Vibration of non-uniform rod using Differential Transform Method

Shali, S.; Nagaraja, S. R.; Jafarali, P.

doi:10.1088/1757-899x/225/1/012027

Cited by 3 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Shali et al [25] analyzed the axial vibration of non-uniform rods with different end conditions using the differential transform method. Šalinić et al [26] proposed a non-iterative computational technique to study the free vibrations of axially functionally graded tapered, stepped, and continuously segmented rods and beams with elastically restrained ends with attached masses.…”

Section: Calio and Elishakoffmentioning

confidence: 99%

Analysis of the Axial Vibration of Non-Uniform and Functionally Graded Rods via an Analytical-Based Numerical Approach

Kondakcı,

Coşkun

2023

Vibration

View full text Add to dashboard Cite

In this study, an analytical-based numerical approach was proposed for the analysis of the free axial vibration of homogeneous and functionally graded rods with varying cross-sectional areas. The proposed approach is based on analytical approximation techniques, such as the Adomian decomposition method, variational iteration method, and homotopy perturbation method. However, the governing equations of the problems solved in this study were variable coefficient differential equations. These equations provide analytical solutions for strictly limited cases. Analytical approximation methods easily handle problems with uniform material properties and constant cross-sections, whereas with varying cross-sectional areas, the analytical integration process becomes a difficult task for the software. If the rod’s material is functionally graded with varying cross-sectional areas, the analytical integration process becomes a cumbersome task. The proposed approach eliminates all difficulties and requires computation within several seconds. The application of this method is straightforward, and the results obtained in this study are in excellent agreement with the solutions provided in the literature.

show abstract

Section: Calio and Elishakoffmentioning

confidence: 99%

Analysis of the Axial Vibration of Non-Uniform and Functionally Graded Rods via an Analytical-Based Numerical Approach

Kondakcı,

Coşkun

2023

Vibration

View full text Add to dashboard Cite

show abstract

“…en, substitute these terms into the four boundary conditions of equation (17). A set of homogeneous equations of quaternion polynomials can be obtained, which can be assembled into a matrix equation of the following form:…”

Section: Extracting the Frequencies And Mode Shapes By The Dtmmentioning

confidence: 99%

“…e differential transformation method (DTM) is particularly effective when solving the initial and boundary value problem of the nonlinear partial differential equations [16], and thus has been used with some success in applied mathematics in recent years. e DTM, a transformation technique based on Taylor series expansion, is used to solve the ordinary and partial differential equation approximately [17]. is method reduces the governing differential equation and the boundary conditions to a set of algebraic equations according to certain transformation rules.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

Xiao

Qin

Liu

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this study, experimental and numerical investigations on the vibration characteristics of a drill pipe during the lowering of a subsea Xmas tree were presented. A fourth-order partial differential equation with variable coefficients was established based on Euler–Bernoulli beam theory. The natural frequencies and mode shapes are obtained by using the differential transformation method. Four drill pipe models of different sizes were used in the experiments which were measured using piezoelectric acceleration sensors and fiber Bragg grating sensors, respectively. The factors that affect the natural frequencies and mode shapes, such as length, diameter, lumped mass, and boundary conditions, were analyzed. The results show that all factors have remarkable effects on the natural frequency, but changes in the length and diameter of the pipe have little effect on the mode shapes; the main factors affecting the mode shape are the boundary conditions and lumped mass. The results of the numerical calculation were validated by a comparison with the experimental results and showed good agreement.

show abstract

“…Mei [7] studied the vibrations in uniform and stepped rods using four rod theories, the elementary theory, the Love theory, the Mindlin-Herrman theory and the three mode theory in which the motion of the rod is described by the propagation and reflection of waves through the rod. Shali et al [8] studied the vibration of non-uniform rods having clamped-clamped and clamped-free ends to find the natural frequency using differential transform method by solving ordinary and partial differential equations. Collini et al [9] studied the vibration analysis of tie rods having elastic bed type boundary conditions and compared with a model having both end fixed boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Transient Dynamic Analysis of a Cantilever Rod with Axial Impulse Loading Using Finite Element Method

2018

View full text Add to dashboard Cite

The behavior of bodies subjected to impulse loading is of prime importance in the study of forces that occur in impulse facilities. Before performing the actual tests, theoretical and numerical simulations are carried out to obtain the response of bodies subjected to impulse loading. The simplest model for this study can be considered as a rod of circular cross section fixed at one end and free at other end. When a transient impulse load is applied on a body, vibrations occur in the body for the brief period of time. In this paper, the effect of a half sine impulse force applied on a cantilever rod in the axial direction has been discussed. The displacements at the tip of the rod were obtained based on two theories, the basic vibration formulae and FEM analysis. Simulations were performed using ANSYS and compared with the displacements obtained from the two theoretical methods.

show abstract

Vibration of non-uniform rod using Differential Transform Method

Cited by 3 publications

References 8 publications

Analysis of the Axial Vibration of Non-Uniform and Functionally Graded Rods via an Analytical-Based Numerical Approach

Analysis of the Axial Vibration of Non-Uniform and Functionally Graded Rods via an Analytical-Based Numerical Approach

Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

Transient Dynamic Analysis of a Cantilever Rod with Axial Impulse Loading Using Finite Element Method

Contact Info

Product

Resources

About