• Journal of the Korean Physical Society
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• v.73 no.12
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• pp.1840-1844
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• 2018

Working in an arbitrary Lorentz frame, we address the question of formulating the covariant variational principle for classical, single-particle, dissipative, relativistic mechanics. First, within a Minkowskian geometry, the basic properties of the proper time ${\tau}$ and the covariant velocity $u_{\mu}$ are recapitulated. Next, using a scalar function ${\psi}(x)$ and its negative derivatives ${\varphi}_{\mu}{^{\prime}}s$, we construct a covariant Lagrangian ${\Lambda}$ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ${\psi}$ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.

• Steel and Composite Structures
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• v.51 no.4
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• pp.457-471
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• 2024

In this research, for the first time the instability boundaries for a spinning shaft reinforced with graphene nanoplatelets undergone the principle parametric resonance are determined and examined taking into account the gyroscopic effect. In this respect, the extracted equations of motion in our previous research (Ref. Asadi et al. (2023)) are implemented and efficiently upgraded. In the upgraded discretized equations the effect of the Rayleigh's damping and the varying spinning speed is included that leads to a different dynamical discretized governing equations. The previous research was about the free vibration analysis of spinning graphene-based shafts examined by an eigen-value problem analysis; while, in the current research an advanced mechanical analysis is addressed in details for the first time that is the dynamics instability of the aforementioned shaft subjected to the principal parametric resonance. The spinning speed of the shaft is considered to be varied harmonically as a function of time. Rayleigh's damping effect is applied to the governing equations in order to regard the energy loss of the system. Resorting to Bolotin's route, Floquet theory and β-Newmark method, the instability region and its accompanied boundaries are defined. Accordingly, the effects of the graphene nanoplatelet on the instability region are elucidated.

• The KIPS Transactions:PartD
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• v.9D no.1
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• pp.75-80
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• 2002

Putnam develops SLIM (Software LIfecycle Management) model based upon the assumption that the manpower utilization during software project development is followed by a Rayleigh distribution. To obtain the manpower distribution, we have to be estimate the total development effort and difficulty ratio parameter. We need a way to accurately estimate these parameters early in the requirements and specification phase before investment decisions have to be made. Statistical tests show that system attributes are highly correlation (redundant) so that Putnam discards one and get a parameter estimator from the other attributes. But, different statistical method has different system attributes and presents different performance. To select the principle system attributes, this paper uses the principle component analysis (PCA) instead of Putnam's method. The PCA's results improve a 9.85 percent performance more than the Putnam's result. Also, this model seems to be simple and easily realize.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.217-224
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• 2016

In this study, a transfer matrix method (TMM) for a twisted uniform beam considering the effect of rotary inertia is developed, and the differential equation and the displacements and forces are derived from Hamilton's principle. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. In addition, the results obtained from this method are independent for a number of subdivided elements, and this method can determine the exact solutions for the free vibration characteristics of a twisted uniform Rayleigh beam. To validate the accuracy of the proposed TMM, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of rotary inertia for a twisted beam.

• Steel and Composite Structures
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• v.52 no.5
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• pp.557-569
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• 2024

Nonlinear internal modals interactions analysis of axially functionally graded nanorods is evaluated on the basis of nonlocal elasticity theory and Rayleigh beam model for the first time. Functionally graded materials can be determined as nonhomogeneous composites which are obtained by combining of two various materials in order to get a new ideal material. In this research, material properties of nanorods are supposed to be calmly varied along the axial direction. Hamilton's principle is used to derive the equations with consideration of Von-Kármán's geometrically nonlinearity. Harmonic Differential Quadrature (HDQ) and Multiple Scale (MS) solution techniques are used to derive an approximate-analytic solution to the linear and nonlinear free axial vibration problem of non-classical nanorods for clamped-clamped and clamped-free boundary conditions. A parametric study is carried out to indicate the effects of index of AFG, aspect ratio, mode number, internal resonances and nonlinear amplitude on nonlinear nonlocal frequencies of axially functionally graded nanorods. Also, the effects of nonlocal and nonlinear coefficients and AFG index on relationships of internal resonances have been investigated. The presented theatrical-semi analytical model has the ability to predict very suitable results for extracting the internal modal interactions in the AFG nanorod.

• Journal of the korean Society of Automotive Engineers
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• v.3 no.1
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• pp.38-45
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• 1981

In this paper, the natural frequencies of curved taper leaf springs using on vehicle suspension systems are studied. By applying the Castigliano's definition, Rayleigh's principle and Dunkerley's equation, new formulas defining the natural frequency of such shaped spring are derived. Numerical calculations are in very good agreement with experimental results on actual models. We found that the natural frequencies of curved taper spring are increased by 21-28% compared with the spring having same weight, span and curve but uniform section.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.2
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• pp.435-442
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• 2010

The analysis of rigid body traveling along the rotating Timoshenko shaft has been a topic of interest. The problem arose from the observations that as a structure is subjected to moving loads, dynamic deflection as well as stresses can be significantly higher than those for static loads. The establishment of analytical method for the development and maintenance of performance is required in the fields of the machining operations and the position control using ball screw. The equations of motion for the rotating shaft subjected to the two moving forces are derived by using Hamilton's principle. Influence of system parameters such as the speed ratio, the mass ratio and the Rayleigh coefficient is discussed on the response of the moving system.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.383-386
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• 1996

In this paper, we propose a design method and control law for plannar type two-link flexible manipulator. In designing flexible links, we use Rayleigh's principle. To control flexible manipulator, input distribution controller is used, which is primarily on the basis of nonlinear variable structure control(VSC). The simulation results are also shown.

• Advances in nano research
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• v.9 no.3
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• pp.157-172
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• 2020

The aim of this present research is the effect of the higher-order terms of the governing equation on the forced longitudinal vibration of a nanorod model and making comparisons of the results with classical nonlocal elasticity theory. For this purpose, the free axial vibration along with forced one under the two various linear and harmonic axial concentrated forces in zigzag Single-Walled Carbon Nanotube (SWCNT) are analyzed dynamically. Three various theories containing the classical theory, which is called Eringen's nonlocal elasticity, along with Rayleigh and Bishop theories (higher-order theories) are established to justify the nonlocal behavior of constitutive relations. The governing equation and the related boundary conditions are derived from Hamilton's principle. The assumed modes method is adopted to solve the equation of motion. For the free axial vibration, the natural frequencies are calculated for the various values of the nonlocal parameter only based on Eringen's theory. The effects of the nonlocal parameter, thickness, length, and ratio of the excitation frequency to the natural frequency over time in dimensional and non-dimensional axial displacements are investigated for the first time.

• Steel and Composite Structures
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• v.29 no.6
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• pp.785-802
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• 2018

In this paper, two different computational methods, called Rayleigh-Ritz and collocation are developed to estimate the ultimate strength of composite plates. Progressive damage behavior of moderately thick composite laminated plates is studied under in-plane compressive load and uniform lateral pressure. The formulations of both methods are based on the concept of the principle of minimum potential energy. First order shear deformation theory and the assumption of large deflections are used to develop the equilibrium equations of laminated plates. Therefore, Newton-Raphson technique will be used to solve the obtained system of nonlinear algebraic equations. In Rayleigh-Ritz method, two degradation models called complete and region degradation models are used to estimate the degradation zone around the failure location. In the second method, a new energy based collocation technique is introduced in which the domain of the plate is discretized into the Legendre-Gauss-Lobatto points. In this new method, in addition to the two previous models, the new model named node degradation model will also be used in which the material properties of the area just around the failed node are reduced. To predict the failure location, Hashin failure criteria have been used and the corresponding material properties of the failed zone are reduced instantaneously. Approximation of the displacement fields is performed by suitable harmonic functions in the Rayleigh-Ritz method and by Legendre basis functions (LBFs) in the second method. Finally, the results will be calculated and discussions will be conducted on the methods.