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Highlights • The first and second derivatives for the transient response of non-viscously damped systems are calculated. • The direct differentiate method is adopted. • The sensitivities are derived by using a modified precise integration method. • The computational considerations of the methods are investigated and compared. • Two numerical examples are given to show the performances of the method. Abstract Calculation of the first and second derivatives of transient response with respect to design variables is a prerequisite when gradient-based methods are adopted for optimization design in time-domain. In this paper, a design sensitivity analysis (DSA) method for calculating the first and second derivatives of the transient response for non-viscously damped systems is developed. The assumed damping forces depend on the past history of motion via convolution integrals over some kernel functions. The direct differentiate method (DDM) is selected to derive the DSA method. By introducing a generalized damping model in expression of fraction formula, the equations of motion of the non-viscously damped system are transformed into a state-space form without the convolution integral terms. Then, the first and second derivatives of the transient response are formulated based on a modified precise integration method using the DDM. The numerical stability, accuracy and implementation effort of the DDM are discussed. Two numerical examples are comparatively demonstrated using the DDM, the discretize-then-differentiate adjoint variable method (AVM) and the differentiate-then-discretize AVM. The results indicate that, by considering all the computational considerations, the proposed DDM is more suitable than the other two methods for the sensitivity analysis of transient response for non-viscously damped systems. Besides, it is also the only existing method to capture the second-order derivatives of transient response for the non-viscously damped systems. [ABSTRACT FROM AUTHOR]

In this paper, design sensitivity analysis methods for the transient response of non-viscously damped systems are considered. The damping forces of the non-viscously damped systems depend on the past history of motion via convolution integrals over some suitable kernel functions. The adjoint variable method (AVM) is adopted to develop the design sensitivity analysis. Two numerical solution schemes, namely the discretize-then-differentiate method and the differentiate-then-discretize method, are introduced to complete the AVM for the sensitivity analysis of non-viscously damped systems. The discretize-then-differentiate AVM discretizes the equations of motion based on the Newmark- β implicit integration method first and then differentiates the discrete equations. On the contrary, the differentiate-then-discretize AVM firstly differentiates the equations of motion after transforming it into a state-space form, and then discretizes the equations based on a modified precise integration method (PIM). The numerical accuracy, efficiency, consistency and implementation effort are discussed and compared. Two numerical examples are presented to show the effectiveness of both methods. The results indicate that, by considering both computational accuracy and efficiency, the PIM based differentiate-then-discretize method is more suitable than the Newmark- β based discretize-then-differentiate method for the sensitivity analysis of transient responses for non-viscously damped systems. [ABSTRACT FROM AUTHOR]

Sophisticated engineering systems are usually assembled by subcomponents with significantly different levels of energy dissipation. Therefore, these damping systems often contain multiple damping models and lead to great difficulties in analyzing. This paper aims at developing a time integration method for structural systems with multiple damping models. The dynamical system is first represented by a generally damped model. Based on this, a new extended state-space method for the damped system is derived. A modified precise integration method with Gauss-Legendre quadrature is then proposed. The numerical stability and accuracy of the proposed integration method are discussed in detail. It is verified that the method is conditionally stable and has inherent algorithmic damping, period error and amplitude decay. Numerical examples are provided to assess the performance of the proposed method compared with other methods. It is demonstrated that the method is more accurate than other methods with rather good efficiency and the stable condition is easy to be satisfied in practice. [ABSTRACT FROM AUTHOR]

The analysis of large, complex systems can be simplified and more computationally efficient if smaller, simpler subcomponents can be treated and assembled. Component Mode Synthesis (CMS) methods allow one to reduce the order of the model at the subcomponent level. Although CMS methods are widely applied in the field of structure dynamics for undamped or viscously damped systems, their counterparts for viscoelastically damped systems seem not well-developed. Motivated by such points, this paper develops a model-order-reduction approach for viscoelastically damped systems based on a free interface CMS method. Due to the fact that the nonviscous modes and higher-order elastic modes are difficult to be obtained accurately for viscoelastic systems, the mode truncation error is often introduced. To reduce the mode truncation error problem, two residual attachment modes of viscoelastically damped systems are proposed in terms of the lower modes and system matrices by using the first one or two terms of Neumann expansion. Finally, three numerical studies are provided to illustrate the accuracy and effectiveness of the derived methods. It is shown that the proposed methods can receive good results and reduce the modal truncation error significantly over the conventional method. [ABSTRACT FROM AUTHOR]

• The first and second derivatives for PSD function subject to stochastic excitations are derived. • The proposed methods are applicable to non-classically damped systems. • The highly efficient Pseudo-Excitation-Method (PEM) is adopted. • Two correction methods are developed without the need to calculate the eigen-sensitivities. • Computational accuracy is greatly improved by considering truncated high-order complex modes. Calculating the first and second derivatives of Power Spectrum Density (PSD) function with respect to various design variables is a prerequisite for random responses when gradient-based algorithms are adopted. This paper presented two numerical methods to capture the sensitivity and Hessian matrix of the PSD function for non-classically damped systems subject to stationary stochastic excitations. The direct differentiate method (DDM) is adopted to develop the design sensitivity analysis (DSA). By using Pseudo-Excitation Method (PEM), the governing equations of the non-classically damped system subject to stationary stochastic excitations are transformed into a corresponding deterministic harmonic response problem. Then, the first and second derivatives of the PSD function are given in detail using the DDM. Two numerical methods, namely PEM-modal displacement method (MDM) and PEM-hybrid expansion method (HEM), are proposed to compute the sensitivity and Hessian matrix of the PSD function. The computational accuracy and efficiency of both methods are discussed and compared theoretically and numerically by two illustrations. The results indicate that both methods are valid for the DSA of the PSD function for non-classically damped systems and the PEM-HEM is more suitable than the PEM-MDM with all computational considerations. [ABSTRACT FROM AUTHOR]

X-ray diffraction has been used to study the changes in the surface properties of a montmorillonitic clay through the changes in the basal spacings of montmorillonite (SWy-2) and surfactant-intercalated organoclays. Variation in the d-spacing was found to be a step function of the surfactant concentration. High-resolution thermogravimetric analysis (HRTG) shows that the thermal decomposition of SWy-2-MMTs modified with the surfactant octadecyltrimethylammonium bromide takes place in four steps. A mass-loss step is observed at room temperature and is attributed to dehydration of adsorption water. A second mass-loss step is observed over the temperature range 87.9 to 135.5 °C and is also attributed to dehydration of water hydrating metal cations such as Na+. The third mass loss occurs from 178.9 to 384.5 °C and is assigned to a loss of surfactant. The fourth mass-loss step is ascribed to the loss of OH units through dehydroxylation over the temperature range 556.0 to 636.4 °C. A model is proposed in which, up to 0.4 CEC, a surfactant monolayer is formed between the montmorillonitic clay layers; up to 0.8 CEC, a lateral-bilayer arrangement is formed; and above 1.5 CEC, a pseudotrimolecular layer is formed, with excess surfactant adsorbed on the clay surface. [Copyright &y& Elsevier]

Copper was adsorbed onto Ca-exchanged montmorillonite (Cheto clay) under basic conditions. Differential thermogravimetric analysis (DTGA) combined with evolved gas mass spectroscopy (MS) was employed as the principal technology to study the distribution and structure of adsorbed copper species on the montmorillonite clay. The results showed that the original clay was easily rehydrated. After copper adsorption, a step-by-step replacement of hydrated calcium ions by copper–ammonia complex was observed through the gradual decrease of the first DTGA dehydration peak intensity with increasing copper loading. Compared with the original clay, copper loaded samples showed new DTGA peaks assigned to NH3 and N2O. The presence of the N2O peak suggested that the loaded copper species were in agglomerated copper oxide form, which dispersed well over the edges and external surfaces of the clay layers. [Copyright &y& Elsevier]

The activity and fate of heavy metals (HMs) from mining and smelting activities in farmland soil is of great significance to effectively prevent the excessive enrichment of HMs in crops. This study focuses on Baiyin area, a typical mining city in northwest China. In this example, the sources, speciation, and fate of HMs in the farmland soil, and the migration and enrichment characteristics of HMs in the different parts of crops planted in different areas were studied in detail combining the chemical sequential extraction and Pb isotope approaches. Results showed that the mean anthropogenic contributions of HMs in farmland soils were approximately 85%, 88%, 76%, and 41% for the ore district (OD), Xidagou sewage irrigation area (XSIA), Dongdagou sewage irrigation area, and the Yellow River irrigation area, respectively, and the risk that HMs were excessively accumulated in crops in OD and XSIA was high. Compared with soil residual fractions, the isotope ratios 206Pb/207Pb in non-residual fractions (1.1304–1.1669) were closer to the values of local ores, suggesting that anthropogenic HMs from mining and smelting activities were mainly enriched in the non-residual fractions. The isotope ratios 206Pb/207Pb in crops (1.1398–1.1686) further confirmed that those anthropogenic HMs were more easily absorbed and concentrated by crops. HMs contents in leaves from OD and XSIA were generally higher than that in roots, suggesting that atmospheric deposition in OD and XSIA had a greater impact on the HMs concentration of crop leaves，while the excess rate of HMs in grain/fruit was the lowest in all parts of crops. The division and classification of crop planting in mining area can effectively help minimize the risk that HMs from anthropogenic source enter the human body through the food chain. Image 1 • Anthropogenic HMs were mainly enriched in the non-residual fractions of farmland soil. • Soil HMs that from mining and smelting activities can be easily absorb by crops. • Division and classification planting helps minimize the ecological risks of HMs pollution. [ABSTRACT FROM AUTHOR]

In this paper, by considering higher-order effects of residual attachment modes, a new free-interface component mode synthesis (CMS) method is developed for non-classically damped systems. Firstly, based on the Neumann expansion, the higher-order effects of the residual attachment modes are accurately expressed by the available lower-order modes and the system matrices. Secondly, by using the residual attachment modes and complex modes, the non-classically damped subcomponents are reduced and assembled in the physical space instead of the frequently-used state-space. Then, the new free-interface CMS method is derived and solved built on a frequency shifting technique and an iteration method. Finally, the performances of the presented method are illustrated by two numerical examples and compared with other first- and second-order approximated CMS methods. The results indicate that the presented CMS method for the non-classically damped systems is more accurate than other methods and suitable for the case when both high- and low-order modes are truncated. • A new CMS method for non-classically damped system is presented. • The CMS method considers the higher-order effects of residual attachment modes. • Residual attachment modes are derived explicitly by lower-order modes and system matrices. • Subcomponents are assembled in physical space instead of state-space. • The proposed method is applicable to the case when both low- and high-order modes are truncated. [ABSTRACT FROM AUTHOR]

We analyze a basis-independent definition of quantum coherence. The maximally mixed state is used as the reference state, which allows for a way of defining coherence that is invariant under arbitrary unitary transformations. Such a basis independent formulation is related to the purity of system rather than the superposition in a particular basis. The basis-independent approach is applied to finding the distribution of the coherence within a multipartite system, where the contributions due to correlations between the subsystems and within each subsystem are isolated. The use of the square root of the Jensen–Shannon divergence allows for inequality relations to be derived between these quantities, giving a geometrical picture within the Hilbert space of the system. We describe the relationship between the basis-independent and the basis-dependent approaches, and argue that many advantages exist for the former method. The formalism is illustrated with several numerical examples which show that the states can be characterized in a simple and effective manner. [ABSTRACT FROM AUTHOR]

The mode superposition method (MSM), which is used for dynamic response calculations of nonviscously damped systems, requires state–space eigensolutions, which incur a high computational cost. This study proposed an alternative symmetric formulation-based time integration method for analyzing structural dynamic systems. An anelastic displacement field (ADF) model was introduced to capture damping mechanisms in nonviscous systems. The differential equation describing the ADF model was transformed into an augmented coupled system via the introduction of dissipative variables. Two symmetric state formulations based on coupled augmented systems were derived for nonviscous systems. Consequently, alternative asymmetric state formulations were derived for nonviscous systems involving the ADF model. Thereafter, a new method was developed based on these state–space formulations by assuming linear approximations. A numerical implementation of the new method for dynamic systems was demonstrated. Three benchmark examples of discrete and continuous systems were considered to evaluate the asymmetric formulation and the computational efficiency, accuracy, stability, and time-step-size sensitivity of the new method. Further, the response of the new method was validated using MSM and precise time integration (PTI) methods. An asymmetric state formulation was also validated against MSM and direct frequency response methods. The results revealed that the new method accurately matched the MSM and PTI methods at various time steps. The results also showed that the new method was more efficient than the MSM and PTI methods, rendering it suitable for solving large-scale structural dynamics problems. • Mode superposition method (MSM) requires significant computation for the dynamic response calculations of non-viscously damped systems. • New method is proposed for the response calculations of large-scale dynamic systems. • Symmetric and asymmetric formulations based on the ADF model are derived for non-viscous systems. • New method gives precise results that approach accurate solutions at different time-step sizes. • New method has a much higher computational efficiency than the MSM and PTI methods. [ABSTRACT FROM AUTHOR]

Highlights: [•] This paper proposed a new grooming algorithm in IP over WDM network. [•] The algorithm takes comprehensive and careful considerations of the link weight. [•] The algorithm can use resources more efficiently and achieve load balancing. [ABSTRACT FROM AUTHOR]

• A fading-free broadband Φ-OTDR system is proposed for distributed vibration sensing. • Fading-free sensing is realized by fiber embedded with artificial microstructures. • An FDM structure helps the system to expand its frequency response bandwidth. The phase-sensitive optical time domain reflectometers (Φ-OTDR), which can realize distributed acoustic sensing, has been widely applied in health monitoring of civil structures. To break through the limit of the frequency response bandwidth (FRB) and to reduce the fading positions of traditional Φ-OTDR systems, we propose an Φ-OTDR system based on the ultra-weak fiber Bragg grating (UWFBG) array and the frequency-division-multiplexing (FDM) scheme. Taking advantage of UWFBGs, the probability of fading positions occurred on the Rayleigh backscattering (RBS) waveforms can be dramatically reduced, which means the visibility of the system can be enhanced. The FDM structure can enhance the sampling rate by interleaving algorithm, which helps the Φ-OTDR system to expand its FRB. The experimental results show that the frequency of vibration up to 440 kHz can be detected along 330 m UWFBGs, which is approximately three times higher than the upper limit of the FRB of traditional systems. When compared with the traditional scheme that adopts ordinary single-mode fiber as the sensing part, the probability of fading occurrence in the proposed system has been reduced from 10−2 to 10−10. The proposed sensing system in this paper reveals a promising option for the performance enhancement of the Φ-OTDR system, which can offer wider FRB as well as the enhanced visibility characteristic. [ABSTRACT FROM AUTHOR]