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Metallic thin-walled beams with continuously varying cross-sections loaded in compression are particularly sensitive to instability problems due to lateral-torsional buckling. Such a phenomenon depends on several parameters, including the cross-sectional properties along the entire length, material properties, load distribution, support, and restraint conditions. Due to the difficulty of obtaining analytic solutions for the problem under consideration, the present study takes a numerical approach based on a variational formulation of the lateral-torsional buckling problem of tapered C-beams. Numerical simulations are compared with experimental results on the buckling of a physical model of at thin-walled beam with uniformly varying cross-section, with the aim of assessing the accuracy of the proposed approach. The good agreement between numerical and experimental results and the reduced computational effort highlight that the proposed variational approach is a powerful tool, provided that the geometry of the structure and the boundary conditions are accurately modeled.

Reproducibility of experimental results lies at the heart of scientific disciplines. Here we propose a signal processing method that extracts task-related components by maximizing the reproducibility during task periods from neuroimaging data. Unlike hypothesis-driven methods such as general linear models, no specific time courses are presumed, and unlike data-driven approaches such as independent component analysis, no arbitrary interpretation of components is needed. Task-related components are constructed by a linear, weighted sum of multiple time courses, and its weights are optimized so as to maximize inter-block correlations (CorrMax) or covariances (CovMax). Our analysis method is referred to as task-related component analysis (TRCA). The covariance maximization is formulated as a Rayleigh–Ritz eigenvalue problem, and corresponding eigenvectors give candidates of task-related components. In addition, a systematic statistical test based on eigenvalues is proposed, so task-related and -unrelated components are classified objectively and automatically. The proposed test of statistical significance is found to be independent of the degree of autocorrelation in data if the task duration is sufficiently longer than the temporal scale of autocorrelation, so TRCA can be applied to data with autocorrelation without any modification. We demonstrate that simple extensions of TRCA can provide most distinctive signals for two tasks and can integrate multiple modalities of information to remove task-unrelated artifacts. TRCA was successfully applied to synthetic data as well as near-infrared spectroscopy (NIRS) data of finger tapping. There were two statistically significant task-related components; one was a hemodynamic response, and another was a piece-wise linear time course. In summary, we conclude that TRCA has a wide range of applications in multi-channel biophysical and behavioral measurements. ► Task-relatedness is defined by consistent appearance of a signal in task blocks. ► Task-related components are constructed by a weighted sum of multiple time courses. ► The weights are optimized to maximize covariance of components between blocks. ► Task-related component analysis (TRCA) is successfully applied to fNIRS data.

A numerical approach based on the Rayleigh-Ritz method and using a modification of the so-called xyz algorithm is introduced to calculate the acoustic vibrations of clamped objects whose shape is delimited by superquadrics. It is then used to improve the convergence for the free vibrations of core-shell objects. The issue in this case is first illustrated in the simpler one-dimensional case of the thickness breathing vibration of an infinite \"core-shell\" plate. Functions suitable for solving the clamped vibrations of the core are added to the original xyz basis of functions to improve the convergence for core-shell superquadrics. The new basis obeys the same symmetry rules as the original one, which allows calculating vibrations for individual irreducible representations when the objects are made of cubic, tetragonal, or orthorhombic materials whose principal axes are aligned with those of the superquadrics. This method is validated for an isotropic spherical core-shell system for which analytic solutions exist.

This paper deals with the active vibration control of piezoelectric sandwich plate. The structure consists of a substrate plate layer sandwiched between two layers of piezoelectric sensor and actuator. Based on laminate theory and constitutive equation of piezoelectric material, the vibration active control dynamic equation of the sandwich structure is established by using hypothetical mode method and Hamilton principle. The Rayleigh-Ritz method is used to solve it. The form of hypothetical solution is used for approximate solution, which is simple and accurate. The method of this paper is verified by several examples. The parametric studies of the sandwich plate structures are carried out. The results show that applying different boundary conditions and piezoelectric patch positions to the structures have a great influence on the natural frequency. When the driving voltage increases, the deflection of the plate structures increase approximately linearly. The active vibration control studies are investigated as well. The results show that within a certain range, the larger the value of the speed feedback coefficient, the better the active control effect. The positions of the piezoelectric patches affect the effectiveness and cost of active control. When the piezoelectric plate is located at the fixed end, the effect and cost of active control are better than that at the midpoint and free end of the plate.

In this paper, for the first time, the deep learning technique of the artificial neural network method is used to determine the free vibration parameters of the rectangular bistable composite plates. For this purpose, first, the static and free vibration behaviours of a cross-ply bistable composite plate are studied using analytical, finite element and experimental methods. By comparing them, it is turned out that there is a considerable difference among obtained natural frequencies so that the analytical method is only able to determine the fourth natural frequency and cannot estimate the first three natural frequencies. To solve this problem, the deep neural network is employed to model the modal parameters of the bistable laminate as an explicit mathematical relationship that can be generalized to the other bistable composite plates. This mathematical relation makes it possible to obtain the natural frequencies in each of the stable configurations based on the geometric dimensions of the plate. In the following that, the inverse problem method is considered and the mode management capability is investigated. A fast swarm intelligence algorithm called firefly algorithm is used to optimize the optimization function of the mode management problem. Mode management using the evolutionary algorithm provides the appropriate physical dimensions of the plate according to the scenarios for natural frequencies arrangement. The results are validated by comparing them with those obtained by the finite element method and experiment test, which results show that this method estimates the modal parameters with high accuracy. The method used in this paper can also be applied to determine the modal parameters of other morphing structures.

The limited memory steepest descent method (LMSD, Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex quadratic objective functions, we study the numerical behavior of different techniques to compute new stepsizes. In particular, we introduce a method to improve the use of harmonic Ritz values. We also show the existence of a secant condition associated with LMSD, where the approximating Hessian is projected onto a low-dimensional space. In the general nonlinear case, we propose two new alternatives to Fletcher’s method: first, the addition of symmetry constraints to the secant condition valid for the quadratic case; second, a perturbation of the last differences between consecutive gradients, to satisfy multiple secant equations simultaneously. We show that Fletcher’s method can also be interpreted from this viewpoint.

An optimization design of the bending-vibration resistance of magnetorheological elastomer carbon fibre reinforced polymer sandwich sheets (MECFRPSSs) was studied in this paper. Initially, by adopting the classical laminate theory, the Reddy’s high-order shear deformation theory, the Rayleigh-Ritz method, etc., an analytical model of the MECFRPSSs was established to predict both bending and vibration parameters, with the three-point bending forces and a pulse load being considered separately. After the validation of the model was completed, the optimization design work of the MECFRPSSs was conducted based on an optimization model developed, in which the thickness, modulus, and density ratios of magnetorheological elastomer core to carbon fibre reinforced polymer were taken as design variables, and static bending stiffness, the averaged damping, and dynamic stiffness parameters were chosen as objective functions. Subsequently, an artificial bee colony algorithm was adopted to execute single-objective, dual-objective, and multi-objective optimizations to obtain the optimal design parameters of such structures, with the convergence effectiveness being examined in a validation example. It was found that it was hard to improve the bending, damping, and dynamic stiffness behaviours of the structure simultaneously as the values of design variables increased. Some compromised results of design parameters need to be determined, which are based on Pareto-optimal solutions. In further engineering application of the MECFRPSSs, it is suggested to use the corresponding design parameters related to a turning point to better exert their bending-vibration resistance.

The results of semianalytical calculation of the critical buckling loads and load-bearing capacity of laminated composite panels having different geometric shapes in plan in the course of loading with compressive and tangential forces in the plane of the layers are presented. The stability problems of orthotropic layered plates with variable geometric parameters have been solved by the Rayleigh–Ritz method with approximation of the deflection function by orthogonal Krylov polynomials. The effect of shape, the method of fastening the panels, and the arrangement pattern of reinforcing fibers in the layers of the composite has been studied. Rational reinforcement patterns that correspond to the highest critical buckling load for nonrectangular and shallow curved panels have been revealed. The load-bearing capacity under supercritical strain has been assessed based on the Tsai–Wu strength criterion.

Rayleigh-Ritz discriminant analysis (RRDA) is an effective algorithm for linear discriminant analysis (LDA), but there are some drawbacks in its implementation. In this paper, we first improved Rayleigh-Ritz discriminant analysis (IRRDA) to make its framework more concise, and established the equivalence theory of the solution space between our discriminant analysis and RRDA. Second, we proposed a new model based on positive definite systems of linear equations for linear discriminant analysis, and certificated the rationality of the new model. Compared with the traditional linear regression model for linear discriminant analysis, the coefficient matrix of our model avoided forming a centralized matrix or appending the original data matrix, but the original matrix itself, which greatly reduced the computational complexity. According to the size of data matrix, we designed two solution schemes for the new model based on the block conjugate gradient method. Experiments in real-world datasets demonstrated the effectiveness and efficiency of our algorithm and it showed that our method was more efficient and faster than RRDA.