A modified excitation force model consisting of a combination of standing and traveling wave excitation regions is demonstrated to predict the location of the peak response more accurately. This work presents the idea of modifying the VIV excitation model to include traveling wave characteristics and using mode superposition method for computing the response to this modified force. Examples of the implementation of this method are shown for the two distinct cases of the location of the power-in region — the power-in region adjacent to the boundary and the power-in region away from the boundary. Depending on the location of the power-in region, different proportions of standing and traveling wave excitations are used to yield predicted responses that match the measured response characteristics.

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