Method for analyzing random response of non-proportional damping structure under earthquake action

A random response, damping structure technology, used in special data processing applications, instruments, electrical digital data processing, etc.

Active Publication Date: 2019-08-02
SOUTHWEST JIAOTONG UNIV
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  • Abstract
  • Description
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Problems solved by technology

For long-span flexible structures with dense frequency distribution, tens of thousands of time-history analyzes may be required, and the above methods still face challenges at this time

Method used

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  • Method for analyzing random response of non-proportional damping structure under earthquake action
  • Method for analyzing random response of non-proportional damping structure under earthquake action
  • Method for analyzing random response of non-proportional damping structure under earthquake action

Examples

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example 1

[0087] Example 1: Linear structures for response analysis of tall buildings excited by earthquakes.

[0088] Consider a 20-story non-proportional damped building structure under earthquake action, its simplified model is as follows figure 1 shown. The structure parameter is m i = 10000kg and k i =16000kN / m (1≤i≤20). Its equation of motion is given as follows:

[0089]

[0090] Where: M=diag[m i ]; K = diag[k i ]; is the seismic acceleration process; E is the unit vector. Assume the damping matrix of the structure is C=C s +C r , where C s =0.3M+0.002K, C r (1,1)=20×C s (1,1), C r All other elements are 0.

[0091] Assumed earthquake acceleration process is a non-stationary random process, and its EPSD is given as

[0092]

[0093] In the formula: f is the Hertz frequency; S 0 =1 / 690m 2 the s -3 ; c=2; d=0.2. In order to evaluate the accuracy and efficiency of the fast convolution method, the response of the structure under this completely non-statio...

example 2

[0096] Example 2: Nonlinear structure for response analysis of delayed systems subjected to earthquakes.

[0097] Consider one such as Figure 4 The 100 degrees of freedom hysteresis system shown. The lumped mass of each layer of the system and the initial linear stiffness between layers are m i = 3000kg and k i =8×10 7 N / m(1≤i≤50), m i = 2500kg and k i =7.5×10 7 N / m (51≤i≤100). The stiffness reduction factor of each layer is γ i =0.6 (1≤i≤100). The parameter of the hysteresis displacement of each layer is φ i = 1, beta i =300m -1 and θ i =1 (1≤i≤100). The damping matrix C is defined by the Rayleigh damping model, and its proportional coefficient is determined by the damping ratio of the first mode and the 100th mode of the initial linear system as 0.05. The system is excited by a non-stationary ground acceleration Its EPSD is defined by the formula, where S 0 =0.02m 2 the s -3 . In the response calculation, the cut-off frequency is selected as 8Hz, and t...

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Abstract

The invention discloses a method for analyzing a random response of a non-proportional damping structure under an earthquake effect. The method comprises the following specific steps: 1, acquiring a unit impulse response of the structure about any excitation; 2, based on a random vibration theory, establishing a direct convolution formula responding to power spectrum calculation; 3, performing PODfeature orthogonal decomposition on the non-uniform modulation function excited by each point; and 4, calculating an evolution frequency response matrix by using FFT, and further determining an evolution power spectrum matrix and a variance matrix of the structure response. According to the method, the response statistics is explicitly represented as the convolution form about the pulse response,and the convolution is calculated by using the FFT technology, so that the response calculation efficiency is greatly improved; the method is suitable for a linear structure, is also suitable for a nonlinear structure, and can also be used for a linear system subjected to order reduction through a modal superposition method.

Description

technical field [0001] The invention belongs to the field of random vibration analysis, in particular to an analysis method for the random response of a non-proportional damping structure under earthquake action. Background technique [0002] The non-proportional damping characteristics have a considerable influence on the dynamic response of the structure. In some cases, the structural damping cannot be assumed to be proportional damping, such as the mixed structural system of the bottom concrete structure-superior steel structure, structures with dampers and seismic isolation structures. Wait. In addition, in the nonlinear random vibration analysis based on equivalent linearization, the equivalent linear system is also a non-proportional damping system due to the introduction of an additional equivalent matrix. [0003] Engineering structures are often affected by non-stationary excitations such as earthquakes, and the analysis of such problems usually relies on non-stati...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
CPCG06F2119/06G06F30/20
Inventor 赵宁黄国庆刘瑞莉
Owner SOUTHWEST JIAOTONG UNIV
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