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The multibody system transfer matrix method (MSTMM), a novel dynamics approach developed during the past three decades, has several advantages compared to conventional dynamics methods. Some of these advantages include avoiding global dynamics equations with a system inertia matrix, utilizing low‐order matrices independent of system degree of freedom, high computational speed, and simplicity of computer implementation. MSTMM has been widely used in computer modeling, simulations, and performance evaluation of approximately 150 different complex mechanical systems. In this paper, the following aspects regarding MSTMM are reviewed: basic theory, algorithms, simulation and design software, and applications. Future research directions and generalization to more applications in various fields of science, technology, and engineering are discussed.

In this study, we designed a novel hybrid underwater sound-absorbing material of the metastructure that contains a viscoelastic substrate with a microperforated panel. Two types of sound-absorbing metastructures were combined to achieve satisfactory sound absorption performance in the low-frequency range. A homogenized equivalent layer and the integrated transfer matrix method were used to theoretically evaluate the sound absorption performance of the designed nonhomogeneous hybrid metastructure. The theoretical results were then compared with the results obtained using the finite-element method. The designed hybrid sound-absorbing metastructure exhibited two absorption peaks because of its different sound-absorbing mechanisms. The acoustic performance of the developed metastructure is considerably better than that of a traditional sound absorber, and the sound absorption coefficient of the developed metastructure is 0.8 in the frequency range of 3–10 kHz. In addition, an adjustment method for the practical underwater application of the designed metastructure is described in this research. Further studies show that the sound absorption coefficient of the adjusted metastructure still has 0.75 in the frequency range of 3–10 kHz, which indicates that this metastructure has the potential to be used as an underwater sound-absorbing structure. The results of this study can be used as a reference in the design of other novel hybrid underwater sound-absorbing structures.

Efficient transient analysis is critical in rotor dynamics. This study proposes the super‐element (SE) differential‐quadrature discrete‐time transfer matrix method (DQ‐DT‐TMM), a novel approach that eliminates the requirement for initial component accelerations and effectively handles beam and solid finite element (FE) models with high‐dimensional degrees of freedom (DOFs) in rotor systems. The primary methodologies of this approach include: (1) For the beam substructure FE dynamic equation, the Craig–Bampton method is employed for the order reduction of internal coordinates, followed by the differential‐quadrature method for temporal discretization. Using SE technology, the internal accelerations are condensed into the boundary accelerations, and the transfer equation and matrix for beam SEs are derived. (2) For the solid substructure FE dynamic equation formulated in the rotating reference frame, in addition to applying the procedures used for beam substructures, rigid multipoint constraints are introduced to condense the boundary coordinates for hybrid modeling with lumped parameter components. The transfer equation is subsequently formulated in the inertial reference frame, enabling the derivation of the transfer matrix for solid SEs. Comparative analysis with full‐order FE models in commercial software demonstrates the advantages of the SE DQ‐DT‐TMM for linear rotor systems: (i) Accurately captures system dynamics using only a few primary modes. (ii) Achieves a 99.68% reduction in computational time for a beam model with 1120 elements and a 99.98% reduction for a solid model with 75 361 elements. (iii) Effectively recovers dynamic responses at any system node using recovery techniques. This research develops a computationally efficient framework for the transient analysis of large‐scale rotor systems, effectively addressing the challenges associated with high‐dimensional DOF models in conventional DT‐TMMs.

This paper gives an update of the RTTOV (Radiative Transfer for TOVS) fast radiative transfer model, which is widely used in the satellite retrieval and data assimilation communities. RTTOV is a fast radiative transfer model for simulating top-of-atmosphere radiances from passive visible, infrared and microwave downward-viewing satellite radiometers. In addition to the forward model, it also optionally computes the tangent linear, adjoint and Jacobian matrix providing changes in radiances for profile variable perturbations assuming a linear relationship about a given atmospheric state. This makes it a useful tool for developing physical retrievals from satellite radiances, for direct radiance assimilation in NWP models, for simulating future instruments, and for training or teaching with a graphical user interface. An overview of the RTTOV model is given, highlighting the updates and increased capability of the latest versions, and it gives some examples of its current performance when compared with more accurate line-by-line radiative transfer models and a few selected observations. The improvement over the original version of the model released in 1999 is demonstrated.

Multiple natural frequencies may be encountered when analyzing the essential natural vibration of a symmetric mechanical system or sub-structure system or a system with special parameters. The transfer matrix method (TMM) is a useful tool for analyzing the natural vibration characteristics of mechanical or structural systems. It derives a nonlinear eigen-problem (NEP) in general, even a transcendental eigen-problem. This investigation addresses the NEP in TMM and proposes a novel method, called the determinant-differentiation-based method, for calculating multiple natural frequencies and determining their multiplicities. Firstly, the characteristic determinant is differentiated with respect to frequency, transforming the even multiple natural frequencies into the odd multiple zeros of the differentiation of the characteristic determinant. The odd multiple zeros of the first derivative of the characteristic determinant and the odd multiple natural frequencies can be obtained using the bisection method. Among the odd multiple zeros, the even multiple natural frequencies are picked out by the proposed judgment criteria. Then, the natural frequency multiplicities are determined by the higher-order derivatives of the characteristic determinant. Finally, several numerical simulations including the multiple natural frequencies show that the proposed method can effectively calculate the multiple natural frequencies and determine their multiplicities.

The mining industry is a fundamental source for building infrastructures and an enabler for a country’s growth. Over the last decade, the act of mining has been among the top in the list of human activities which has the most disturbing and catastrophic impacts on environment, therein extensively affecting the ecological, economic, and social elements in the vicinity. There is an exigency for a pragmatic balance to exist between the global demand satisfaction of metal and environmental sustenance. In this paper, a comprehensive case study on Environmental Impact Assessment (EIA) of a mining site has been presented using the new approach. This new approach is an improved version of the traditional matrix method, incorporating a modified version of Rapid Impact Assessment Matrix (RIAM) integrated with analytical hierarchy process (AHP), thereby knocking out the limitations in the existing EIA techniques. The data used in this study is an outcome of a broad survey conducted among the people associated in both direct and indirect ways to the project actions related to the mining industry and, hence, minimizing issues such as assessors’ reproducibility, subjectivity, and non-inclusivity of all stakeholders’ opinion, which can contribute to misleading outcomes. This new approach delivers more precise and practical results for the assessment of environmental impact data.

The transfer matrix method for multibody systems is a new method with very high computational speed developed in recent 20 years for studying multibody system dynamics. By combining transfer matrix method for multibody systems, computer graphics, and open-source software, this article puts forward an approach and software MSTMMSim for visualized simulation and design of mechanical system dynamics. The approach includes the following procedures in sequence: design of functional model, design of three-dimensional solid model, design of dynamics model, automated formation of dynamics equations, and software MSTMMSim for visualized simulation and design of mechanical system dynamics. The proposed method and software provide a platform to realize the simulation and design of complex mechanical systems with the following characteristics: (1) automatic deduction of the overall transfer equation, (2) high computational speed, and (3) high visualization and programming of dynamics simulation and design process. The proposed method and software are verified by the practical example of simulation and design of a tank system dynamics using this platform.

The present study exhibits excellent sensing characteristics of graphene-based prism-coupled surface plasmon resonance (SPR) biosensor for effectual sensing of both glucose concentrations in human blood samples in the range 25–175 mg/dl and gas with refractive index variations from 1.0000 to 1.0007 at a wavelength of 589 nm. The foremost attractiveness of the proposed SPR biosensor lies with excellent optical properties of N-FK51A-based glass prism along with the inclusion of a gold layer and a thin graphene layer. Transfer matrix method and angular interrogation technique are employed to envisage sharp SPR reflectance curves by optimizing the thickness of the gold layer and number of graphene layers. Aside this, an excellent electric field enhancement factor is accomplished near the graphene and sensing layer interface, which dramatically escalates the absorption of glucose and gas analytes. Subsequently, several performance measuring factors such as sensitivity, detection accuracy, resonance angle shift, and quality factor are thoroughly scrutinized and compared with other conventional SPR sensors. Moreover, simulation results reveal some noteworthy upshots like sensitivity of 275.15°/RIU, detection accuracy of 1.41/°, and quality factor of 76.2 that are obtained for glucose analytes, whereas sensitivity of 92.1°/RIU, detection accuracy of 2.55/° and quality factor of 230.2 are attained for gaseous analytes. Interestingly, it is found that the aforementioned parameters fitted excellently with a linear trend line, which leads to accurate investigation of glucose concentration as well as gaseous analytes. Hence the suggested structure opens up an avenue for suitable biomedical application.

In the multibody system transfer matrix method (MSTMM), the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations. However, regarding the transfer matrices of hinge elements, typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t. various types of outboard body's output links. This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper. Systematic procedures for chain, tree, closed‐loop, and arbitrary general systems are defined, respectively, to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process. As a result, accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.

In vision science, cascades of Linear+Nonlinear transforms are very successful in modeling a number of perceptual experiences. However, the conventional literature is usually too focused on only describing the forward input-output transform. Instead, in this work we present the mathematics of such cascades beyond the forward transform, namely the Jacobian matrices and the inverse. The fundamental reason for this analytical treatment is that it offers useful analytical insight into the psychophysics, the physiology, and the function of the visual system. For instance, we show how the trends of the sensitivity (volume of the discrimination regions) and the adaptation of the receptive fields can be identified in the expression of the Jacobian w.r.t. the stimulus. This matrix also tells us which regions of the stimulus space are encoded more efficiently in multi-information terms. The Jacobian w.r.t. the parameters shows which aspects of the model have bigger impact in the response, and hence their relative relevance. The analytic inverse implies conditions for the response and model parameters to ensure appropriate decoding. From the experimental and applied perspective, (a) the Jacobian w.r.t. the stimulus is necessary in new experimental methods based on the synthesis of visual stimuli with interesting geometrical properties, (b) the Jacobian matrices w.r.t. the parameters are convenient to learn the model from classical experiments or alternative goal optimization, and (c) the inverse is a promising model-based alternative to blind machine-learning methods for neural decoding that do not include meaningful biological information. The theory is checked by building and testing a vision model that actually follows a modular Linear+Nonlinear program. Our illustrative derivable and invertible model consists of a cascade of modules that account for brightness, contrast, energy masking, and wavelet masking. To stress the generality of this modular setting we show examples where some of the canonical Divisive Normalization modules are substituted by equivalent modules such as the Wilson-Cowan interaction model (at the V1 cortex) or a tone-mapping model (at the retina).