Moduluation-Function Technique in Nonuniform Mechanical Systems

1985 ◽  
Vol 52 (2) ◽  
pp. 479-483
Author(s):  
Y. Frostig ◽  
G. Rosenhouse
Keyword(s):  
Dynamic Response ◽  
Longitudinal Vibration ◽  
Mechanical Systems ◽  
Efficient Solutions ◽  
Second Order ◽  
Function Technique ◽  
Structural Systems ◽  
Time Varying ◽  
Numerical Examples ◽  
Modulation Function

This note demonstrates the advantages of the modulation-function technique, proposed here as means of finding efficient solutions for second-order structural systems, the inhomogeneity of which may also vary quickly. The problems dealt with, include buckling of columns, longitudinal vibration of rods, and the dynamic response of time-varying SDF’s. The basic formulas are presented and numerical examples are worked out for buckling.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

2021 ◽  
pp. 1-16
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Response ◽  
Hydrodynamic Lubrication ◽  
Helical Gear ◽  
Calculation Model ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Wear ◽  
Mesh Stiffness ◽  
Helical Gear Pair

Abstract Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

scholarly journals Time-Varying Impedance Control of Port Hamiltonian System with a New Energy-Storing Tank

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Min Zheng ◽  
Tangqing Yuan ◽  
Tao Huang
Keyword(s):  
Control Method ◽  
Impedance Control ◽  
Conservative System ◽  
Time Varying ◽  
Control Performance ◽  
Singularity Problem ◽  
Numerical Examples ◽  
New Energy ◽  
Simulation Results ◽  
New Framework

In order to guarantee the passivity of a kind of conservative system, the port Hamiltonian framework combined with a new energy tank is proposed in this paper. A time-varying impedance controller is designed based on this new framework. The time-varying impedance control method is an extension of conventional impedance control and overcomes the singularity problem that existed in the traditional form of energy tank. The validity of the controller designed in this paper is shown by numerical examples. The simulation results show that the proposed controller can not only eliminate the singularity problem but can also improve the control performance.

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