Dynamics of structures: theory and applications to earthquake engineering

Chandler, Adrian

doi:10.1016/s0141-0296(97)83366-4

Cited by 50 publications

(82 citation statements)

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“…By substituting Equation () into Equation (), the following is derived:

{\bf{u}}(t)=\sum _{i=1}^{N}[{{\boldsymbol{\rho }}}_{i}{\dot{q}}_{i}(t)+{{\boldsymbol{\varphi }}}_{i}{q}_{i}(t)]

where

{{\boldsymbol{\rho }}}_{i}=2\text{Re}({\eta }_{i}{{\boldsymbol{\phi }}}_{i})

and

{{\boldsymbol{\varphi }}}_{i}=-2\text{Re}({\bar{\lambda }}_{i}{\eta }_{i}{{\boldsymbol{\phi }}}_{i})

. The modal responses,

{q}_{i}(t)

and

{\dot{q}}_{i}(t)

, can be solved by typical numerical approaches, 33,34 such as the Newmark‐β method. Compared with Equation (), the coefficient vector (

{{\boldsymbol{\rho }}}_{i}

{{\boldsymbol{\varphi }}}_{i}

) and unknown quantity (

{q}_{i}(t)

) in the foregoing equation are all in the form of real numbers, which are convenient to use in actual calculations.…”

Section: Complex Mode Analysis Methods For Damped Structuresmentioning

confidence: 99%

“…, can be solved by typical numerical approaches, 33,34 such as the Newmark-β method. Compared with Equation (29), the coefficient vector (ρ i , φ i ) and unknown quantity (q t ( ) i ) in the foregoing equation are all in the form of real numbers, which are convenient to use in actual calculations.…”

Section: Fundamental Equation Of Motion Of Ccqc Mode Superposition Me...mentioning

confidence: 99%

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Investigation of nonproportional damping characteristics of structure with energy dissipation system

Wang

Tan

Huang

et al. 2023

Earthquake Engineering and Resilience

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The spatial and traveling wave effects on a structure with an energy dissipation system can be conveniently considered using the random vibration method. In this study, the pseudo‐excitation method is introduced to perform random spatial seismic response analysis of such a structure considering different damper arrangements. The analysis results show the effects of nonproportional damping characteristics due to these arrangements, and the nonproportional damping characteristic index can estimate the strength of these characteristics. Moreover, the virtual excitation method can be used to determine the weak parts of the structure. The effect of the traveling wave on the energy dissipation system and damping structure is relatively low. The response results of the structure in the case of multipoint consistent excitation obtained by the complex vibration decomposition reaction spectrum method are compared. The method accounts for the effects of nonproportional damping and vibration velocity. Accurate time history results can be obtained by complex vibration decomposition time history analysis.

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“…By substituting Equation () into Equation (), the following is derived:

{\bf{u}}(t)=\sum _{i=1}^{N}[{{\boldsymbol{\rho }}}_{i}{\dot{q}}_{i}(t)+{{\boldsymbol{\varphi }}}_{i}{q}_{i}(t)]

where

{{\boldsymbol{\rho }}}_{i}=2\text{Re}({\eta }_{i}{{\boldsymbol{\phi }}}_{i})

and

{{\boldsymbol{\varphi }}}_{i}=-2\text{Re}({\bar{\lambda }}_{i}{\eta }_{i}{{\boldsymbol{\phi }}}_{i})

. The modal responses,

{q}_{i}(t)

and

{\dot{q}}_{i}(t)

, can be solved by typical numerical approaches, 33,34 such as the Newmark‐β method. Compared with Equation (), the coefficient vector (

{{\boldsymbol{\rho }}}_{i}

{{\boldsymbol{\varphi }}}_{i}

) and unknown quantity (

{q}_{i}(t)

) in the foregoing equation are all in the form of real numbers, which are convenient to use in actual calculations.…”

Section: Complex Mode Analysis Methods For Damped Structuresmentioning

confidence: 99%

Section: Fundamental Equation Of Motion Of Ccqc Mode Superposition Me...mentioning

confidence: 99%

Investigation of nonproportional damping characteristics of structure with energy dissipation system

Wang

Tan

Huang

et al. 2023

Earthquake Engineering and Resilience

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“…The stresses needed to perform fatigue assessment can be predicted using finite element dynamic analysis in the time or frequency domains. Dynamic behaviour is defined by mass, damping and stiffness matrices (Beards, 1996;Chopra, 2019;Clough and Penzien, 1993) and simplified fatigue loading models from codes and standards (API, 2000;British Standards Institution, 2005;ISO 13819-2:1995ISO 13819-2: , 1995NORSOK Standar, 2004) are usually considered in fatigue analysis.…”

Section: Fatigue Monitoring Of Structures 133mentioning

confidence: 99%

A review on fatigue monitoring of structures

García-Fernández

Aenlle

Álvarez-Vázquez

et al. 2023

IJSI

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PurposeThe purpose of this study is to review the existing fatigue and vibration-based structural health monitoring techniques and highlight the advantages of combining both approaches.Design/methodology/approachFatigue monitoring requires a fatigue model of the material, the stresses at specific points of the structure, a cycle counting technique and a fatigue damage criterion. Firstly, this paper reviews existing structural health monitoring (SHM) techniques, addresses their principal classifications and presents the main characteristics of each technique, with a particular emphasis on modal-based methodologies. Automated modal analysis, damage detection and localisation techniques are also reviewed. Fatigue monitoring is an SHM technique which evaluate the structural fatigue damage in real time. Stress estimation techniques and damage accumulation models based on the S-N field and the Miner rule are also reviewed in this paper.FindingsA vast amount of research has been carried out in the field of SHM. The literature about fatigue calculation, fatigue testing, fatigue modelling and remaining fatigue life is also extensive. However, the number of publications related to monitor the fatigue process is scarce. A methodology to perform real-time structural fatigue monitoring, in both time and frequency domains, is presented.Originality/valueFatigue monitoring can be combined (applied simultaneously) with other vibration-based SHM techniques, which might significantly increase the reliability of the monitoring techniques.

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“…The governing equation of the generalised SDOF system with damping ratio ζ can be expressed as 41 :

\begin{equation}\ddot u + 2\zeta {\omega _1}\dot u + \omega _1^2u\; = \frac{{ - \tilde L{{\ddot u}_g}\left( t \right)}}{{\tilde m}}\;\end{equation}

where

{\ddot u_g}( t )

is the base excitation,

- \tilde L{\ddot u_g}( t )

is the generalised excitation and ω 1 is the frequency:

\begin{equation}\tilde L = \mathop \int \nolimits_0^H \frac{{{m_c}}}{H}\;\;\psi \left( h \right)dh + {m_p}\psi \;\left( H \right) = \frac{1}{2}\;{m_c} + {m_p}\end{equation}

\begin{equation}{\omega _1} = {\left( {\frac{{\tilde k}}{{\tilde m}}} \right)^{0.5}}\; = \sqrt {\frac{{12EI}}{{\left( {\frac{{13}}{{35}}{m_c} + {m_p}} \right){H^3}}}} \;\end{equation}

where

\tilde{m}

…”

Section: Modelling Of Rocking Shear Frame With Tendon Restraintmentioning

confidence: 99%

Seismic internal force in rocking shear frame with superelastic tendon restraint

Tsang

Lam

2023

Earthq Engng Struct Dyn

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A structure with rocking mechanism is able to prolong the period of vibration and reduce seismic internal force. Recent research demonstrated the effectiveness of a tendon made of superelastic material wire connected in series with steel wire in controlling the amount of rotation and providing a source of hysteretic energy dissipation, thereby lowering the risk of overturning to a rigid structure undergoing whole‐body rotation. This article proposed to extend the use of superelastic tendon restraint on a (flexible) shear frame to strike a balance between the need to reduce the seismic force demand and the need to exercise control of the overturning risk. Initially, an analytical model for the rocking response of shear frame with the superelastic tendon restraint was developed. In addition, a physical model of the shear frame with tendon restraint was fabricated and tested under base excitations. Analysis results showed to match with experiment on both strain gauge and rotation sensor readings in the dynamic testing. Simulations and tests were also applied to an unrestrained shear frame for comparison. It was also found that the total deflection of the shear frame during the rocking phase could be described as horizontal vibration about a non‐constant balancing deflection. The analytical models developed for flexible rocking systems were extended in the current study to deal with superelastic tendon restrained rocking shear frames. The validity and versatility were confirmed by shaker table test results.

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Dynamics of structures: theory and applications to earthquake engineering

Cited by 50 publications

References 0 publications

Investigation of nonproportional damping characteristics of structure with energy dissipation system

Investigation of nonproportional damping characteristics of structure with energy dissipation system

A review on fatigue monitoring of structures

Seismic internal force in rocking shear frame with superelastic tendon restraint

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