The existing available research outcomes on vibration attenuation control for time-delay feedback indicate that, for the delay dynamic vibration absorber with fixed time-delay control parameters, under harmonic excitation, a good vibration attenuation control effect occurs on the vibration of the main system. However, the effect is not obvious for complex excitation. Aiming at the above problems, in a short time interval, a harmonic excitation with the same displacement size as the complex excitation was established. Then, by calculating its equivalent amplitude and equivalent frequency, a harmonic equivalent method for complex excitation was proposed in this paper. The time-delay parameters were adjusted according to the equivalent frequency of harmonic equivalent excitation in real time; therefore, a good vibration attenuation control effect was obtained through the delay dynamic vibration absorber in the discrete time interval. In this paper, research on a time-varying delay dynamic vibration absorber was conducted by taking the two-degree-of-freedom vibration system with a delay dynamic vibration absorber as an example. The simulation results show that the proposed control method can reduce the vibration of the main system by about 30% compared with the passive vibration absorber. This can obviously improve the performance of the time-delay dynamic vibration absorber. It provides a new technical idea for the design of vehicle active frame system.

The ground motions in the orientation corresponding to the strongest pulse energy impose more serious demand on structures than that of ordinary ground motions. Moreover, not all near-fault ground motion records present distinct pulses in the velocity time histories. In this paper, the parameterized stochastic model of near-fault ground motion with the strongest energy and pulse occurrence probability is suggested, and the Monte Carlo simulation (MSC) and subset simulation are utilized to calculate the first excursion probability of inelastic single-degree-of-freedom (SDOF) systems subjected to these types of near-fault ground motion models, respectively. Firstly, the influences of variation of stochastic pulse model parameters on structural dynamic reliability with different fundamental periods are explored. It is demonstrated that the variation of pulse period, peak ground velocity and pulse waveform number have significant effects on structural reliability and should not be ignored in reliability analysis. Then, subset simulation is verified to be unbiased and more efficient for computing small reliable probabilities of structures compared to MCS. Finally, the reliable probabilities of the SDOF systems with different fundamental periods subjected to impulsive, non-pulse ground motions and the ground motions with pulse occurrence probability are performed, separately. It is indicated that the ground motion model with the pulse occurrence probability can give a rational estimate on structural reliability. The impulsive and ordinary ground motion models may overestimate and underestimate the reliability of structures with fundamental period much less than the mean pulse period of earthquake ground motions.

The nonlinear time-delay dynamic absorber has a good control effect on the main system under harmonic excitation, but the control effect on the main system under complicated excitation is not obvious. In the previous study, they do not have an effective method to obtain the time-delay control parameters under different external excitations. Because of the above problems, this paper proposed an innovative method to obtain the control parameters of time-delay dynamic absorbers. For the vibration system including the nonlinear time-delay dynamic absorber, the transient time-integration method was used to solve the nonlinear delay dynamic differential equation of the system under the specific excitation. Then, the quantitative relationship was established between the time-domain responses of the vibration system, the external excitation, and time-delay control parameters. The time-delay control parameters would be obtained when the time-domain response of the main system is minimized under specific excitation using an algorithm that continuously compares the objective function that is related to the time-domain response of the main system. This paper took the two-degree-of-freedom vibration system with a nonlinear time-delay dynamic absorber as the target system to simulate the time-domain response of the main system. The simulation results show that the time-delay control parameters calculated by the new method can obtain significant vibration reduction effects for both harmonic excitation and multiharmonic excitation. The suppression performance of the nonlinear time-delay dynamic absorber is significantly improved.

Uncertainties of the ground motions and structural parameters are the main factors that limit the accuracy of embankment seismic fragility assessment. In response to the uncertainties of the ground motions, artificial synthesizing method of the near‐fault pulse‐like ground motions was proposed, and 15 ground motions with the rupture fault distances ranging from 1 to 15 km were synthesized by taking the Chi‐Chi earthquake in Taiwan, China, as an example. The Xi’an‐Baoji expressway K1125 + 470 embankment was taken as the research object, and a total of 12 structural parameters were selected as the design variables, namely, the elastic modulus, bulk modulus, shear modulus, density, cohesion force, and internal friction angle of the embankment fill and soil foundation, respectively. In response to the uncertainties of these parameters, 3 principal components with large impacts on the embankment seismic fragility were extracted based on the principal component analysis. Mapping relationships among the principal components and embankment seismic damages were analyzed using the uniform design response surface method, and the seismic fragility assessment was carried out and the fragility curves were plotted. The research results are consistent with the actual embankment seismic damage conditions of the Chi‐Chi earthquake, indicating that the proposed method is scientific and reasonable. It also shows that it would obviously overestimate the seismic performance in the embankment seismic fragility assessment without considering the uncertainties of the ground motions and structural parameters.

Manufacturing inaccuracies in vehicle suspension systems inevitably lead to uncertainties in the parameters of their structural components. Simultaneously, the road excitation impacting nonlinear vehicle systems exhibits pronounced randomness and time-variant characteristics. Consequently, it is crucial to conduct a stochastic dynamics analysis on nonlinear suspension systems, taking into account these uncertain factors. In this paper, a seven-degree-of-freedom (7-DOF) nonlinear suspension system dynamics model has been established. The stochastic process of road irregularities is simulated using the harmonic superposition method. Moreover, based on the direct probability density integral method, the stochastic dynamic equations of the nonlinear suspension system and their corresponding solution strategies have been developed and explored. Through MATLAB, the time-varying probability density function of the vibration response for a nonlinear vehicle suspension system was calculated under the combined effects of stochastic road irregularity excitation and random coupling of system structural parameters. Additionally, analyses were conducted on how different coefficients of variation and the intensity of nonlinearity in the suspension system influence the probability density of the output body displacement of the nonlinear vehicle suspension system. The research outcomes demonstrate that the direct probability density integral method offers superior efficiency and accuracy when computing nonlinear vehicle suspension systems. Furthermore, altering the coefficients of variation for various system parameters reveals that as these coefficients increase, the disparity in the probability density of body displacement becomes more pronounced, leading to more intense vehicle vibrations. Under soft nonlinear conditions with lower suspension spring stiffness, the probability density function of body displacement shifts slightly to the right with minimal change. However, under strong nonlinear conditions, body displacement significantly increases, resulting in diminished vibration isolation capabilities of the suspension system. This leads to severe jolts and a noticeable decline in ride comfort during vehicle operation.