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This paper develops an efficient method termed as PE-PIM to address the exact nonstationary responses of pavement structure, which is modeled as a rectangular thin plate resting on bi-parametric Pasternak elastic foundation subjected to stochastic moving loads with constant acceleration. Firstly, analytical power spectral density (PSD) functions of random responses for thin plate are derived by integrating pseudo excitation method (PEM) with Duhamel's integral. Based on PEM, the new equivalent von Mises stress (NEVMS) is proposed, whose PSD function contains all cross-PSD functions between stress components. Then, the PE-PIM that combines the PEM with precise integration method (PIM) is presented to achieve efficiently stochastic responses of the plate by replacing Duhamel's integral with the PIM. Moreover, the semi-analytical Monte Carlo simulation is employed to verify the computational results of the developed PE-PIM. Finally, numerical examples demonstrate the high accuracy and efficiency of PE-PIM for nonstationary random vibration analysis. The effects of velocity and acceleration of moving load, boundary conditions of the plate and foundation stiffness on the deflection and NEVMS responses are scrutinized. [ABSTRACT FROM AUTHOR]

Resonance can be avoided by preventing the structural natural frequencies from falling within the operating frequency range. However, structural natural frequencies are influenced by uncertain parameters, such as material properties and geometric sizes. Therefore, it is essential to consider these uncertainties during the conceptual design phase. To address this problem, a novel reliability-based eigenvalue topology optimization model under frequency-band constraints is established, in which the uncertainties of the material properties and structural size are considered. Owing to the high computational costs of dealing with frequency-band reliability constraints, a frequency-band constraint shifting method (FBCSM) is proposed to ease the heavy computational burden without sacrificing accuracy. In addition, the sensitivities of simple and multiple eigenfrequencies with respect to the design and random variables are derived. The "bound formulation" and "robust formulation" are used to reduce the gray elements and checkerboard phenomenon. Four examples are used to determine the effectiveness of the proposed reliability-based eigenvalue topology model and FBCSM. The results confirmed their superiority in terms of validity and efficiency. [ABSTRACT FROM AUTHOR]

Highlights • The implementation of multichannel adaptive active vibration control system is discussed. • A novel multichannel FXLMS algorithm with online secondary path modeling is designed. • New variable step-size and auxiliary noise power scheduling strategy are presented. • Details concerning experimental setup and piezoelectric smart plate are disclosed. • Vibration reduction of smart cantilever plate with a high convergence rate. Abstract Reducing the vibration of smart structures based on adaptive active vibration control (AAVC) has been extensively studied in recent years, because it is a light weight and effective method for reducing low-frequency structural vibrations. The multi-channel AAVC methodology based on the filtered-X least mean square (FXLMS) algorithm is widely implemented in active control applications owing to its self-adjustment ability to adapt to dynamically varying structures. In this paper, a new multi-channel FXLMS with online secondary path modelling (SPM) is designed based on the auxiliary random noise technique. Through a defined indirect error signal, the proposed variable step-size (VSS) strategies can ensure that every online SPM filter and every active control filter have their own exclusive step size to update the coefficients. Moreover, the proposed auxiliary noise power scheduling (ANPS) strategy can ensure that the variation rules of auxiliary noise power applied to different secondary paths are different. A complete multi-channel AAVC real-time experimental system based on NI compact RIO is set up to conduct the experimental investigation. A series of AAVC control experiments on a piezoelectric smart cantilever plate with PZT sensors and actuators are conducted to demonstrate the validity and efficiency of the proposed method. The experimental results show that the vibration of the smart cantilever plate could be effectively attenuated with a high convergence rate. The proposed methodology has an important advantage in applications where active vibration control of piezoelectric smart structures is required. [ABSTRACT FROM AUTHOR]

Random vibration analysis of structures subjected to combined Gaussian and Poisson white noise excitation is a challenging issue. In this paper, a novel direct probability integral method (DPIM) is suggested to address stochastic responses and dynamic reliability of nonlinear multi-degree-of-freedom (MDOF) systems under combined excitation. Firstly, probability density integral equation (PDIE) of MDOF system under combined excitation is derived based on the principle of probability conservation. Then, DPIM is proposed to achieve the probability density function of stochastic response by solving deterministic motion equation of MDOF system and PDIE in sequence. To solve PDIE, two techniques, i.e., partition of input probability space and smoothing of Dirac delta function, are introduced. From the perspective of probability conservation, furthermore, the equivalent relationship between the PDIE and the corresponding probability density differential equation of a Markov system under combined Gaussian and Poisson noise is established. Since Dirac delta function is analytically integrated as Heaviside function, the first-passage dynamic reliability of MDOF system under combined excitation is readily evaluated by introducing the extreme value mapping of stochastic response. Finally, two nonlinear MDOF systems, including multiple-span bridge under combined vehicle load and non-stationary seismic excitation, are solved. Results demonstrate that the proposed DPIM is effective for random vibration and dynamic reliability analyses of MDOF structures excited by combined Gaussian and Poisson noise, and considering the randomness of vehicle load and seismic excitation simultaneously in the bridge design benefits the safe operation of bridge. [ABSTRACT FROM AUTHOR]