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This paper aims to establish a comprehensive model for evaluating the response characteristics of functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates under stationary random acceleration excitation. Utilizing the first-order shear deformation theory (FSDT) and Halpin–Tsai assumptions, a dynamic model for the rectangular plate is derived, followed by obtaining the variational solution using the Rayleigh–Ritz method. To describe displacement components associated with dynamic equations and boundary conditions, a spectral geometry method (SGM) is employed. Additionally, a pseudo-excitation method (PEM) is utilized for the analysis of stationary random vibration. The proposed calculation method is validated through convergence analysis and comparative evaluation with existing literature and finite element models. Furthermore, the study investigates the influence of various factors, such as boundary conditions, the number and size of functionally graded rectangular plate layers, GPL distribution types, and material parameters, on the stationary random response attributes of FG rectangular plates. This research contributes to a deeper understanding of the dynamic response of functionally graded materials in structural configurations and offers a valuable analytical approach for researchers in this field.

The stationary random response characteristics of irregular quadrilateral plates under the base acceleration excitation are investigated in this paper. The computational model chosen in this paper is functionally graded graphene platelet reinforced composites (FG-GPLRC). Simultaneously, the material parameters are calculated employing the modified Halpin–Tsai model. A unified dynamic model based on the first-order shear deformation theory (FSDT) is proposed for FG-GPLRC irregular plates, where the displacement variables are considered as the first kind Chebyshev polynomials combined with coordinate transformation. The Chebyshev–Ritz method is utilized to derive the kinetic equations of irregular quadrilateral plates, and then the pseudo-excitation method (PEM) is employed to solve the stationary stochastic response of the system under the base acceleration excitation. The free vibration and stationary stochastic response of the plates under various boundaries are validated by a sufficient number of numerical studies, and the computational results display a favorable match with the published literature and finite element method (FEM), which verifies the correctness and reliability of the present method. Finally, a detailed parametric analysis of the stationary stochastic response characteristics of FG-GPLRC irregular quadrilateral plates is presented. The effects of various mass fractions, number of layers, geometric dimensions of GPL, and boundary constraints on the stationary stochastic vibration behaviors of FG-GPLRC irregular quadrilateral plates are considered.

This study proposes a method for assessing the effect of stochastic vibrations resulting from track irregularities which are rarely studied but significant on bridge fatigue. First, the pseudo-excitation method is utilized to determine the power spectrum density of stress. Subsequently, the trigonometric series method is employed to acquire the stress time history set. Then, a traditional fatigue life calculation method is employed for analysis. By utilizing a post-sampling method, the need for costly repetitive solutions of the vehicle-bridge coupling system is eliminated. Numerical simulations are conducted on a steel truss bridge, revealing the non-negligible effect of track irregularity on bridge fatigue performance. The study investigates the underlying mechanism, highlighting the pronounced influence of long-wave track irregularity. Moreover, the research explores the correlation between track smoothness and bridge fatigue performance, demonstrating that a decrease in track smoothness leads to an increase in fatigue loss. These findings emphasize the necessity of considering stochastic vibrations when evaluating bridge fatigue, providing valuable insights for bridge design and maintenance.

Impellers of centrifugal compressors are generally loaded by fluctuating aerodynamic pressure in operations. Excessive vibration of the impellers can be induced by unsteady airflows and lead to severe fatigue failures. Traditional transient stress analyses implemented in time domain generally require multiple load-step, very time-consuming computations using input of temporal pneumatic force previously obtained from Computational fluid dynamics (CFD) analyses. For quick evaluation of structural integrity of impellers, it is necessary to develop random vibration models and solution approaches defined in frequency domain. In this paper, the Pseudo-Excitation Method (PEM) is used to obtain power spectral density of three-dimensional, dynamic displacement and stress of impellers. A finite element model of an unshrouded impeller of a centrifugal compressor is generated based on the result of unsteady CFD analysis. Compared with the direct transient stress analyses in time domain, the pseudo-excitation method provides accurate and fast estimation of dynamic response of the impeller, making it an applicable and efficient method for analyzing random vibration of impellers.

Stochastic equivalent linearization (SEL) method has gained wide popularity because of its versatility in application to multiple-degree-of-freedom (MDOF) nonlinear systems. It is restricted in the random vibration analysis of flexible structures because of the implicit nonlinear system. This paper presents a new method for the equivalent nonlinear system of flexible structures. Using this method, the implicit geometrically nonlinear system can be represented as an explicit equivalent nonlinear system. According to the modal analysis method, the geometrically nonlinear force is replaced by a high-order moment of modal coordinate. The MDOF physical system is translated into a modal system, which could be solved easily. Based on the equivalent nonlinear system, the nonlinear random vibration method is presented by using SEL technology. By using the pseudo-excitation method, the efficiency of the nonlinear random vibration method is increased obviously. The rapid calculation makes it possible to analyze the nonlinear random vibration of MDOF flexible structure. The validation shows that the method has reasonable precision and high efficiency and it could be used in the random vibration analysis of practical flexible structures.