Spatial Rigid-Flexible-Liquid Coupling Dynamics of Towed System Analyzed by a Hamiltonian Finite Element Method

An effective Hamiltonian finite element method is presented in this paper to investigate the three-dimensional dynamic responses of a towed cable-payload system with large deformation. The dynamics of a flexible towed system moving in a medium is a classical and complex rigid-flexible-liquid coupling problem. The dynamic governing equation is derived from the Hamiltonian system and built-in canonical form. A Symplectic algorithm is built to analyze the canonical equations numerically. Logarithmic strain is applied to estimate the large deformation effect and the system stiffness matrix will be updated for each calculation time step. A direct integral solution of the medium drag effect is derived in which the traditional coordinate transformation is avoided. A conical pendulum system and a 180° U-turn towed cable system are conducted and the results are compared with those retraced from the existing Hamiltonian method based on small deformation theory and the dynamic software of Livermore software technology corp. (LS-DYNA). Furthermore, a circularly towed system is analyzed and compared with experimental data. The comparisons show that the presented method is more accurate than the existing Hamiltonian method when large deformation occurred in the towed cable due to the application of logarithmic strain. Furthermore, it is more effective than LS-DYNA to treat the rigid-flexible-liquid coupling problems in the costs of CPU time.

Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications

We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.

A Robust Approach for Blur and Sharp Regions’ Detection Using Multisequential Deviated Patterns

Blur detection (BD) is an important and challenging task in digital imaging and computer vision applications. Accurate segmentation of homogenous smooth and blur regions, low-contrast focal regions, missing patches, and background clutter, without having any prior information about the blur, are the fundamental challenges of BD. Previous work on BD has emphasized much effort on designing local sharpness metric maps from the images. However, the smooth/blurred regions having the same patterns as sharp regions make them problematic. This paper presents a robust novel method to extract the local metric map for blurred and nonblurred regions based on multisequential deviated patterns (MSDPs). Unlike the preceding, MSDP extracts the local sharpness metric map on the images at multiple scales using different adaptive thresholds to overcome the problems of smooth/blur regions and missing patches. By using the integral values of the image along with image masking and Otsu thresholding, highly accurate segmented regions of the images are acquired. We argue/hypothesize that the local sharpness map extraction by using direct integral information of the image is highly affected by the threshold selected for distinction between the regions, whereas MSDP feature extraction overcomes the limitations substantially by using automatic threshold computation over multiple scales of the images. Moreover, the proposed method extracts the relatively accurate sharp regions from the high-dense blur and noisy images. Experiments are conducted on two commonly used SHI and DUT datasets for blur and sharp region classifications. The results indicate the effectiveness of the proposed method in terms of sharp segmented regions. Experimental results of qualitative and quantitative comparisons of the proposed method with ten comparative methods demonstrate the superiority of our method. Moreover, the proposed method is also computationally efficient over state-of-the-art methods.

Bloch wave homogenisation of quasiperiodic media

Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a ‘cut and project’ procedure. Quasiperiodic media displays some extraordinary optical, electronic and conductivity properties which call for the development of methods to analyse their microstructures and effective behaviour. In this paper, we develop the method of Bloch wave homogenisation for quasiperiodic media. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A suitable direct integral decomposition is not available for almost periodic operators. To remedy this, we lift a quasiperiodic operator to a degenerate periodic operator in higher dimensions. Approximate Bloch waves are obtained for a regularised version of the degenerate operator. Homogenised coefficients for quasiperiodic media are obtained from the first Bloch eigenvalue of the regularised operator in the limit of regularisation parameter going to zero. A notion of quasiperiodic Bloch transform is defined and employed to obtain homogenisation limit for an equation with highly oscillating quasiperiodic coefficients.

Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume

This paper deals with the transverse free vibration of axially functionally graded (AFG) cantilever columns under the influence of axial compressive load. The columns possessing a regular polygon in their cross-section are tapered and their material properties vary along the axis of the column. An emphasis is placed on the columns with constant volume for admissible geometries and materials. The governing differential equation of the problem is derived and solved using the direct integral approach in conjunction with the determinant search technique. The obtained results are in good agreement with those in the available literature and computed by finite element analysis. Numerical examples for the natural frequency and mode shape of the columns are presented to investigate the effects of parameters related to geometrical nonuniformity and material inhomogeneity.

Damage Detection for Large-Scale Grid Structure Based on Virtual Axial Strain

To identify the damaged beams in large-scale spatial structure, a damage indicator based on virtual axial strain calculated from mode shape vectors was proposed. The damage detection process was performed based on the dynamic simulation flowchart. Firstly, random signals were used for excitation and the damage was simulated by decreasing beam elasticity modulus. Then, the NEWMARK-β precision direct integral method was appreciated for calculating time history response. Finally, the frequency-domain decomposition method only using output response signal was selected for modal parameter estimation. A double-layer grid structure was taken as example for verifying the damage detection method. Results indicate that the proposed indicator was insensitive to environmental noise and capable of localizing multiple damaged members in space structure without the baseline data.

Comparison of Two Efficient Methods for Calculating Partition Functions

In the long-time pursuit of the solution to calculating the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral approach that works at least four orders faster. In present work, the above two methods were applied to solid argon at temperatures up to 300 K. The derived internal energy and pressure were compared with the molecular dynamics simulation as well as experimental measurements, showing that the calculation precision of our approach is about 10 times higher than that of the nested sampling method.

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.