scholarly journals On the Euler method of summability and concerning Tauberian theorems

2021 ◽  
Vol 42 (1) ◽  
pp. 141-144
Author(s):  
Sefa Anıl SEZER ◽  
İbrahim ÇANAK
2020 ◽  
Vol 48 (4) ◽  
pp. 287-314
Author(s):  
Yan Wang ◽  
Zhe Liu ◽  
Michael Kaliske ◽  
Yintao Wei

ABSTRACT The idea of intelligent tires is to develop a tire into an active perception component or a force sensor with an embedded microsensor, such as an accelerometer. A tire rolling kinematics model is necessary to link the acceleration measured with the tire body elastic deformation, based on which the tire forces can be identified. Although intelligent tires have attracted wide interest in recent years, a theoretical model for the rolling kinematics of acceleration fields is still lacking. Therefore, this paper focuses on an explicit formulation for the tire rolling kinematics of acceleration, thereby providing a foundation for the force identification algorithms for an accelerometer-based intelligent tire. The Lagrange–Euler method is used to describe the acceleration field and contact deformation of rolling contact structures. Then, the three-axis acceleration vectors can be expressed by coupling rigid body motion and elastic deformation. To obtain an analytical expression of the full tire deformation, a three-dimensional tire ring model is solved with the tire–road deformation as boundary conditions. After parameterizing the ring model for a radial tire, the developed method is applied and validated by comparing the calculated three-axis accelerations with those measured by the accelerometer. Based on the features of acceleration, especially the distinct peak values corresponding to the tire leading and trailing edges, an intelligent tire identification algorithm is established to predict the tire–road contact length and tire vertical load. A simulation and experiments are conducted to verify the accuracy of the estimation algorithm, the results of which demonstrate good agreement. The proposed model provides a solid theoretical foundation for an acceleration-based intelligent tire.


Author(s):  
Ümit Totur

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0


2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.


2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.


Author(s):  
Bo Li ◽  
Xiaoting Rui ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
Qinbo Zhou

Dynamics analysis is currently a key technique to fully understand the dynamic characteristics of sophisticated mechanical systems because it is a prerequisite for dynamic design and control studies. In this study, a dynamics analysis problem for a multiple launch rocket system (MLRS) is developed. We particularly focus on the deductions of equations governing the motion of the MLRS without rockets by using a transfer matrix method for multibody systems and the motion of rockets via the Newton–Euler method. By combining the two equations, the differential equations of the MLRS are obtained. The complete process of the rockets’ ignition, movement in the barrels, airborne flight, and landing is numerically simulated via the Monte Carlo stochastic method. An experiment is implemented to validate the proposed model and the corresponding numerical results.


1998 ◽  
Vol 193 (1) ◽  
pp. 211-234 ◽  
Author(s):  
Richard Warlimont
Keyword(s):  

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