• Steel and Composite Structures
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• v.22 no.3
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• pp.677-690
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• 2016

In this paper, the effect of damping ratio on nonlinear dynamic analysis response and dynamic increase factor (DIF) in nonlinear static analysis of structures against column removal are investigated and a modified empirical DIF is presented. To this end, series of low and mid-rise moment frame structures with different span lengths and number of storeys are designed and the effect of damping ratio in DIF is investigated, performing several nonlinear static and dynamic analyses. For each damping ratio, a nonlinear dynamic analysis and a step by step nonlinear static analysis are carried out and the modified empirical DIF formulas are derived. The results of the analysis reveal that DIF is decreased with increasing damping ratio. Finally, an empirical formula is recommended that relates to damping ratio. Therefore, the new modified DIF can be used with nonlinear static analysis instead of nonlinear dynamic analysis to assess the progressive collapse potential of moment frame buildings with different damping ratios.

• Steel and Composite Structures
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• v.48 no.3
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Smart Structures and Systems
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• v.30 no.3
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• pp.239-243
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• 2022

We investigate the influence of nonlinear viscoelastic damping on the response of a cantilever sensor covered by piezoelectric layers in a symmetric or asymmetric configuration. We formulate an initial-boundary-value problem which consistently incorporates both geometric and material nonlinearities including the effect of viscoelastic damping which cannot be ignored for micro- and nano-mechanical sensor operation in a vacuum environment. We employ an asymptotic multiple-scales methodology to yield the system nonlinear frequency response near its primary resonance and employ a model-based estimation procedure to deduce the system damping backone curve from controlled experiments in vacuum. We discuss the effect of nonlinear damping on sensor applications for scanning probe microscopy.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.5
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• pp.445-455
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• 2013

A new linearization model for MR dampers is analyzed. The nonlinear hysteretic damping force model of MR damper can be modeled as a hyperbolic tangent function of currents, positions, and velicities, which is an algebraic function with constant parameters. Model parameters can be identified with numerical method using experimental force-velocity-position data obtained from various operating conditions. The nonlinear hysteretic damping force can be linearized with a given slope of damping coefficient if there exist corresponding currents to compensate for the nonlinearity. The corresponding currents can be calculated from the inverse model when the given linear damping force is set equal to the nonlinear hysteretic damping force. The linearization controller is realized in a DSP controller such that the corresponding currents to satisfy a given damping coefficient should be calculated. Experiments show that the current inputs to the MR damper produce linearized damping force with a given slope of the damping coefficient.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.105-112
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• 2006

The nonlinear damping force model is made to identify the properties of the ER (electro-rheological) fluid suspension damper. The instrumentation is carried out to measure the damping force of the ER damper. The higher order spectral analysis method is used to investigate the nonlinear frequency coupling phenomena with the damping force signal according to the sinusoidal excitation of the damper. The distinctive higher order nonlinear characteristics are observed. The nonlinear damping force model, which has the higher order velocity terms, is proposed with the result of higher order spectrum analysis. The higher order terms coefficients, which vary according to the strength of the electric field, are calculated using the least square method.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.295-303
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• 2018

The semi-analytical method to study the nonlinear dynamic behavior of simply supported spiral stiffened functionally graded (FG) cylindrical shells subjected to an axial compression is presented. The FG shell is surrounded by damping and linear/nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties of the shell and stiffeners are assumed to be FG. Based on the classical plate theory of shells and von $K{\acute{a}}rm{\acute{a}}n$ nonlinear equations, smeared stiffeners technique and Galerkin method, this paper solves the nonlinear vibration problem. The fourth order Runge-Kutta method is used to find the nonlinear dynamic responses. Results are given to consider effects of spiral stiffeners with various angles, elastic foundation and damping coefficients on the nonlinear dynamic response of spiral stiffened simply supported FG cylindrical shells.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.460-465
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• 2002

The nonlinear vibration of the CRT shadow mask is analyzed in consideration of the V-shaped tension distribution and the effect of wire impact damping. The reduced order FEM model of the shadow mask is obtained from dynamic condensation for the mass and stiffness matrices. Damping wire is modeled using the lumped parameter method to effectively describe its contact interactions with the shadow mask. The nonlinear contact-impact model is composed of spring and damper elements, of which parameters are determined from the Hertzian contact theory and the restitution coefficient, respectively. The analysis model of the shadow mask with damping wires is experimentally verified through impact tests of shadow masks performed in a vacuum chamber. Using the validated analysis model of the shadow mask with damping wires, the‘design of experiments’technique is applied to search fur the optimal damping wire configuration so that the vibration attenuation of the shadow mask is maximized.

• Journal of the Korean Geotechnical Society
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• v.24 no.3
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• pp.13-23
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• 2008

In a nonlinear site response analysis which is performed in time domain, small strain damping is modeled as viscous damping through use of various forms of Rayleigh damping formulations. Small strain damping of soil is known to be independent of the loading frequency, but the viscous damping is greatly influenced by the loading frequency. The type of Rayleigh damping formulation has a pronounced influence on the dependence. This paper performs a series of nonlinear analyses to evaluate the degree of influence of the viscous damping formulation on Korean soil profiles. Analyses highlight the strong influence of the viscous damping formulation for soil profiles exceeding 30 m in thickness, commonly used in simplified Rayleigh damping formulation overestimating energy dissipation at high frequencies due to artificially introduced damping. When using the full Rayleigh damping formulation and carefully selecting the optimum modes, the artificial damping is greatly reduced. Results are further compared to equivalent linear analyses. The equivalent linear analyses can overestimate the peak ground acceleration even for shallow profiles less than 20 m in thickness.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.04a
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• pp.120-129
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• 2000

As structure-soil interaction analysis for the seismic analysis of structures requires a nonlinear analysis of a structure-soil system considering the inelastic characteristics of soil layers nonlinear analyses of the foundation-soil system with the horizontal excitation were performed considering the nonlinear soil conditions for the nonlinear seismic analysis of structures. Stiff soil profile of SD and soft soil profile of SE specified in UBC were considered for the soil layers of a foundation and Ramberg-Osgood model was assumed for the nonlinear characteristics of soil layers. Studies on the changes of dynamci stiffnesses and damping rations of surface and embedded foundations depending on foundation size soil layer depth and piles were performed to investigate the effects of the nonlinear soil layer on the horizontal and rotational dynamic stiffnesses and damping ratios of the foundation-soil system According to the study results nonlinear prperties of a soil laryer decreeased horizontal and rotational linear stiffnesses and increased damping ratios largely Effects of foundation size soil layer depth and piles were also significant suggesting the necessity of nonlinear seismic analyses of structures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.341-348
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• 2001

In this study, nonlinear vibration analysis of the cylindrical orthotropic porous thin plate under V-shaped tension distribution with wire impact damping is considered. We make dynamic model of the plate under the tension using commercial FEM code and reduce the number of its degrees of freedom using dynamic condensation. The dynamic model of wire is obtained as lumped mass model from string equation. And then we analyze the nonlinear vibration of the plate including the impact phenomenon between the plate and the wire using the reduced mass and stiffness matrices of the plate and lumped model of the wire. The contact phenomenon between them can be described by impact contact elements composed of contact stiffness coefficients from Hertzian contact theory and contact damping coefficients from restitution coefficient between them. And we discussed the results of nonlinear vibration analysis for variations of their design parameters.