Equivalent Mode Research Articles

Coupled critical plane-pseudo excitation method for multiaxial fatigue analysis of structures under random vibration

This study proposes a coupled critical plane–pseudo excitation method for assessing multiaxial fatigue damage in mechanical structures subjected to random loads. Within the modal coordinate framework, we derive an expression for the spectral moment of the structural stress response using the pseudo excitation method, which facilitates the decoupling of spatial characteristics from frequency domain properties. For the input power spectral density, represented as an integer power function, we employ eigenvalue decomposition and the residue theorem to derive an analytical expression for the spectral moment of the modal displacement response. By constructing equivalent stress modes based on the maximum shear stress and normal stress criteria, we obtain an expression for the equivalent stress variance. Intelligent optimization algorithms are utilized to determine the critical plane position and the corresponding equivalent stress spectral moments, followed by the application of the Dirlik method for fatigue assessment. A numerical example involving random vibration multiaxial fatigue analysis of an L-shaped thin-walled plate demonstrates the effectiveness of the proposed coupled critical plane–pseudo excitation method in comparison to the traditional critical plane method that relies on the stress covariance matrix for calculating equivalent variance. The results confirm the accuracy and efficiency of our approach, and we further explore the impact of different forms of the excitation power spectral density and the damping ratios on the computational outcomes.

SUMER: A New Family of Lightweight and Traditional Block Ciphers with Multi-Modes

With the recent increase in the risks and attacks facing our daily lives and digital environment around us,the trend towards securing data has become inevitable. Block ciphers play a crucial role in modern crypto-applicationssuch as secure network storage and signatures and are used to safeguard sensitive information. The present paperdevelops a new variant of the symmetric model called SUMER family ciphers with three equivalent modes: lightweight,conventional (traditional), and extended ciphers. SUMER name belongs to one of the oldest civilizations inMesopotamia and stands for Secure Universal Model of Encryption Robust Cipher. The SUMER cipher is based on asimple and robust symmetric structure and involves solid algebraic theories that completely depend on the Galois FieldGF(28). SUMER cipher is designed to work with two involutional structures of the Substitution-Permutation Network(SPN) and Feistel structure. These two involutional structures mean that the same algorithm is used for the encryptionand decryption process, and only the algorithm of the ciphering key is used in reverse order in both structures. TheSUMER lightweight structure is an elegant mode that does not need building an S-Box that requires a large amount ofmemory and a number of electronic logical gates as S-Box construction has been canceled and replaced by the on-flycomputation clue, which does not need a reserved memory for building S-Box. SUMER family ciphers also can work ina traditional mode or as an extended mode with high margin security. This family of ciphers is applicable with multimodes of various utilizations. The proposed ciphers are designed to be byte-oriented, showing good evaluation andresults under several measurement tests for speed, time implementation, and efficiency.

Vertical Structure and Energetic Constraints for a Backscatter Parameterization of Ocean Mesoscale Eddies

AbstractMesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy‐permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime.

Экспериментальное исследование влияния температуры распылителя на характеристики сжигания дизельного топлива в атмосферном горелочном устройстве

In this work, using diesel fuel as an example, we studied the combustion characteristics of liquid hydrocarbons when atomized by a high-speed air jet. This approach to spraying liquid fuel in combustion processes has a number of advantages over traditional spraying: the ability to supply fuel with a low degree of purification and to reduce the likelihood of fuel equipment coking. Using an atmospheric burner device with natural air supply into the mixing chamber, the depen¬dences of the composition of intermediate and final combustion products were studied, and the flame temperature was measured at various fuel flow rates and parameters of the atomizing air jet (flow rate, temperature). A comparison was made of the obtained characteristics for equivalent modes at different temperatures of the supplied atomizer. It was found that when heated air is used as a sprayer, higher flame temperatures are ensured, which ensures a more complete fuel burnout and a decrease in CO concentration in the flue gases, but at the same time, a slight increase in NOx is observed.

Fatigue Analysis of Composite Bolted Joints under Random and Constant Amplitude Fatigue Loadings.

This paper attempts to analyze the random fatigue life and failure modes of joints using two calculation methods. Three kinds of tests were carried out, which were the static test, constant amplitude fatigue test and the random fatigue test, and four kinds of joints were designed. After the static test, the joint was subjected to a constant amplitude fatigue test by selecting different percentages of load according to the static strength. In order to predict the random fatigue life more precisely, two calculation methods were carried out, which were the linear cumulative damage method and the equivalent loading finite element method. Based on the linear cumulative damage hypothesis, the fatigue life of the joint was established as a function of the load amplitude, and then, the random life prediction was calculated by the amplitude distribution of the random loading. Another method was the equivalent loading method, which was to obtain the equivalent constant amplitude fatigue loading of the random loading spectrum. The finite element model was established based on the stiffness and strength degradation rule. The equivalent random life and fatigue failure modes of the joint were modeled. The two life prediction methods show good agreement with the fatigue experimental result, and all prediction results were included in a scatter band of the factor of 2.

Моделирование динамики связанных гиротронов методом крупных частиц

The problem of mutual synchronization of two coupled gyrotrons in the 170 GHz waveband was simulated using the particle-in-cells method. To reduce the calculation time, an approach based on replacing the asymmetric operating mode with an equivalent axisymmetric mode was used. As a result, the dimension of the problem is reduced, and instead of three-dimensional modeling, 2.5-dimensional modeling can be used. The limiting case is considered when the lowest axisymmetric mode of the circular waveguide TE01 is chosen as the equivalent mode. The results obtained are demonstrated to be in good agreement with the traditional approach based on modeling of averaged equations.

An Efficient MLFMA for Accurately Analyzing Electromagnetic Radiation and Coupling Characteristics of Large-scale Antenna Arrays Mounted on Platform

A multilevel fast multipole algorithm (MLFMA) for analyzing electromagnetic radiation and coupling characteristics of large-scale antenna arrays mounted on the platforms is presented in this paper. Compared with the method of moments (MoM), the MLFMA can be used to calculate larger scale problems with limited resources. First, waveport model of the MLFMA based on the equivalence principle and mode matching theory is established to efficiently and accurately simulate the antenna array. Then, a preconditioning approach for solving the radiation problems with the waveports is designed to improve convergence of the MLFMA. An initial guess construction method is proposed to accelerate the MLFMA computation for the multi-excitation problems, which can reduce the iteration time by at least 50%. Numerical results demonstrate accuracy and efficiency of the proposed method.

Equivalent Fracture Patterns Demonstrate Poorer Postoperative Functional Outcomes Among Pronation-External Rotation IV Ankle Fractures.

Pronation-external rotation IV (PER IV) ankle fractures are relatively uncommon among rotational ankle fractures, but they are the most severe type. Although recent studies have shown satisfactory functional recovery in PER IV after surgical treatment, the different outcomes between fracture patterns and equivalent fracture patterns have not yet been evaluated. This study aims to compare short-term outcomes in PER IV ankle injuries between fracture patterns and equivalent fracture patterns. This retrospective study was conducted at Quzhou Affiliated Hospital of Wenzhou Medical University, Quzhou, China, from July 2023 to October 2023. A total of 41 PER IV injuries from 2018 to 2022 were included and followed for at least one year. The American Orthopaedic Foot and Ankle Society (AOFAS) Ankle‑Hindfoot Scale, Ankle Range of Motions (ROM), and Visual Analogue Scale (VAS) for pain scores were the main outcome measures. The rate of postoperative complications was the secondary outcome measure. Patient demographics were compared in PER IV fractures and PER IV ankle equivalent fractures. The mean follow-up time was 18.2 ± 4.2 (range, 12-24) months. Postoperative X-ray and CT scans showed a satisfactory reduction of the ankle joint and syndesmosis. No reduction loss of distal tibiofibular syndesmosis or ankle joints was found at the 12-month follow-up. The average AOFAS scores after one year in both groups were satisfactory (fracture group vs. fracture equivalent group, 96.72 ± 4.21 vs. 92.63 ± 5.36; P < 0.05). The average VAS scores after one year in both groups were satisfactory (fracture group vs. fracture equivalent group, 1.45 ± 2.01 vs. 1.38 ± 1.96; P > 0.05). The average ROM scores after one year in both groups were satisfactory (dorsiflexion, fracture group vs. fracture equivalent group, 15.21 ± 5.62 vs. 13.46 ± 4.35; P > 0.05; plantar flexion, fracture group vs. fracture equivalent group, 38.62 ± 9.68 vs. 42.32 ± 5.28; P > 0.05). For patients with PER-IV ankle injuries, the fracture mode had a better prognosis than the fracture equivalent mode.

Optically transparent wideband metamaterial absorber based on equivalent aperture and characteristic mode analysis

In this work, a low-profile optical transparent wideband metamaterial absorber based on radiation–absorption reciprocal theory is proposed. The top layer and bottom layer are composed of indium tin oxide–polyethylene terephthalate films, and the middle layer is a transparent substrate polymethyl methacrylate. The method of transparent wideband absorption using reciprocal theory is proposed to guide the design. Based on characteristic mode analysis and calculated equivalent aperture efficiency, the absorber consisting of composite resonators is analyzed and designed. The equivalent circuit model and surface current distributions are studied to verify the design. The numerical results show that high absorption of greater than 90% in the frequency range of 5.7–16.4 GHz is obtained. A wideband absorption rate of greater than 80% at a 60° incident angle under TM polarization and an absorption rate of greater than 65% at a 60° incident angle under TE polarization are obtained. The proposed design has the advantages of broadband absorption, polarization insensitivity, light transmittance of more than 70%, and compact structure, which can be applied to special scenes that require optical transparency, such as anechoic chamber glass and cockpit glass.

Combustion of diesel fuel sprayed with cold or heated air in an atmospheric burner

In this work the combustion characteristics of liquid hydrocarbons when atomized by a high speed air jet were studied, using diesel fuel as an example. This approach to spraying liquid fuel in combustion processes has a number of advantages over traditional spraying: the ability to supply fuel with a low degree of purification, reducing the chance of coking of fuel equipment. Using an atmospheric burner device with natural air supply into the mixing chamber, the dependences of the composition of intermediate and final combustion products were studied, and the flame temperature was measured at various fuel flow rates and parameters of the atomizing air jet (flow rate, temperature). A comparison of the obtained characteristics was made for equivalent modes at different temperatures of the supplied atomizer. It was found that when heated air is used as a sprayer, higher flame temperatures are ensured, which ensures more complete fuel burnout and a decrease in CO concentration in the flue gases, but at the same time, a slight increase in NOx was observed.

The super-chirality of vector twisted light

Vector vortex light of topological order m arises as a superposition of two twisted modes with phase functions e±imϕ (with ϕ the azimuthal variable) and circular polarizations (σ=∓1). We demonstrate that when m is sufficiently large these modes exhibit enhanced helicity densities when compared with the equivalent circularly-polarized Gaussian modes. The enhancement stems from the presence of longitudinal field components which become significant even for moderate beam widths. The super-chirality of light–matter interactions enabled by such modes suggests a high degree of enantioselectivity, surpassing conventional techniques for the chiral selection, so promising useful applications.

Space-time POD and the Hankel matrix.

Time-delay embedding is an increasingly popular starting point for data-driven reduced-order modeling efforts. In particular, the singular value decomposition (SVD) of a block Hankel matrix formed from successive delay embeddings of the state of a dynamical system lies at the heart of several popular reduced-order modeling methods. In this paper, we show that the left singular vectors of this Hankel matrix are a discrete approximation of space-time proper orthogonal decomposition (POD) modes, and the singular values are square roots of the POD energies. Analogous to the connection between the SVD of a data matrix of snapshots and space-only POD, this connection establishes a clear interpretation of the Hankel modes grounded in classical theory, and we gain insights into the Hankel modes by instead analyzing the equivalent discrete space-time POD modes in terms of the correlation matrix formed by multiplying the Hankel matrix by its conjugate transpose. These insights include the distinct meaning of rows and columns, the implied norm in which the modes are optimal, the impact of the time step between snapshots on the modes, and an interpretation of the embedding dimension/height of the Hankel matrix in terms of the time window on which the modes are optimal. Moreover, the connections we establish offer opportunities to improve the convergence and computation time in certain practical cases, and to improve the accuracy of the modes with the same data. Finally, popular variants of POD, namely the standard space-only POD and spectral POD, are recovered in the limits that snapshots used to form each column of the Hankel matrix represent flow evolution over short and long times, respectively.

Improved K-SVD Model in Higher Vocational Physics Teaching

Abstract In physics class, the residual data before and after noise elimination contains more image information. In the equivalent wave domain, the K-SVD method is used to eliminate noise in the noise image of each frequency band and the residual of each frequency band. The main objective is to improve the image quality of noise. The method is combined with the denoised sub-spectrum to obtain the denoised sub-spectrum with the residual signal. An inverse isomorphic wave is used for noise reduction. The simulation results show that the noise reduction algorithm using K-SVD is better than the equivalent waveform and K-SVD mode. This method has achieved good results in practical application.

An Efficient Straightforward Pushover Method for Buildings with Two-Way Unsymmetric-Plan Subjected to Two Components of Ground Motions

ABSTRACT A straightforward pushover method is developed for unsymmetric-plan buildings under bidirectional seismic excitation. To this end, a single innovative torsional-lateral load pattern is introduced based on the response spectrum analysis. The joint contribution of two horizontal seismic excitations and the joint contribution of all considered modes to internal structural forces in forming plastic hinges are considered by implementing the single load pattern. An equivalent dominant mode shape derived from the load pattern is defined to establish capacity spectra in both directions. The accuracy of the proposed procedure in estimating the seismic demands of buildings is demonstrated through two unsymmetric-plan buildings.

A Miniaturized Active Dual SIW Re-Entrant Resonators for High-Resolution and Ultra-low-Limit-Concentration Detection to Glucose Solutions

Two passive re-entrant cavity resonators (RECRs) in substrate integrated waveguide (SIW) configuration are vertically stacked to implement a miniaturized dual RECRs sensor. Only one negative resistance circuit (NRC) is innovatively proposed to be connected with these two RECRs in the common stacked metal layer between them and implement an active dual RECRs sensor, and the corresponding equivalent lumped circuit mode is proposed to analyze the dielectric sensing characteristics. Then, the compensated power obtained from the NRC is simultaneously fed into these two RECRs embedded with two microfluidics, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor of either of these two RECRs can be greatly enhanced by simply changing the bias voltages of the transistor and varactor in the NRC. Finally, the active sensor is utilized to perform high-resolution detection to glucose solutions in high concentration range from 100 to 1000 mmol/L and low concentration range from 1 to 50 mmol/L. By gradually approximating the resonant frequency self-shift noise <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta f_{\mathrm {Aself}}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta f_{\mathrm {Bself}}$ </tex-math></inline-formula> ) of the active RECR-A (RECR-B) by the resonant frequency shift <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta f_{\mathrm {s}}$ </tex-math></inline-formula> determined by glucose solutions, minimum detectable glucose concentration of 1 mmol/L is experimentally achieved. The linear relationship between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta f_{\mathrm {s}}$ </tex-math></inline-formula> and the glucose concentration is experimentally demonstrated, and shows good potential for glucose sensing.

Equivalent Modes of Reimbursement in Augmented Contests

This article presents an equivalence theorem in the context of Tullock’s augmented lottery contest with external or internal cost reimbursement. Three alternative modes of reimbursement are studied. The equivalence implies that, even though the augmented contest is vulnerable to framing biases, it is strategically neutral.

Parallel-Connected Voltage Source Converters With a DC Common Mode and an AC Differential Mode PWM Filter

Two 3-phase converters can be connected in parallel using a range of inductor types. Coupled inductors used together with interleaved pulsewidth modulated (PWM) techniques can produce a high-quality multilevel PWM line output voltage. These inductors can be designed to have a high inductance between the two converter outputs to control circulating currents, combined with a low per-phase output inductance. Since the 3-phase PWM voltage between the two converters consists of two components, a differential mode and common mode, two inductor types can be used to separately filter the circulating currents produced by these two components. The inductor types presented places one coupled inductor between the 3-phase output terminals of the two converters, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-limb CI</i> , and a second coupled inductor located between the two converter dc input terminals, a dc coupled inductor or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc choke</i> . The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-limb CI</i> filters circulating currents due to the differential mode PWM voltage and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc choke</i> filters circulating currents due to the common mode PWM voltage. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc choke</i> uses four windings in contrast to the six required of an equivalent common mode 3-phase ac choke. The two converters are operated with a filter capacitor across their dc input terminals. The 3-phase output of the two parallel converters is located at the center tap of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-limb CI</i> windings in each phase and a very low effective per-phase output inductance is obtained. Consequently, the converter structure can supply very high-frequency fundamental output voltages with high-quality multilevel PWM line voltages. The performance of the coupled inductors presented is compared with a conventional coupled inductor and designs show that they can be 13% smaller with 16% lower losses. The parallel converter structure presented is suitable for high-power high-speed electric drives with applications in aerospace and electric vehicles where lightweight magnetics is required. Simulations and experimental results are presented for an 8 kW (300 Vdc, 208 Vac/22A) prototype operating with a fundamental frequency of 60 Hz –1.1 kHz.

Numerical simulation of deformations of a specimen of a composite helicopter blade as part of a resonant vibration set-up

To determine the fatigue life of the tail rotor blade of a helicopter made of polymer composite materials (CM), a method of fatigue testing of the specimens of the blade with accompanied numerical modeling of the deformed state has been developed. The tests are carried out on a resonant vibration set-up, with simultaneous reproduction of a forcing harmonic transverse force and a constant longitudinal tensile force. The tests are carried out by a vibration loading mode equivalent in fatigue damage, which includes one level of variable load in the thrust plane and in the plane of rotation. The equivalent mode is formed based on the variable loading spectrum of the blade, which is obtained from the results of flight measurements of the loads on the tail rotor, as well as the repeatability of the expected operating conditions of the helicopter. The tests are accompanied by computational and experimental studies, which include finite element calculation of the stress state and modal analysis of the standard blade and the test specimen, as well as the strain measuring of the structure. According to the results of the research, the vibration loading modes are corrected.

Математическая модель мостового статического преобразователя напряжения

The article presents the equivalent circuits and operation modes of a full-bridge static converter. A presented mathematical model of a voltage converter describes the operation of its elements and provides a study of power transformer magnetization. The results of mathematical and simulation modeling obtained in Matlab/Simulink and OrCAD are compared.

Concepts and Key Technologies of Microelectromechanical Systems Resonators.

In this paper, the basic concepts of the equivalent model, vibration modes, and conduction mechanisms of MEMS resonators are described. By reviewing the existing representative results, the performance parameters and key technologies, such as quality factor, frequency accuracy, and temperature stability of MEMS resonators, are summarized. Finally, the development status, existing challenges and future trend of MEMS resonators are summarized. As a typical research field of vibration engineering, MEMS resonators have shown great potential to replace quartz resonators in timing, frequency, and resonant sensor applications. However, because of the limitations of practical applications, there are still many aspects of the MEMS resonators that could be improved. This paper aims to provide scientific and technical support for the improvement of MEMS resonators in timing, frequency, and resonant sensor applications.