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The role of the spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates is investigated in this study. The key achievement of this work is that the classical nonlocal elasticity theory is modified to take into account the dependence of nonlocal parameters on the varying of materials through the thickness of the functionally graded sandwich nanoplates. Hamilton’s principle is adopted to establish the governing equations of motion using a new inverse hyperbolic shear deformation theory. Numerical results are carried out via Navier’s solution for the fully simply supported rectangular functionally graded sandwich nanoplates, and they are compared with the available results to confirm the accuracy and efficiency of the proposed algorithm. Besides, the effects of some parameters such as the spatial variation of the nonlocal parameters, the aspect ratio, the side-to-thickness ratio as well as the power-law index on the free vibration of the nanoplates are also investigated cautiously. The results show that the variation of the nonlocal parameters plays a significant role in the free vibration of the functionally graded sandwich nanoplates, which is never investigated in the literature. The present methodology could be applied to the design and application of the micro/nanostructures.

Rolling bearing and squeeze film damper will introduce structural nonlinearity into the dynamic model of aeroengine. Rubbing will occur due to the clearance reduction design of the engine. The coupling of structural nonlinearity and fault nonlinearity will make the engine present rich vibration responses. This paper aims to analyze the nonlinear vibration behavior of the whole aeroengine including rolling bearing and squeeze film damper under rubbing fault. Firstly, the dynamic model of a turboshaft engine with nonlinear support and rubbing fault is established; The rolling bearing force, the oil film force and the rubbing force are introduced into a dual-rotor–casing model with six support points. Secondly, the linear part of the model is verified by the dynamic characteristics of the three-dimensional finite element model. Finally, the varying compliance vibration, the damping effect and the bifurcation mechanism are analyzed in detail in which the bearing clearance, speed ratio and rubbing stiffness are considered. Results show that the rubbing fault in the nonlinear support case will excite more significant varying compliance vibration in the low-speed region and expand the rotating speed range of the chaotic region in the high-speed region compared with that in the linear support case.

This study investigates the application of physics-informed neural networks (PINN) for bending and free vibration analysis of three-dimensional functionally graded (TDFG) porous beams. The beam material properties are assumed to vary continuously in three dimensions according to an arbitrary function. The governing equations of motion are obtained using Hamilton's principle and solved by a PINN computational approach. The beam deflection is approximated with a deep feedforward neural network which its input is the spatial coordinate. The network parameters are trained by minimizing a loss function comprised of the governing differential equation and the boundary conditions. The beam natural frequency is considered as an unknown parameter in the governing equation; thus, it has to be obtained by solving an inverse problem. This procedure makes it possible to find higher modes’ natural frequencies, which is impossible according to the previous PINN methods. A systematic procedure for tuning the network's hyperparameters is done based on the Taguchi design of the experiment and the grey relational analysis. The PINN results are validated with analytical and numerical reference solutions. Effects of material distribution, elastic foundation and porosity factor, and porosity distribution type on the bending behavior and natural frequencies of TDFG beams are investigated.

A smart active vibration control (AVC) system containing piezoelectric (PZT) actuators, jointly with a linear quadratic regulator (LQR) controller, is proposed in this article to control transverse deflections of a wind turbine (WT) blade. In order to apply controlling rules to the WT blade, a state-of-the-art semi-analytical solution is developed to obtain WT blade lateral displacement under external loadings. The proposed method maps the WT blade to a Euler–Bernoulli beam under the same conditions to find the blade’s vibration and dynamic responses by solving analytical vibration solutions of the Euler–Bernoulli beam. The governing equations of the beam with PZT patches are derived by integrating the PZT transducer vibration equations into the vibration equations of the Euler–Bernoulli beam structure. A finite element model of the WT blade with PZT patches is developed. Next, a unique transfer function matrix is derived by exciting the structures and achieving responses. The beam structure is projected to the blade using the transfer function matrix. The results obtained from the mapping method are compared with the counter of the blade’s finite element model. A satisfying agreement is observed between the results. The results showed that the method’s accuracy decreased as the sensors’ distance from the base of the wind turbine increased. In the designing process of the LQR controller, various weighting factors are used to tune control actions of the AVC system. LQR optimal control gain is obtained by using the state-feedback control law. The PZT actuators are located at the same distance from each other an this effort to prevent neutralizing their actuating effects. The LQR shows significant performance by diminishing the weights on the control input in the cost function. The obtained results indicate that the proposed smart control system efficiently suppresses the vibration peaks along the WT blade and the maximum flap-wise displacement belonging to the tip of the structure is successfully controlled.

This paper analyses different modes and cycles of seat vibration in city buses by analysing acceleration peak magnitudes and their trends and fluctuations in the time domain. The purpose is to find peak vibration modes that exist in the driving patterns of city buses. Analysing peaks in a time series is essential for many applications specifically in vibration analysis because they represent significant events. Using a 6-axis inertial measurement unit device which has accelerometer and gyroscope sensors data were collected from a number of city buses operating. By applying algorithmic filters the g-force peaks present in different acceleration modes were analysed. The particularity of city bus seat vibration and g-force acceleration levels due to effective acceleration in 3-axes are presented and discussed, namely: longitudinal (forward motion), lateral (side-to-side) and vertical (bounce mode) accelerations. It was found that the bus seat root mean square acceleration magnitude of approximately 0.33 g occurred from the major acceleration cycles during bus running. In longitudinal, lateral and vertical directions, 20% of peak acceleration cycles were above 0.20 g, 0.18 g and 0.27 g respectively. Jerk may be a better indicator of passenger discomfort. The results from this study can provide future reference to research directions into understanding city bus seat vibration levels in longitudinal, lateral and vertical directions and also initiatives to mitigate excess bus seat vibration for the riders.

In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.

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.

A least squares recursive gradient meshfree collocation method is proposed for the superconvergent computation of structural vibration frequencies. The proposed approach employs the recursive gradients of meshfree shape functions together with smoothed shape functions in the context of least squares formulation, where both meshfree nodes and auxiliary points are taken as the collocation points. It turns out that this least squares formulation can effectively suppress the spurious modes arising from a direct meshfree collocation formulation using recursive gradients. Meanwhile, a detailed theoretical analysis with explicit frequency error measure is presented for the least squares recursive gradient meshfree collocation method in order to assess the frequency accuracy of structural vibrations. This analysis discloses the salient basis degree discrepancy issue regarding the frequency accuracy for the least squares meshfree collocation formulation, and it is shown that this issue can be essentially resolved by the proposed least squares recursive gradient meshfree collocation method. In fact, the proposed method leads to superconvergent vibration frequencies when odd degree basis functions are used, i.e., the frequency convergence rate is improved from ( p - 1 ) for the standard least squares meshfree collocation to ( p + 1 ) for the proposed approach in case of an odd p th degree basis function. This desirable frequency superconvergence of the proposed least squares recursive gradient meshfree collocation method is congruously demonstrated by numerical results.

Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera’s unified formulation (CUF) has been successful in previous works for buckling, vibrational, and stress analysis of VAT plates. Typically, one-dimensional (1D) and two-dimensional (2D) CUF models are used, with a linear law describing the fiber orientation variation in the main plane of the structure. The objective of this article is to expand the CUF 2D plate finite elements family to perform free vibration analysis of composite laminated plate structures with curvilinear fibers. The primary contribution is the application of Reissner’s mixed variational theorem (RMVT) to a CUF finite element model. The principle of virtual displacements (PVD) and RMVT are both used as variational statements for the study of monolayer and multilayer VAT plate dynamic behavior. The proposed approach is compared to Abaqus three-dimensional (3D) reference solutions, classical theories and literature results to investigate the effectiveness of the developed models. The results demonstrate that mixed theories provide the best approximation of the reference solution in all cases.

Studying the wind-induced vibration model and response characteristics of lightning rods is crucial for achieving their rational design and wind stability. To address the current shortcomings in considering on-site wind load characteristics and the lack of differentiated considerations in the design phase of lightning rods, it is essential to establish an effective simulation model that accurately reproduces the wind induced vibration response of lightning rods and extracts key parameters for analysis. In this study, a 330kV independent lightning rod in Ningxia province, China, was identified as the subject of analysis. Building upon the structural vibration model, the response of the lightning rod to wind induced vibrations was calculated, and the simulation results were systematically validated through on-site measurements. The results indicate that the simulation model developed in this study can effectively replicate the vibration process of the lightning rod under wind load, providing comprehensive mechanical data. The research findings contribute to a deeper understanding of the wind induced characteristics of on-site lightning rods, facilitating the simulation analysis of lightning rod wind induced responses. Furthermore, the vibration law and characteristic parameters of the lightning rod structure hold great significance for the differentiated design and structural health monitoring of independent lightning rods.