Moment Of Inertia Research Articles

Mechanical attributes of fractal dragons

Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how the geometries of fractals can be exploited to determine their important mechanical properties, such as the first and second moments, which physically correspond to the center of mass and the moment of inertia, using a family of complex fractals known as the dragons.

Relativistic model for anisotropic compact stars in embedding class-I spacetime

In the present article, we introduce a completely new regular model for static, spherically symmetric celestial fluid spheres in embedding class I spacetime. In this regard, needfully, we propose a new suitable metric potential e λ(r) to generate the present model. The various analyses on energy density, pressure, anisotropic factor, mass, compactness parameter, redshift, and energy condition make sure the model is physically viable on the ground of model stars Vela X-1, Cen X-3, SMC X-4, and LMC X-4. The reported solutions also respect the equilibrium state by satisfying the Tolman–Oppenheimer–Volkoff (TOV) equation and ensure stability by satisfying the causality condition, condition on the adiabatic index, and Harrison–Zeldovich–Novikov condition. The generated M − R graph matches the ranges of masses and radii for the model compact stars. Additionally, this study provides estimates of the moment of inertia based on the I − M graph.

Calcium plus vitamin D supplementation during pregnancy has no impact on postpartum transient longitudinal changes in hip geometry in adolescent mothers: a secondary analysis of a randomised controlled trial.

We have previously demonstrated that calcium plus vitamin D supplementation during adolescent pregnancy reduces the magnitude of transient postpartum bone mass loss. In the present post hoc analysis, we further investigated the effect of calcium plus vitamin D supplementation during pregnancy in hip geometry throughout one year postpartum in Brazilian adolescents with low daily calcium intake (∼600 mg/d). Pregnant adolescents (14-19 years) were randomly assigned to receive calcium (600 mg/d) plus vitamin D3 (200 μg/d) or a placebo from 26 weeks of gestation until parturition. Dual-energy X-ray absorptiometry images were obtained at 5 (n 30 and 26 for calcium plus vitamin D and placebo, respectively), 20 (n 26 and 21) and 56 (n 18 and 12) weeks postpartum, and hip geometry parameters were analysed by Advanced Hip Assessment software. The effects of the intervention, time point and their interaction were assessed using repeated-measures mixed-effects models. No significant intervention effects or intervention × time interactions were observed on hip geometry parameters (P > 0·05). Time effects were observed in cross-sectional area, cross-sectional moment of inertia and section modulus parameters with decreases from the 5th to the 20th week postpartum followed by recovery from the 20th to the 56th week (P < 0·05). Our findings indicate that the postpartum period is associated with transient changes in the hip geometry of lactating adolescent mothers, regardless of the low calcium intake and the supplementation offered during pregnancy, suggesting that a physiological adaptation of these adolescents to low calcium intake is at play.

Inertial analyses based on the generalized inertia matrix for parallel robots

Analyzing the inertial properties is meaningful for parallel robots, especially those interacting with the environment. This paper provides tools for the analysis of the inertial properties of parallel robots based on the generalized inertia matrix (GIM). Since most interactions between the environment and robots happen through the mobile platform, the inertia of the whole robot reflected at the platform is considered. In this framework, the GIM is expressed in Cartesian space to yield inertial characteristics with a clear physical meaning. Then, the inertia of the whole robot is thereby reduced to an equivalent mass/inertia at the platform. Unlike for serial robots, obtaining the GIM of parallel robots in Cartesian space is complex due to the inherent closed-loop structures and the possibility of including two different types of redundancy. Two methods are proposed to solve the mentioned problems, which can simplify the derivations of the required GIMs for parallel robots. Detailed analysis and usages of the proposed methods are given based on different examples, and the results demonstrate the effectiveness of the proposed approaches.

Hovering Control on a Variable-Parameters Model of a Small Unmanned Helicopter Based on a Backstepping Sliding Mode Method

In order to strengthen the hovering precision of a small unmanned helicopter with a manipulator for completing a hovering operation, in this study, a double-loop control strategy of position and attitude is designed. In the position loop, a sliding mode controller is proposed. It attains high precision and strong robustness under continuous disturbance. With the manipulator continuously operating during helicopter hovering, the overall center of gravity and the moment of inertia of the system will also change. Therefore, a backstepping sliding mode controller is proposed in the attitude loop for controlling the hovering attitude of the helicopter. The high precision and strong robustness of the control system are proven. The digital simulation presents a position steady-state error of less than 2% under constant disturbance, and the hovering attitude angle fluctuation amplitude of the helicopter is less than 0.05 rad.

Stochastic dissipative Euler’s equations for a free body

Abstract Intrinsic thermal fluctuations within a real solid challenge the rigid body assumption that is central to Euler’s equations for the motion of a free body. Recently, we have introduced a dissipative and stochastic version of Euler’s equations in a thermodynamically consistent way (European Journal of Mechanics – A/Solids 103, 105,184 (2024)). This framework describes the evolution of both orientation and shape of a free body, incorporating internal thermal fluctuations and their concomitant dissipative mechanisms. In the present work, we demonstrate that, in the absence of angular momentum, the theory predicts that the principal axes unit vectors of a body undergo an anisotropic Brownian motion on the unit sphere, with the anisotropy arising from the body’s varying moments of inertia. The resulting equilibrium time correlation function of the principal eigenvectors decays exponentially. This theoretical prediction is confirmed in molecular dynamics simulations of small bodies. The comparison of theory and equilibrium MD simulations allow us to measure the orientational diffusion tensor. We then use this information in the Stochastic Dissipative Euler’s Equations, to describe a non-equilibrium situation of a body spinning around the unstable intermediate axis. The agreement between theory and simulations is excellent, offering a validation of the theoretical framework.

Torsional damper design for diesel engine: theory and application

Abstract Torsional vibration is the primary cause of engine crankshaft failure. Consequently, the reduction of engine vibration is of paramount importance for the enhancement of automotive safety and comfort. However, the lack of comprehensive insight into the damping mechanism of the torsional damper has impeded the effective control of engine torsional vibration. In order to gain insight into the vibration characteristics of the shaft system in an inline six-cylinder diesel engine, an analysis of the system’s behaviour during both free and forced vibration was conducted. A mathematical relationship was deduced between the dimensions, material, operational temperature and damping properties of the silicone oil damper. The objective was to determine the optimal damping and moment of inertia of the damper, with the aim of minimizing the torsional amplitude of the sixth harmonic. The results demonstrate a reduction in the six-harmonic torsional amplitude from 0.32° to 0.14° following the installation of the damper. The mean and relative deviations between the calculated and experimental results are 0.0018° and 0.83%, respectively. To facilitate the design of the silicone oil damper, a software program, Vibsim, was developed based on Visual Studio for the design and torsional vibration analysis of the silicone oil damper. This software is reliable in calculating results and is user-friendly.

Current Compensation for Faulted Grid-Connected PV Arrays Using a Modified Voltage-Fed Quasi-Z-Source Inverter

Large-scale photovoltaic (PV) systems are being widely deployed to meet global environmental goals and renewable energy targets. Advances in PV technology have driven investment in the electric sector. However, as the size of PV arrays grows, more obstacles and challenges emerge. The primary obstacles are the occurrence of direct current (DC) faults and shading in a large array of PV panels, where any malfunction in a single panel can have a detrimental impact on the overall output power of the entire series-connected PV string and therefore the PV array. Due to the abrupt and frequent fluctuations in power, beside the low-PV systems’ moment of inertia, various technical problems may arise at the point of common coupling (PCC) of grid-connected PV generations, such as frequency and voltage stability, power efficiency, voltage sag, harmonic distortion, and other power quality factors. The majority of the suggested solutions were deficient in several crucial transient operating features and cost feasibility; therefore, this paper introduces a novel power electronic DC–DC converter that seeks to mitigate these effects by compensating for the decrease in current on the DC side of the system. The suggested solution was derived from the dual-source voltage-fed quasi-Z-source inverter (VF-qZSI), where the PV generation power can be supported by an energy storage element. This paper also presents the system architecture and the corresponding power switching control. The feasibility of the proposed method is investigated with real field data and the PSCAD simulation platform during all possible weather conditions and array faults. The results demonstrate the feasibility and capability of the proposed scheme, which contributes in suppressing the peak of the transient power-to-time variation (dP/dt) by 72% and reducing its normalized root-mean-square error by about 38%, with an AC current total harmonic distortion (THD) of only 1.04%.

Adaptive Virtual Synchronous Generator Control Strategy Based on Frequency Integral Compensation

With the increasing proportion of power electronic equipment in the power system, improving the inertia and damping characteristics of the system through virtual synchronous generator (VSG) control technology has become a hot research topic. In terms of adjusting the output frequency, traditional primary frequency modulation control cannot ensure that the output frequency is maintained within the safe operating range when the load disturbance is large, so secondary frequency modulation with the integral link is usually adopted. However, the fixed integral coefficient cannot solve the contradiction between system regulation time and frequency oscillation. In this paper, a strategy of coordinated adaptive control based on the integral coefficient, moment of inertia, and damping coefficient is proposed. According to the offset of frequency and the change rate of the frequency offset, the value of parameters is determined, and the specific parameter setting method is determined. Finally, the correctness of the proposed control strategy is verified on a simulation platform and a semi-physical experimental platform.

Effects of transverse loading on the ultimate strength prediction of stiffened panels under biaxial loads: Potential improvements to the IACS rule formulation

The current International Association of Classification Societies (IACS) rule for designing stiffened panels was found in Wang et al. (2024) to conservatively predict the ultimate strength of panels when transverse loads predominate. This conservatism arises from the overestimation of bending moments acting on stiffeners by directly applying the beam analogy in both longitudinal and transverse directions in the rule formulation when evaluating stiffener yielding.To address this issue, this paper applies the orthotropic plate theory to calculate bending moments experienced by the stiffeners of panels under biaxial loads. Orthotropic properties are derived from equivalent sectional areas and moments of inertia. The predicted bending moments are validated through comparisons with numerical simulations. The effects of boundary conditions and deflection patterns with varying numbers of half-waves are discussed. Based on the analytical results, a modification of the IACS rule formulation is proposed by introducing a correction factor to account for transverse loading effects in the bending moment calculations. The factor is a function of the ratio between longitudinal and transverse loading.The modified IACS rule formulation is verified through numerical simulations of aluminium panels using ABAQUS and comparisons with results from existing literature on steel stiffened panels under various biaxial loading conditions. The modified rule formulation shows improved accuracy in predicting the ultimate strength of stiffened panels, particularly in cases with dominating transverse loads. The modified IACS rule formulation can be useful for more reliable and cost-effective design of ships and offshore structures.

Enhancing the bending strength, load-carrying capacity and material efficiency of aspen and black alder plywood through thermo-mechanical densification of face veneers

Many research papers highlight the positive impact of wood densification on mechanical properties of solid wood as well as wood veneers. Previous experimental studies comparing densified to non-densified wood materials of the same thickness consistently demonstrated higher strength properties in bending for densified materials. However, these studies often overlooked an important comparison: the strength and load-carrying capacity of non-densified wood material to its densified state, in which the thickness is reduced and thus the material’s moment of inertia. The current study, aims to address this gap for plywood made from low-quality, underutilized hardwood species, encompassing both non-densified and densified veneers. Additionally, these plywood panels are compared with high-quality birch plywood. Plywood samples made from common aspen (Populus tremula L.) and black alder (Alnus glutinosa L.) species, incorporating densified veneers, are compared to conventional silver birch (Betula pendula Roth.) plywood. The study also considers material utilization efficiency. Results showed that plywood made from non-densified aspen and black alder veneers exhibited comparable strength to standard birch plywood, positioning them as competitive alternatives to high-quality wood species. While densified black alder veneers increased strength in average from 83.6 MPa to 126.3 MPa, a loss in load-carrying capacity was observed from 1930 N to 1637 N due to reduced thickness and moment of inertia.

Effective Moment of Inertia of Reinforced Concrete and Reinforced Steel Fiber-Reinforced Concrete One-Way Slabs

Effective Moment of Inertia of Reinforced Concrete and Reinforced Steel Fiber-Reinforced Concrete One-Way Slabs

Teaching labs for blind students: Equipment to measure the inertia of simple objects

This article describes a laboratory experiment for blind students to measure the moment of inertia of simple objects; in this case, that of a disc about its axis of symmetry. We adapted our usual lab to modify the data collection process, using an open-source electronic platform to convert visual signals into acoustic signals. This allowed blind students at our University to participate alongside their classmates in the mechanics lab.

Analyze the moment of inertia of an object in uniformly accelerated linear motion and angular motion

Abstract. In studying particle kinematics, calculus plays an important role in analyzing and solving motion problems as a key mathematical tool. This paper mainly discusses the application of calculus in uniformly accelerated linear motion (LM) and angular motion (AM), focusing on the relationship between position, velocity, and acceleration and the analysis of the rate of change of motion. Through the study of uniformly accelerated LM, this paper guides researchers to use calculus to establish the mathematical relationship between position, velocity, and acceleration and verifies the accuracy of these formulas through practical cases. Similarly, in AM, this paper provides an in-depth understanding of the dynamic behavior of an object rotating around a fixed axis through calculus and calculates and applies important parameters in AM to solve practical problems by analyzing angular velocity and acceleration. In addition, this paper demonstrates the potential of calculus for a wide range of applications in dealing with variable speed motion and rate of change analysis. By integrating the rate of change of displacement and acceleration, it provides a precise tool for the optimization and resolution of engineering problems. In conclusion, calculus not only enriches the theory of kinematics but also demonstrates its important value in practical applications.

EVALUATION OF FISSION FRAGMENT MOMENTS OF INERTIA FOR SPONTANEOUS FISSION OF CF-252

Abstract The paper discusses methods for estimating the moments of inertia of fission fragments for spontaneous fission of the isotope Cf-252, in particular, two main approaches are mentioned: statistical and microscopic. In addition, the methods of the classical and superfluid approaches to the calculation of the moments of inertia are discussed, as well as their application to different models of nuclei. Within this framework, the influence of different vibrational modes and nucleon exchange on the moments of inertia and spin distributions of fission fragments is evaluated. The paper emphasizes the need for a comparative analysis of theoretical predictions with experimental data for a deeper understanding of the internal structure of nuclei and fission mechanisms.

Artificial Neural Network-Based Data-Driven Parameter Estimation Approach: Applications in PMDC Motors

The optimal performance of direct current (DC) motors is intrinsically linked to their mathematical models’ precision and their controllers’ effectiveness. However, the limited availability of motor characteristic information poses significant challenges to achieving accurate modeling and robust control. This study introduces an approach employing artificial neural networks (ANNs) to estimate critical DC motor parameters by defining practical constraints that simplify the estimation process. A mathematical model was introduced for optimal parameter estimation, and two advanced learning algorithms were proposed to efficiently train the ANN. The performance of the algorithms was thoroughly analyzed using metrics such as the mean squared error, epoch count, and execution time to ensure the reliability of dynamic priority arbitration and data integrity. Dynamic priority arbitration involves automatically assigning tasks in real-time depending on their relevance for smooth operations, whereas data integrity ensures that information remains accurate, consistent, and reliable throughout the entire process. The ANN-based estimator successfully predicts electromechanical and electrical characteristics, such as back-EMF, moment of inertia, viscous friction coefficient, armature inductance, and armature resistance. Compared to conventional methods, which are often resource-intensive and time-consuming, the proposed solution offers superior accuracy, significantly reduced estimation time, and lower computational costs. The simulation results validated the effectiveness of the proposed ANN under diverse real-world operating conditions, making it a powerful tool for enhancing DC motor performance with practical applications in industrial automation and control systems.

Educational Software for Stress Analysis of Open Thin-Walled Structures

Thin-walled structures are commonly employed in aerospace and automotive structures because of their high strength to weight ratio. Design and hence the stress analysis of thin-walled structures is tedious and time-consuming. An educational software which can aid students in stress analysis of thin-walled open sections will enhance the teaching-learning process. With the present available software, the number of sections that can be analysed is limited, hence in this work, a generalized section has been developed through which many new complex sections can be generated and analysed for stresses. The objective of the present work is to develop educational software that will provide a solution for the section properties like centroid, moment of inertia and shear centre, and the stresses on the section for a given loading. The software enables students to select different cross-sections which may be subjected to bending, shear or torsional loads and evaluate the stresses on it. Results obtained through this software have been validated against literature. The software has been developed using MATLAB with graphical user interface (GUI). The software is expected to be a useful tool for effective teaching learning process of courses on thin-walled structures, aircraft structures and advanced mechanics of materials.

Odd-even mass differences of well and rigidly deformed nuclei in the rare earth region: A test of a newly proposed fit of average pairing matrix elements

Abstract We discuss a test of a recently proposed approach to determine average pairing matrix elements within a given interval of single-particle states (sp) around the Fermi level $\lambda$ as obtained in the so-called uniform gap method (UGM). It takes stock of the crucial role played by the averaged sp level density $\tilde{\rho}(e)$. These matrix elements are deduced within the UGM approach, from microscopically calculated $\tilde{\rho}(e)$ and gaps obtained from analytical formulae of a semi-classical nature. Two effects generally ignored in similar fits have been taken care of. They are: (a) the correction for a systematic bias in choosing to fit pairing gaps corresponding to equilibrium deformation solutions as discussed by M"{o}ller and Nix [Nucl. Phys. A 476, 1 (1992)] and (b) the correction for a systematic spurious enhancement of $\tilde{\rho}(e)$ for protons in the vicinity of $\lambda$, because of the local Slater approximation used for the treatment of the Coulomb exchange terms in most calculations (see e.g. [Phys. Rev C 84, 014310 (2011)]). This approach has been deemed to be very efficient upon performing Hartree-Fock + BCS (with seniority force and self-consistent blocking when dealing with odd nuclei) calculations of a large sample of well and rigidly deformed even-even rare-earth nuclei. The reproduction of their experimental moments of inertia has been found to be at least of the same quality as what has been obtained in a direct fit of these data [Phys. Rev C 99, 064306 (2019)]. We extend here the test of our approach to the reproduction, in the same region, of three-point odd-even mass differences centered on odd-$N$ or odd-$Z$ nuclei. The agreement with the data is again roughly of the same quality as what has been obtained in a direct fit, as performed in [Phys. Rev C 99, 064306 (2019)].

Adaptive Sliding Mode Control for Trajectory Tracking of Quadrotor Unmanned Aerial Vehicles Under Input Saturation and Disturbances

This paper addresses the challenging issue of trajectory tracking for uncertain quadrotor unmanned aerial vehicles (UAVs), particularly under the constraints of input saturation and external disturbances. It introduces adaptive laws for managing uncertainties in mass and inertia moments without requiring prior knowledge, ensuring effective control even with varying system parameters. To counteract the effects of input saturation, the study incorporates an auxiliary system designed to compensate for these limitations. Additionally, a disturbance observer (DO) is utilized to manage and mitigate the impact of time-varying external disturbances. The proposed control strategy integrates a sliding mode adaptive control approach with an inner–outer loop structure, enhancing robustness and adaptability. Numerical simulations demonstrate the effectiveness of the designed control strategy.

Description of moments of inertia of superdeformed bands using two and three parameter models in A ≈ 60-90 mass region

Description of moments of inertia of superdeformed bands using two and three parameter models in A ≈ 60-90 mass region