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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.

The optical filter is critical in many applications requiring wide-angle imaging perception. However, the transmission curve of the typical optical filter will change at an oblique incident angle due to the optical path of the incident light change. In this study, we propose a wide-angular tolerance optical filter design method based on the transfer matrix method and automatic differentiation. A novel optical merit function is proposed for simultaneous optimization at normal and oblique incidents. The simulation results demonstrate that such a wide-angular tolerance design can realize a similar transmittance curve at an oblique incident angle compared to a normal incident angle. Furthermore, how much improvement in a wide-angular optical filter design for oblique incident contributes to image segmentation remains unclear. Therefore, we evaluate several transmittance curves along with the U-Net structure for green pepper segmentation. Although our proposed method is not perfectly equal to the target design, it can achieve an average 50% smaller mean absolute error (MAE) than the original design at 20∘ oblique incident angle. In addition, the green pepper segmentation results show that wide-angular tolerance optical filter design improves the segmentation of the near-color object about 0.3% at 20∘ oblique incident angle compared to the previous design.

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.

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 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.

This paper presents a novel investigation of a magnetic sensor that employs Fano/Tamm resonance within the photonic band gap of a one-dimensional crystal structure. The design incorporates a thin layer of gold (Au) alongside a periodic arrangement of Tantalum pentoxide ( $$\\:{\\text{T}\\text{a}}_{2}{\\text{O}}_{5}$$ ) and Cesium iodide ( $$\\:\\text{C}\\text{s}\\text{I}$$ ) in the configuration $$\\:[\\:\\text{A}\\text{u}/{\\:\\left(\\right({\\text{T}\\text{a}}_{2}{\\text{O}}_{5})/(\\text{C}\\text{s}\\text{I}\\left)\\right)}^{\\text{N}}]$$ . We utilized the transfer matrix method in conjunction with the Drude model to analyze the formation of Fano/Tamm states and the permittivity of the metallic layer, respectively. These states can be manipulated based on the left-handed and right-handed circular polarization of electromagnetic waves, along with an applied magnetic field. Several key parameters were optimized, including material selection, layer thickness, unit cell periodicity, and the angle of incidence, to enhance the sensor performance. Additionally, we investigated how variations in magnetic field strength influence the position of Fano/Tamm resonance in the reflectivity spectrum of the interacting electromagnetic waves within a specific wavelength range of 60 μm to 140 μm. The proposed sensor displays good performance investigated by calculating several parameters like, sensitivity, figure of merit, quality factor and resolution. One of them, it shows a maximum sensitivity of 57 nm/Tesla within a magnetic field strength of 20 to 140 Tesla, positioning it as a promising candidate for various applications in magnetic field measurement and telecommunications, particularly in the unique far-infrared region.

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.

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.

The dynamics of an ultra‐precision machine tool determines the precision of the machined surface. This study aims to propose an effective method to model and analyze the dynamics of an ultra‐precision fly‐cutting machine tool. First, the dynamic model of the machine tool considering the deformations of the cutter head and the lathe head is developed. Then, the mechanical elements are classified into M subsystems and F subsystems according to their properties and connections. The M‐subsystem equations are formulated using the transfer matrix method for multibody systems (MSTMM), and the F‐subsystem equations are analyzed using the finite element method and the Craig–Bampton reduction method. Furthermore, all the subsystems are assembled by combining the restriction equations at connection points among the subsystems to obtain the overall transfer equation of the machine tool system. Finally, the vibration characteristics of the machine tool are evaluated numerically and are validated experimentally. The proposed modeling and analysis method preserves the advantages of the MSTMM, such as high computational efficiency, low computational load, systematic reduction of the overall transfer equation, and generalization of its computational capability to general flexible‐body elements. In addition, this study provides theoretical insights and guidance for the design of ultra‐precision machine tools.