To investigate the effect of higher modes on the displacement and inner forces in HWBB(hinged wall with buckling-restrained braces in base)-frame structure,distributed parameter models for both the HWBB-hinged frame s...To investigate the effect of higher modes on the displacement and inner forces in HWBB(hinged wall with buckling-restrained braces in base)-frame structure,distributed parameter models for both the HWBB-hinged frame structure and the HWBB-MRF(moment resisting frame)structure are built.The hinged wall is simplified as a flexural beam.BRBs(bucking-restrained braces)are simplified to a rotational spring.MRF is simplified to a shear beam.Vibration equations of distributed parameter models are derived.Natural periods,natural modes of vibration,inner forces and displacements of the distributed parameter models are derived based on the vibration equations using numerical methods.The effect of the relative stiffness ratio and the rotational stiffness ratio on the higher mode effects is investigated.For elastic structures,the global displacement and shear in MRF are predominantly controlled by the first mode,while the shear and bending moment in the wall are significantly affected by higher mode effects.The effect of the yielding of BRB on the inner forces distribution in the HWBB-hinged frame is investigated.The results indicate that the first mode will no longer contribute to the inner forces and the contribution from higher modes to inner forces increases after the BRBs yield.Displacement is not sensitive to higher mode effects and it is controlled by the first mode after the BRBs yield.Parameter analysis demonstrates that the displacement amplitudes are reduced with the increase in the flexural stiffness of the wall before the flexural stiffness reaches a certain value.The first three periods decrease with the increase in the rotational stiffness.With the increase in the rotational stiffness ratio,the contribution from the first mode decreases while contributions from both the second mode and third mode increase.展开更多
In conventional modal analysis procedures,usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings.The number of modes needed in the dynamic analysis depend...In conventional modal analysis procedures,usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings.The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response,which is called the higher-mode effect.The modal analysis approach, however,may not be directly applied to the dynamic analysis of viscoelastically damped buildings.This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency.Therefore,the structural stiffness and damping contributed from those dampers would be different for each mode.In this study,the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes.Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect.Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response.Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings.The higher-mode effect on base shear is less significant than on story acceleration response.Maximum difference of the seismic response usually occurs at the top story.Also,the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers.For practical application,it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence,is on the conservative side.展开更多
基金The National Key Research and Development Program of China(No.2018YFC0705802)the National Natural Science Foundation of China(No.51978165)+1 种基金the Fundamental Research Funds for the Central Universities(No.3205007720)Postgraduate Research and Practice Innovation Program of Jiangsu Province(No.3205007720).
文摘To investigate the effect of higher modes on the displacement and inner forces in HWBB(hinged wall with buckling-restrained braces in base)-frame structure,distributed parameter models for both the HWBB-hinged frame structure and the HWBB-MRF(moment resisting frame)structure are built.The hinged wall is simplified as a flexural beam.BRBs(bucking-restrained braces)are simplified to a rotational spring.MRF is simplified to a shear beam.Vibration equations of distributed parameter models are derived.Natural periods,natural modes of vibration,inner forces and displacements of the distributed parameter models are derived based on the vibration equations using numerical methods.The effect of the relative stiffness ratio and the rotational stiffness ratio on the higher mode effects is investigated.For elastic structures,the global displacement and shear in MRF are predominantly controlled by the first mode,while the shear and bending moment in the wall are significantly affected by higher mode effects.The effect of the yielding of BRB on the inner forces distribution in the HWBB-hinged frame is investigated.The results indicate that the first mode will no longer contribute to the inner forces and the contribution from higher modes to inner forces increases after the BRBs yield.Displacement is not sensitive to higher mode effects and it is controlled by the first mode after the BRBs yield.Parameter analysis demonstrates that the displacement amplitudes are reduced with the increase in the flexural stiffness of the wall before the flexural stiffness reaches a certain value.The first three periods decrease with the increase in the rotational stiffness.With the increase in the rotational stiffness ratio,the contribution from the first mode decreases while contributions from both the second mode and third mode increase.
文摘In conventional modal analysis procedures,usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings.The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response,which is called the higher-mode effect.The modal analysis approach, however,may not be directly applied to the dynamic analysis of viscoelastically damped buildings.This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency.Therefore,the structural stiffness and damping contributed from those dampers would be different for each mode.In this study,the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes.Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect.Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response.Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings.The higher-mode effect on base shear is less significant than on story acceleration response.Maximum difference of the seismic response usually occurs at the top story.Also,the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers.For practical application,it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence,is on the conservative side.
