Explore the vast range of titles available.

Cable structures commonly experience structural damage due to material aging, adverse environmental conditions, and other various factors like overload. Accordingly, accurate prediction of dynamical response and analysis of their vibrational characteristics of damaged cable systems are crucial for achieving effective health monitoring and formulating appropriate repair strategies in cable bridge engineering. In this paper, the nonlinear random vibration of the damaged cable system is studied. First of all, the mathematical model for the damaged cable system under random excitation is formulated, encompassing the determination of the static configuration of the damaged stay cable and the derivation of the nonlinear stochastic dynamic equations governing the in-plane and out-of-plane motions of the damaged cable system. Subsequently, by adopting the radial basis function neural network (RBFNN) method, the reduced Fokker-Planck-Kolomogrov (FPK) equation associated with the discrete stochastic system of damaged cable system is solved to yield the steady-state probability density function (PDF) of the system. Finally, a specific cable example is studied for illustration. Some trends of the steady-state probability distribution of the PDF and the mean value (MV) under different parameters are examined, respectively. The results show that an increase in damage severity and range significantly amplifies the in-plane displacement response, but little affects the out-of-plane motion. The influence of damage location can be almost negligible. The MVs of in-plane displacement exhibit some linear trends with variations in damage severity and range. Additionally, the Monte Carlo simulations (MCS) data is utilized for validating the accuracy of the RBFNN results. The study can provide a practical approach for assessing the healthy operational condition of cable systems during monitoring processes.

The stationary/nonstationary random vibration responses and dynamic reliability analyses of thin plate structures coupling geometrical nonlinearity and multisource randomness in both structural parameters and external excitations are the important issues to be attacked. In this study, the novel direct probability integral method (DPIM) is proposed to tackle them. Firstly, the differential equations of thin plate vibration with large deflection are revisited based on von Kármán nonlinear theory. Then, the non-intrusive DPIM decouples physical evolution and probability density propagation of structure, which is utilized to calculate nonlinear stochastic dynamic responses and reliability of thin plate in a unified way. Moreover, to determine the resultant large-amplitude nonlinear deformation of thin plate under random concentrated excitation and distributed excitation, an important criterion is devised, which can judge the applicability of geometrically nonlinear theory. Several numerical examples demonstrate the high accuracy and efficiency of proposed approach by comparing the results with those of Monte Carlo simulation. It is indicated that, the changes of structural parameters and random excitation cause the transition of probability density functions of nonlinear deflections from unimodal to bimodal distributions. Stochastic P-bifurcation occurs in nonlinear random vibration analysis of thin plate, which implies that the geometric nonlinearity should be rationally considered in stochastic dynamic analysis of structure. Finally, the remarkable effects of geometric nonlinearity, thickness, random parameter variability and boundary conditions on stochastic responses and reliabilities of thin plates are revealed.

The topic this book is the behavior of structural and mechanical systems when they are subjected to unpredictable, or random, vibrations. These vibrations may arise from natural phenomena such as earthquakes or wind, or from human-controlled causes such as the stresses placed on aircraft at takeoff and landing. Study and mastery of this topic enables engineers to design and maintain structures capable of withstanding random vibrations, thereby protecting human life. This book will lead readers in a user-friendly fashion to a thorough understanding of vibrations of linear and nonlinear systems that undergo stochastic \"random\" excitation.

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.

This study presents a non-linear constitutive equation for the rolling guide-shoes associated with a high-speed elevator system. This was done to accurately evaluate the dynamic behavior of a high-speed elevator car and analyze the action mechanism of random factors during manufacturing and installation on the dispersion of vibration acceleration. Through the combination of the Hertz contact theory and the Bouc-Wen hysteretic model, the non-linear vibration model of the elevator car system was founded. This model was equivalent to a linear system by least squares technique, and then the random parameters and the random excitation were converted by random perturbation method and pseudo excitation method. The acceleration response sensitivities of each random parameters, the means and standard deviations of transverse vibration acceleration responses at the observation point were obtained. In the case, the transverse vibration acceleration responses of the car system were calculated. The elevator car’s vibration instance was analyzed under the different degrees of variation of the random parameters and the random excitation. The results showed that the randomness of geometric parameters has the greatest influence on transverse acceleration. The variability of parameters affects the dispersion degree of the transverse vibration responses while the variability of the excitation mainly affects the amplitude of the vibration response. This study provides an effective method for the analysis of non-linear compound random vibration responses of high-speed elevator car system, and provides a reference for the vibration control design and safety assessment.

Since the well-known Millennium bridge accident happened at the beginning of this century, both researchers and engineers realized that the human-induced vibration may lead to unaffordable consequences. Although such vibrations hardly threaten the safety of the structure, the large vibration may affect the functionalities of the structure, causing the serviceability problem. The first study on the human-induced vibration serviceability problem started from the measurement of human-induced load, with many mathematical models proposed. The strong randomness of the measured data led to the investigation on the randomness feature of the load. With the research going deeper, the phenomenon of human–structure interaction was found, which attracted the researchers to study the randomness of the human body dynamic properties that may affect the structural response. Once the interaction mechanism and the system parameters became available, random vibration analysis methods could be proposed to calculate human-induced random vibration, providing the foundation of the reliability analysis from the perspective of vibration serviceability. Such reliability is highly related to subjective feelings of the human body, which has also been deeply studied in the literature. Furthermore, the purpose of studying the dynamic reliability is to conduct the reliability-based structural design. This paper provides a review of the research on human-induced vibration serviceability following the above logic, from the first attempt on load measurement towards the modern techniques for performance-based vibration serviceability design.

In applications such as carrier attitude control and mobile device navigation, a micro-electro-mechanical-system (MEMS) gyroscope will inevitably be affected by random vibration, which significantly affects the performance of the MEMS gyroscope. In order to solve the degradation of MEMS gyroscope performance in random vibration environments, in this paper, a combined method of a long short-term memory (LSTM) network and Kalman filter (KF) is proposed for error compensation, where Kalman filter parameters are iteratively optimized using the Kalman smoother and expectation-maximization (EM) algorithm. In order to verify the effectiveness of the proposed method, we performed a linear random vibration test to acquire MEMS gyroscope data. Subsequently, an analysis of the effects of input data step size and network topology on gyroscope error compensation performance is presented. Furthermore, the autoregressive moving average-Kalman filter (ARMA-KF) model, which is commonly used in gyroscope error compensation, was also combined with the LSTM network as a comparison method. The results show that, for the x-axis data, the proposed combined method reduces the standard deviation (STD) by 51.58% and 31.92% compared to the bidirectional LSTM (BiLSTM) network, and EM-KF method, respectively. For the z-axis data, the proposed combined method reduces the standard deviation by 29.19% and 12.75% compared to the BiLSTM network and EM-KF method, respectively. Furthermore, for x-axis data and z-axis data, the proposed combined method reduces the standard deviation by 46.54% and 22.30% compared to the BiLSTM-ARMA-KF method, respectively, and the output is smoother, proving the effectiveness of the proposed method.

Topology optimization has been mainly addressed for structures under static loads using a deterministic setting. Nonetheless, many structural systems are subjected to uncertain dynamic loads, and thus efficient approaches are required to evaluate the optimal topology in such kind of applications. Within this framework, the present paper deals with the topology optimization of multi-story buildings subjected to seismic ground motion. Because of the inherent randomness of the earthquakes, the uncertain system response is determined through a random vibration-based approach in which the seismic ground motion is described as filtered white Gaussian noise with time-varying amplitude and frequency content (i.e., fully non-stationary seismic ground motion). The paper is especially concerned with the assessment of the dynamic response sensitivity for the gradient-based numerical solution of the optimization problem. To this end, an approximated construction of the gradient is proposed in which explicit, exact derivatives with respect to the design variables are computed analytically through direct differentiation for a sub-assembly of elements (up to a single element) resulting from the discretization of the optimizable domain. The proposed strategy is first validated for the simpler case of stationary base excitation by comparing the results with those obtained using an exact approach based on the adjoint method, and its correctness is ultimately verified for the more general case of non-stationary seismic ground motion. Overall, this validation demonstrates that the proposed approach leads to accurate results at low computational effort. Further numerical investigations are finally presented to highlight to what extent the features of the non-stationary seismic ground motion influence the optimal topology.

A new approach for creating a non-ergodic pseudo-spectral acceleration ( PSA ) ground-motion model (GMM) is presented, which accounts for the magnitude dependence of the non-ergodic effects. In this approach, the average PSA scaling is controlled by an ergodic PSA GMM, and the non-ergodic effects are captured with non-ergodic PSA factors, which are the adjustment that needs to be applied to an ergodic PSA GMM to incorporate the non-ergodic effects. The non-ergodic PSA factors are based on the effective amplitude spectrum ( EAS ) non-ergodic effects and are converted to PSA through Random Vibration Theory (RVT). The advantage of this approach is that it better captures the non-ergodic source, path, and site effects through small-magnitude earthquakes. Due to the linear properties of the Fourier Transform, the EAS non-ergodic effects of the small events can be applied directly to the large magnitude events. This is not the case for PSA , as response spectra are controlled by a range of frequencies, making PSA non-ergodic effects dependent on the spectral shape, which in turn is magnitude-dependent. Two PSA non-ergodic GMMs are derived using the ASK14 (Abrahamson et al. in Earthq Spectra 30:1025–1055, 2014) and CY14 (Chiou and Youngs in Earthq Spectra 30:1117–1153, 2014) GMMs as backbone models, respectively. The non-ergodic EAS effects are estimated with the LAK21 (Lavrentiadis et al. in Bull Earthq Eng ) GMM. The RVT calculations are performed with the V75 (Vanmarcke in ASCE Mech Eng Mech Division 98:425–446, 1972) peak factor model, the D a 0.05 - 0.85 estimate of AS96 (Abrahamson and Silva in Apendix A: empirical ground motion models, description and validation of the stochastic ground motion model. Tech. rep.,. Brookhaven National Laboratory, New York) for the ground-motion duration, and BT15 (Boore and Thompson in Bull Seismol Soc Am 105:1029–1041, 2015) oscillator-duration model. The California subset of the NGAWest2 database (Ancheta et al. in Earthq Spectra 30:989–1005, 2014) is used to fit both models. The total aleatory standard deviation of each of the two non-ergodic PSA GMMs is approximately 25 % smaller than the total aleatory standard deviation of the corresponding ergodic PSA GMMs. This reduction has a significant impact on hazard calculations at large return periods. In remote areas, far from stations and past events, the reduction of aleatory variability is accompanied by an increase in epistemic uncertainty.

The present article proposes a novel method to reduce phase noise in a PLL based X-Band source consisting of oscillating and non-oscillating components for the use in Pulse Doppler radar. It also provides phase noise performance stabilization under random vibration. The method consists of improved electrical design and PCB layout, noise filtering technique and passive isolation scheme to suppress vibration-induced noise. Acceleration sensitivity is an important requirement for radars and sensors mounted in unmanned aerial vehicles, aircrafts, missiles and other dynamic platforms. These systems provide superior performance when subjected to severe environmental condition. However, mechanical vibration and acceleration can introduce physical deformation that thereby degrades the frequency source generated signal phase noise. It effects the complete radar system that depends on frequency source performance. The development and testing of a stable X-Band source at 10.64 GHz using indirect method has been carried out which proved that the phase noise is stable both in steady state and under random vibration of 7g magnitude. The study of critical design aspects of test fixture, test object mounting arrangement, investigation on vibration response and performance stabilization along with description of test setup and measurement procedure has been reported. An improvement of around 35-40 dB in phase noise is achieved at close-in offset frequencies. Few challenges and suggestions for the accurate measurement of random vibration testing for frequency sources have also been mentioned.