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.

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.