Earthquake Barcode from a Single-Degree-of-Freedom System

Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated.The analysis is based on a special Zhuravlev transformation,which reduces the system to the one without impacts or velocity jumps,and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses.The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset.A perturbation-based moment closure scheme is proposed for the case of nonzero offset.The effects of damping,detuning,and bandwidth and magnitudes of the random excitations are analyzed.The theoretical analyses are verified by the numerical results.The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

Probability-based analytical model for predicting the post-earthquake residual deformation of SDOF systems

A probability-based analytical model for predicting the seismic residual deformation of bilinear single-degreeof-freedom(SDOF)systems with a kinematic/Takeda hysteretic model is proposed based on a statistical analysis of the nonlinear time history response,and the proposed model explicitly incorporates the influence of record-to-record variability.In addition,the influence of primary parameters such as the natural vibration period,relative yield force coefficient,stiffness ratio and peak ground acceleration(PGA)on the seismic residual/maximum deformation ratio(dR/dm)are investigated.The results show that significant dispersion of the dR/dm ratio is observed for SDOF systems under different seismic ground motion records,and the dispersion degree is influenced by the model parameters and record-to-record variability.The statistical distribution of the dR/dm results of SDOF systems can be described by a lognormal distribution.Finally,a case study for seismic residual deformation and reparability assessment of the bridge structure designed with a single pier is carried out to illustrate the detailed analytical procedure of the probability-based analytical model proposed in this study.

A discretely damped SDOF model for the rocking response of freestanding blocks

This paper presents a single-degree-of-freedom(SDOF)constitutive model for assessing the performance of freestanding block contents of buildings.The model incorporates a bespoke damper to account for energy dissipation associated with rocking.It is advantageous in its direct correlation,via energy conservation,to the restitution coefficient for impact during rocking.A comparative study with the existing SDOF rocking models shows that the proposed model significantly improves the accuracy of free-rocking simulations,in which inherent damping predominantly affects response.It provides a promising and efficient tool for computationally intensive performance evaluation of nonstructural components.

Design and Optimization for the Occupant Restraint System of Vehicle Based on a Single Freedom Model

Throughout the vehicle crash event, the interactions between vehicle, occupant, restraint system (VOR) are complicated and highly non-linear. CAE and physical tests are the most widely used in vehicle passive safety development, but they can only be done with the detailed 3D model or physical samples. Often some design errors and imperfections are difficult to correct at that time, and a large amount of time will be needed. A restraint system concept design approach which based on single-degree-of-freedom occupant-vehicle model (SDOF) is proposed in this paper. The interactions between the restraint system parameters and the occupant responses in a crash are studied from the view of mechanics and energy. The discrete input and the iterative algorithm method are applied to the SDOF model to get the occupant responses quickly for arbitrary excitations (impact pulse) by MATLAB. By studying the relationships between the ridedown efficiency, the restraint stiffness, and the occupant response, the design principle of the restraint stiffness aiming to reduce occupant injury level during conceptual design is represented. Higher ridedown efficiency means more occupant energy absorbed by the vehicle, but the research result shows that higher ridedown efficiency does not mean lower occupant injury level. A proper restraint system design principle depends on two aspects. On one hand,the restraint system should lead to as high ridedown efficiency as possible, and at the same time, the restraint system should maximize use of the survival space to reduce the occupant deceleration level. As an example, an optimization of a passenger vehicle restraint system is designed by the concept design method above, and the final results are validated by MADYMO, which is the most widely used software in restraint system design, and the sled test. Consequently, a guideline and method for the occupant restraint system concept design is established in this paper.

On modal energy in civil structural control

A new control strategy based on modal energy criterion is proposed to demonstrate the effectiveness of the control system in reducing structural earthquake responses. The modal control algorithm combining LQR(linear quadratic regulator) control algorithm is adopted in the discrete time-history analysis. The various modal energy forms are derived by definition of the generalized absolute displacement vector. A preliminary numerical study of the effectiveness of this control strategy is carried out on a 20-storey framed steel structural model. The controlled performance of the model is studied from the perspectives of both response and modal energy. Results show that the modal energy-based control strategy is very effective in reducing structural responses as well as in consuming a large amount of modal energy,while augmentation of additional generalized control force corresponding to the modes that contain little modal energy is unnecessary,as it does little help to improve the controlled structural performance.

A simplified model to predict blast response of CFST columns

In order to study the dynamic response of concrete-filled steel tube(CFST) columns against blast loads,a simplified model is established utilizing the equivalent single-degree-of-freedom(SDOF) method,which considers the non-uniform distribution of blast loads on real column and the axial load-bending moment(P-M) interaction of CFST columns.Results of the SDOF analysis compare well with the experimental data reported in open literature and the values from finite element modeling(FEM) using the program LS-DYNA.Further comparisons between the results of SDOF and FEM analysis show that the proposed model is effective to predict the dynamic response of CFST columns with different blast conditions and column details.Also,it is found that the maximum responses of the columns are overestimated when ignoring the non-uniformity of blast loads,and that neglecting the effect of P-M interaction underestimates the maximum response of the columns with large axial load ratio against close range blast.The proposed SDOF model can be used in the design of the blast-loaded CFST columns.

Multi-criteria assessment of offshore wind turbine support structures based on dynamic property optimization

Increasing size of wind turbine and deep water deployment have raised the issue of appropriate selection of the most suitable support structure to make offshore wind energy cost competitive.The paper presents an optimization methodology for decision making process of bottom mounted supports of offshore wind turbines （OWTs） through reasonable engineering attributes derivation.Mathematic models of support structures are reduced by the generalized single-degree-of-freedom theory with relatively fewer structural parameters.Soft-stiff design optimization based on dynamic properties of OWTs is performed for monopile and lattice supports with different wind turbines,water depth and hub height.Attributes of support structures,wind turbines and environment conditions are applied in the multi-criteria decision making method——TOPSIS for benchmarking of those options.The results illustrate the effectiveness of the proposed optimazation methodology combined with economical and environmental attributes together.

Numerical study on the correlation of transonic single-degree-of-freedom flutter and buffet

Transonic single-degree-of-freedom(SDOF) flutter and transonic buffet are the typical and complex aeroelastic phenomena in the transonic flow. In this study, transonic aeroelastic issues of an elastic airfoil are investigated using Unsteady Reynolds-Averaged Navier-Stokes(URANS) equations. The airfoil is free to vibrate in SDOF of pitching. It is found that, the coupling system may be unstable and SDOF self-excited pitching oscillations occur in pre-buffet flow condition, where the free-stream angle of attack(AOA) is lower than the buffet onset of a stationary airfoil. In the theory of classical aeroelasticity, this unstable phenomenon is defined as flutter. However, this transonic SDOF flutter is closely related to transonic buffet(unstable aerodynamic models) due to the following reasons. Firstly, the SDOF flutter occurs only when the free-stream AOA of the spring suspended airfoil is slightly lower than that of buffet onset, and the ratio of the structural characteristic frequency to the buffet frequency is within a limited range. Secondly, the response characteristics show a high correlation between the SDOF flutter and buffet. A similar "lock-in" phenomenon exists, when the coupling frequency follows the structural characteristic frequency. Finally, there is no sudden change of the response characteristics in the vicinity of buffet onset, that is, the curve of response amplitude with the free-stream AOA is nearly smooth. Therefore, transonic SDOF flutter is often interwoven with transonic buffet and shows some complex characteristics of response, which is different from the traditional flutter.

Development of dimensionless P-I diagram for curved SCS sandwich shell subjected to uniformly distributed blast pressure

The curved steel-concrete-steel(SCS)sandwich shell was recently proposed to resist blast loading and it showed better blast resistant performance as compared to flat SCS sandwich shell via developing compressive force along the shell.In this paper,a dimensionless Pressure-Impulse(P-I)diagram was constructed as a convenient tool to predict the damage level of curved SCS sandwich shell subjected to uniformly distributed blast loading.The curved SCS sandwich shell was equivalent to a single-degree-oMreedom(SDOF)system and the equation of motion was established by employing the Lagrange's equation.To construct the dimensionless P-I diagram,the energy balance method was utilized to yield the pressure and impulse asymptotes and the responses in the dynamic response regime were obtained via employing the SDOF method.Then,the finite element method was employed to validate the developed dimensionless P-I diagram.Finally,the procedures of using the constructed dimensionless P-I diagram to quickly conduct the blast resistant design of curved SCS sandwich shell were presented.