scholarly journals Modal Analysis of Vibration of Euler-Bernoulli Beam Subjected to Concentrated Moving Load

2020 ◽  
pp. 2324-2334
Author(s):  
Usman M. A ◽  
Makinde T. A. ◽  
Daniel D. O.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Modal Analysis ◽  
Series Solution ◽  
Moving Load ◽  
Bernoulli Beam ◽  
Partial Differential ◽  
Concentrated Load ◽  
Euler Bernoulli Beam

This paper investigates the modal analysis of vibration of Euler-Bernoulli beam subjected to concentrated load. The governing partial differential equation was analysed to determine the behaviour of the system under consideration. The series solution and numerical methods were used to solve the governing partial differential equation. The results revealed that the amplitude increases as the length of the beam increases. It was also found that the response amplitude increases as the foundation increases at fixed length of the beam.

scholarly journals Numerical methods for the multiplicative partial differential equations

2017 ◽  
Vol 15 (1) ◽  
pp. 1344-1350
Author(s):  
Muhammet Yazıcı ◽  
Harun Selvitopi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Error Estimation ◽  
Truncation Error ◽  
Numerical Solutions ◽  
Partial Differential ◽  
The Matrix ◽  
The Stability ◽  
Truncation Error Estimation

Abstract We propose the multiplicative explicit Euler, multiplicative implicit Euler, and multiplicative Crank-Nicolson algorithms for the numerical solutions of the multiplicative partial differential equation. We also consider the truncation error estimation for the numerical methods. The stability of the algorithms is analyzed by using the matrix form. The result reveals that the proposed numerical methods are effective and convenient.

scholarly journals Dynamic Response of a Beam Subjected to Moving Load and Moving Mass Supported by Pasternak Foundation

2012 ◽  
Vol 19 (2) ◽  
pp. 205-220 ◽  
Author(s):  
Rajib Ul Alam Uzzal ◽  
Rama B. Bhat ◽  
Waiz Ahmed
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Response ◽  
Moving Load ◽  
Bending Moment ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Pasternak Foundation ◽  
Partial Differential ◽  
Foundation Parameters

This paper presents the dynamic response of an Euler- Bernoulli beam supported on two-parameter Pasternak foundation subjected to moving load as well as moving mass. Modal analysis along with Fourier transform technique is employed to find the analytical solution of the governing partial differential equation. Shape functions are assumed to convert the partial differential equation into a series of ordinary differential equations. The dynamic responses of the beam in terms of normalized deflection and bending moment have been investigated for different velocity ratios under moving load and moving mass conditions. The effect of moving load velocity on dynamic deflection and bending moment responses of the beam have been investigated. The effect of foundation parameters such as, stiffness and shear modulus on dynamic deflection and bending moment responses have also been investigated for both moving load and moving mass at constant speeds. Numerical results obtained from the study are presented and discussed.

The Use of Homotopy Analysis Method to Solve the Time-Dependent Nonlinear Eikonal Partial Differential Equation

2011 ◽  
Vol 66 (5) ◽  
pp. 259-271 ◽  
Author(s):  
Mehdi Dehghan ◽  
Rezvan Salehi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Research Work ◽  
Time Dependent ◽  
Test Problems ◽  
Analysis Method ◽  
Partial Differential ◽  
Homotopy Analysis

In this research work a time-dependent partial differential equation which has several important applications in science and engineering is investigated and a method is proposed to find its solution. In the current paper, the homotopy analysis method (HAM) is developed to solve the eikonal equation. The homotopy analysis method is one of the most effective methods to obtain series solution. HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of a series solution. Furthermore, this method does not require any discretization, linearization or small perturbation and therefore reduces the numerical computation a lot. Some test problems are given to demonstrate the validity and applicability of the presented technique.

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