scholarly journals Buckling of Tapered Heavy Columns with Constant Volume

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 657
Author(s):  
Byoung Koo Lee ◽  
Joon Kyu Lee
Keyword(s):  
Cross Section ◽  
Integration Method ◽  
Search Method ◽  
Regular Polygons ◽  
Equilibrium Equations ◽  
Column Volume ◽  
Direct Integration Method ◽  
End Conditions ◽  
Tapered Columns ◽  
Buckling Length

This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.

Free vibration and buckling of heavy column with regular polygon cross-section

2021 ◽  
pp. 095440622110293
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Natural Frequency ◽  
Cross Section ◽  
Buckling Load ◽  
Mode Shapes ◽  
Equilibrium Equations ◽  
Direct Integration Method ◽  
Solution Methods ◽  
Buckling Length

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 675-681
Author(s):  
Rehab M. El-Shiekh ◽  
Mahmoud Gaballah
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Integration Method ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Equation Method ◽  
Direct Integration ◽  
Wave Solutions ◽  
Direct Integration Method

AbstractIn this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Nonlinear structures: soliton, shocklike and explosive waves in quantum semiconductor plasma

2021 ◽  
Author(s):  
Haifa Al-Yousef
Keyword(s):  
Analytical Procedure ◽  
Integration Method ◽  
Fluid Model ◽  
Three Dimensional ◽  
Semiconductor Plasma ◽  
Direct Integration Method ◽  
Solution Methods ◽  
Gradient Forces ◽  
Quantum Semiconductor ◽  
Nonlinear Solutions

Abstract The properties and conditions for the appearance of some nonlinear waves in a three-dimensional semiconductor plasma are discussed, by studying the described plasma fluid system with quantum gradient forces and degraded pressures. Our analytical procedure is built on the reductive perturbation theory to obtain the Kadomtsev-Petvashvili equation for the fluid model and solving it using the direct integration method and the Bäcklund transform. Through different solution methods we got different nonlinear solutions describing different pulse profiles such as soliton, kink and explosive pulses. This model can be used to identify the potential disturbances in a semiconductor plasma.

scholarly journals STABILITY OF AXIALLY LOADED TAPERED COLUMNS/CENTRIŠKAI GNIUŽDOMŲ TRAPECINIŲ KOLONŲ STABILUMAS

2000 ◽  
Vol 6 (3) ◽  
pp. 158-161 ◽  
Author(s):  
Vaidotas Špalas ◽  
Audronis Kazimieras Kvedaras
Keyword(s):  
Critical Load ◽  
Cross Section ◽  
Calculation Methods ◽  
Moments Of Inertia ◽  
Geometrical Characteristics ◽  
Wide Range ◽  
Axially Loaded ◽  
Tapered Columns ◽  
Loaded Column ◽  
Tapered Column

In this paper, theoretical analysis of tapered column's bearing capacity is presented. A slender axially loaded column loses stability, when it achieves critical load (1). Critical load for uniform column can be calculated using L. Euler's formula (3). But this formula is only for uniform members. When we have non-uniform member, column's moment of inertia about strong axis (Fig 3) chances according to law (4). A. N. Dinik [4] suggested a differential equation (6) for non-uniform axially loaded member. So the critical load of tapered column can be calculated as for uniform member with additional factor K using (7) formula. Factor Kdepends only on the moments of inertia ratio (5) of column ends. In this paper, critical load of tapered column was calculated using FE program COSMOS/M. A lot of simulation were carried out with a wide range of moments of inertia ratio. From these simulations factor K was calculated (Fig 4 and Table 1) for axially loaded pin-end column. By computer simulation it was determined that factor K for pin-end column can also be used for other types of column support. After determining critical load, column slenderness (10) can be calculated using column's smallest cross-section A 1. Tapered column must satisfy (12) condition. A couple of examples (Table 2) with various moments of inertia ratio was solved. Three calculation methods were used: the author's suggested (Fig 5 curve 1): using [1, 2] method as for uniform member with the smallest column's cross-section geometrical characteristics (Fig 5 curve 2); and using [1, 2] method as for uniform member with average column's cross-section geometrical characteristics (Fig 5 curve 3). From Fig 5 we see that calculation of tapered column using methods for uniform members with average cross-section geometrical characteristics is not safe.

scholarly journals Piecewise Polynomial Fitting with Trend Item Removal and Its Application in a Cab Vibration Test

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Wu Ren ◽  
Qiongqiong Ren ◽  
Lin Han ◽  
Ying Liu ◽  
Bo Peng
Keyword(s):  
Integration Method ◽  
Vibration Signal ◽  
Vibration Test ◽  
Measured Signal ◽  
Direct Integration ◽  
Piecewise Polynomial ◽  
Modal Parameter ◽  
Polynomial Fitting ◽  
Special Equipment ◽  
Direct Integration Method

The trend item of a long-term vibration signal is difficult to remove. This paper proposes a piecewise integration method to remove trend items. Examples of direct integration without trend item removal, global integration after piecewise polynomial fitting with trend item removal, and direct integration after piecewise polynomial fitting with trend item removal were simulated. The results showed that direct integration of the fitted piecewise polynomial provided greater acceleration and displacement precision than the other two integration methods. A vibration test was then performed on a special equipment cab. The results indicated that direct integration by piecewise polynomial fitting with trend item removal was highly consistent with the measured signal data. However, the direct integration method without trend item removal resulted in signal distortion. The proposed method can help with frequency domain analysis of vibration signals and modal parameter identification for such equipment.

An Improved Transfer Matrix-Direct Integration Method for Rotor Dynamics

1986 ◽  
Vol 108 (2) ◽  
pp. 182-188 ◽  
Author(s):  
Jialiu Gu
Keyword(s):  
Transfer Matrix ◽  
Integration Method ◽  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Direct Integration ◽  
Rotating System ◽  
Direct Integration Method ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Matrix Iteration

A transfer matrix-direct integration combined method is proposed, which employs the transfer matrix method to derive the equations of motion of a “characteristic disk,” and uses the direct integration method to determine the critical speeds, modes and unbalance response of a rotor-bearing system, and to analyze its stability. Despite the complexity of the system, the number of governing equations is not greater than eight. For a single-spool rotating system, the number of equations is only four. A transfer matrix for a uniform shaft is derived to consider its distributed mass, moment of inertia and the effect of shearing force. An impedance matrix iteration method is proposed to consider the effect of a complicated bearing-supporting system on the rotor dynamics. Two examples are given, and the results agree satisfactorily with the experiments.

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