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This paper investigates the topology optimization design of viscoelastic planar shell structures to minimize the random vibration intensity under non-stationary random excitation. The excitation is is modeled as uniformly modulated evolutionary random process. The viscoelastic material is characterized using the Golla Hughes McIavish (GHM) model, and dissipative coordinates are introduced to construct the augmented system equations. To measure the intensity of random responses, the averaged power spectral density (PSD) of the displacement response over a specific frequency band and time interval is considered as the design objective and solved by a scheme that combines the pseudo excitation method (PEM) and the high precision direct (HPD) integration method. The relative density of the viscoelastic material is the design variable. The density-based approach is employed to achieve the optimal distribution. Sensitivity analysis is performed to obtain gradient information. The proposed method is verified through numerical simulation. In addition, the effects of frequency band, time interval, ambient temperature and multiple excitations on the optimization results are also discussed.

As a kind of good damping material, viscoelastic material is widely used in machinery, civil engineering, and other fields. In this paper, the viscoelasticity of the system is described by fractional differentiation. The dynamic response of a unilateral vibro-impact system with a viscoelastic oscillator under joint random excitation is studied, in which joint random excitation is composed of additive and multiplicative white noise. The fractional-order derivative was calculated based on Caputo’s definition, and the fractional derivative was equivalent to the corresponding linear damping force and linear restoring force. As a result, a new random system without fractional-order terms was obtained. A non-smooth transformation was introduced, which was equivalent to the original system to a new system without a velocity jump. The steady-state probability density functions of fractional-order vibro-impact systems under joint random excitation are solved by using the random average method and non-smooth transformation. In addition, the effects of parameters on the steady-state response of the system are analyzed.

The coupling effect of bending and torsion caused by plane irregularity of the isolated curved beam bridge makes its seismic response more complex than that of the isolated straight beam bridge. In order to study the influence of multi-dimensional non-stationary random excitation considering torsion component on seismic response of tqiongw@mls.sinanet.com he isolated curved beam bridge. The classical Bouc-Wen model was used to simulate the hysteretic characteristics of the curved beam bridge, and the nonlinear dynamic equation considering the eccentricity of superstructure was established. The pseudo excitation was transformed into harmonic external load by Euler formula, and combining with the precise integration method, the precise integration forms of the special solution under different modulation functions were derived. By using these integral forms to solve the response at each time, the time-varying variance of displacement of the isolated curved beam bridge under multi-dimensional non-stationary random excitation was obtained, and the law of time-varying variance of displacement, including the upper and lower structures of the isolated curved beam bridge, was analyzed with different deck width, curvature radius and yield ratio of bearing. The results show that the multi-dimensional non-stationary random excitation with torsion component has significant influence on the seismic response of the isolated curved beam bridge. Under the rare non-stationary random excitation, the dynamic response of the isolated curved beam bridge presents strong non-stationarity, and the time-lag phenomenon is apparent. For the isolated curved beam bridge with large deck width and small yield ratio of bearing, the influence of non-stationary random excitation on the structure is particularly obvious. The influence of non-stationary random excitation considering torsion component on dynamic response of the isolated curved beam bridge with large deck width, small curvature radius and large yield ratio of bearing is more significant.

Results on the behaviour of a pendulum which is parametrically excited by large amplitude random loads at its pivot are presented, including a novel experimental case study. Thereby, it is dealt with a random excitation by a non-white Gaussian stochastic process with prescribed spectral density. Special focus is devoted to stochastic processes resulting from random sea wave elevation and the question whether random sea waves can lead to rotational motion of the parametrically excited pendulum. The motivation for such an experimental study is energy harvesting from ocean waves.

The technique of harvesting the energy from base structural vibration through a piezoelectric transducer attached at an appropriate location on the vibrating structure is gaining popularity in recent years. Although the amount of energy harvested depends on the type and magnitude of base excitation, the energy harvest under random excitation as compared to equivalent harmonic excitations is not yet well understood and is investigated in this paper through a cantilever energy harvester. Initially, the energy harvested under harmonic excitations is numerically simulated and experimentally validated under increasing base accelerations with different load resistances. Subsequently, the performance of this energy harvester is experimentally studied under random excitations. The results demonstrate that the harvested energy (a) reaches maximum value when the base excitation matches the natural frequency of the harvester, (b) increases with the increase in base accelerations irrespective of the type of excitation, and (c) increases by 2-14 times under random excitations as compared to equivalent harmonic excitations i.e. under same energy input. It is recommended that the energy harvester be used in aerospace structures where random vibration amplitude is higher, to harvest more energy.

Unwanted vibrations of vehicles are regarded as harmful threats to human health in biomechanical and psychophysical terms. Road roughness is considered as the main cause of unwanted vibrations of bus vehicles. Vertical seat vibrations were found via simulating a 10-Degree-Of-Freedom (10-DOF) model of an intercity bus vehicle under harmonic and random excitations caused by road roughness. To suppress undesirable vibrations, mass-spring-damper passive absorbers were proposed in a 13-Degree-Of-Freedom (13-DOF) model of the bus. Following the optimization of the characteristics of embedded passive absorbers under each seat and implementation of the designed absorbers, the vertical displacement amplitudes in the frequency responses of the seats were reduced, especially near the resonant frequencies of the bus. In addition, vertical displacement and acceleration amplitudes decreased in the random excitation of road roughness. According to the results, optimized mass-spring-damper absorbers were proposed as a practical solution to suppress the effects of unwanted vibration on bus vehicles.

An approximate procedure for predicting the stationary response of a stochastically excited nonlinear Markovian jump system under wide-band random excitation is proposed. Firstly, a weighted-average system in probability can be established to approximate the original one. Then by using the stochastic averaging method, the weighted-average system was reduced to the one described by a one-dimensional averaged Itô equations. The approximate stationary probability densities of the original system are obtained for different jump rules by solving the associated Fokker–Plank–Kolmogorov equation. Finally, an example of Markovian jump Duffing system excited by wide-band random excitation to illustrate the proposed method in detail and the effectiveness of the proposed method is verified via comparing the analytical results with those from Monte Carlo simulation.

hing dynamics in a square tank are numerically investigated when the tank is subjected to horizontal, narrowband random ground excitation. The natural frequencies of the two predominant sloshing modes are identical and therefore 1:1 internal resonance may occur. Galerkin’s method is applied to derive the modal equations of motion for nonlinear sloshing including higher modes. The Monte Carlo simulation is used to calculate response statistics such as mean square values and probability density functions (PDFs). The two predominant modes exhibit complex phenomena including “autoparametric interaction” because they are nonlinearly coupled with each other. The mean square responses of these two modes and the liquid elevation are found to differ significantly from those of the corresponding linear model, depending on the characteristics of the random ground excitation such as bandwidth, center frequency and excitation direction. It is found that the direction of the excitation is a significant factor in predicting the mean square responses. The frequency response curves for the same system subjected to equivalent harmonic excitation are also calculated and compared with the mean square responses to further explain the phenomena. Changing the liquid level causes the peak of the mean square response to shift. Furthermore, the risk of the liquid overspill from the tank is discussed by showing the three-dimensional distribution charts of the mean square responses of liquid elevations.

Hypersonic vehicles are subjected to intense aerodynamic noise loads during service, and noise fatigue life assessment is of great significance in the design stage. Aerodynamic noise load is essentially a broadband random excitation, and its fatigue life assessment mainly consists of three core modules: the compilation of the noise load spectrum, the analysis of random vibration response, and the calculation of structural fatigue damage. In order to improve the computational efficiency and strengthen the correlation between the analysis steps, this study develops a set of computational procedures based on Python programming language, which realizes the integrated and rapid processing of the fatigue life assessment of aerodynamic noise. In terms of the calculation method, a fatigue hotspot localization method based on the modal stress approach is proposed, and the modal contribution coefficient is introduced to narrow the selection range of fatigue hotspots and improve the calculation efficiency. Taking a typical stiffened plate as an example, the new method is demonstrated to have high accuracy in locating fatigue hotspots, as well as the computational program has high accuracy in fatigue life estimation. This method can significantly reduce the calculation time and storage space, and improve the utilization efficiency of resources.

Simultaneously determining the random vibration responses and dynamic reliabilities of thin shell coupling geometric nonlinearity and multisource uncertainties is an intractable task. A novel non-intrusive framework based on direct probability integral method (DPIM) is proposed in the present study, which offers an efficient and competitive solution tool to tackle this challenging issue. New framework incorporating DPIM with adaptive schemes can address efficiently stochastic dynamic responses and reliability determination of geometrically nonlinear thin shells in a unified way. Adaptive choosing strategy of the smoothing parameter of Dirac function and the number of representative points is adopted. Importantly, a judgment criterion is established to adaptively perform nonlinear theory and linear theory of large deflection for thin shell, which breaks the limitation of using a single nonlinear or linear theory and results in more accurate responses. Finally, several numerical examples demonstrate that the proposed framework possesses high accuracy and efficiency when compared to Monte Carlo simulation (MCS) and quasi-MCS for computing stochastic deflection and stress responses and dynamic reliabilities. The transform of probability density function of deflection responses from unimodal to bimodal distribution implies that the stochastic P-bifurcation occurs in random vibration of nonlinear thin shell. The remarkable effects of sound pressure level of noise excitation, power spectral density of random excitation, random parameter variability and boundary conditions on uncertainty quantification of thin shells are revealed.