Azimuth-only Estimation of Target Course Using Trigonometric Function Directly

2021 ◽  
pp. 135-142
Author(s):  
Tao Yu
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.


2018 ◽  
Vol 8 (12) ◽  
pp. 2457 ◽  
Author(s):  
Kangjian Wang ◽  
Man Zhou ◽  
Mostafa Hassanein ◽  
Jitao Zhong ◽  
Hanshan Ding ◽  
...  

Despite the construction of several curved prestressed concrete girder bridges with corrugated steel webs (CSWs) around the world; their shear behavior has seldom been investigated. Accordingly, this paper substitutes the lack of available information on the global elastic shear buckling of a plane curved corrugated steel web (PCCSW) in a curved girder. This is based on the equilibrium equations and geometric equations in the elastic theory of classical shells, combined with the constitutive relation of orthotropic shells. Currently, the global elastic shear buckling process of the PCCSW in a curved girder is studied, for the first time in literature, with an equivalent orthotropic open circular cylindrical shell (OOCCS) model. The governing differential equation of global elastic shear buckling of the PCCSW, as well as its buckling strength, is derived by considering the orthotropic characteristics of a corrugated steel web, the rational trigonometric displacement modes, Galerkin’s method and variational principles. Additionally, the accuracy of the proposed theoretical formula is verified by comparison with finite element (FE) results. Moreover, the expressions of the inner or outer folded angle and radius of curvature are given by the cosine theorem of the trigonometric function and inverse trigonometric function. Subsequently, parametric analysis of the shear buckling behavior of the PCCSW is carried out by considering the cases where the radius of curvature is constant or variable. This parametric analysis highlights the effects of web dimensions, height-to-thickness ratio, aspect ratios of longitudinal and inclined panels, corrugation height, curvature radius and folded angles on the elastic shear buckling strength. As a result, this study provides a theoretical reference for the design and application of composite curved girders with CSWs.


2010 ◽  
Vol 18 (2) ◽  
pp. 129-141
Author(s):  
Bo Li ◽  
Na Ma ◽  
Xiquan Liang

Integrability Formulas. Part II In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.


2020 ◽  
Vol 13 (22) ◽  
Author(s):  
Feng Liu ◽  
Chengda Wang ◽  
Ning Wang ◽  
Yong Wu ◽  
Delong Wang

2011 ◽  
Vol 291-294 ◽  
pp. 286-289
Author(s):  
Jian Ren Sun ◽  
Chi Bing Hu

Control of the motion process of acceleration/deceleration (Acc/Dec) is one of key complicated problems in CNC system development. The excellent Acc/Dec control can improve the processing precision. The traditional Acc/Dec algorithms such as the linear and the exponential are not suitable for high speed motion because there would be flexible impacts existing in feed motion, especially that the jerk of the S-shape curve Acc/Dec is discontinuous. A new flexible Acc/Dec algorithm for high speed motion system based on the squared sine function is introduced. The modeling of the Acc/Dec algorithm with Trigonometric Function Squared Sine(TFSS) shape curve is constructed.In this algorithm, the sine curve in jerk, acceleration, velocity and displacement are all continuous. The simulation experiments result demonstrate that the Acc/Dec algorithm with TFSS shape curve is a new method of continuous Jerk for the design flexible Acc/Dec.


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