Unified analytical solution for various boundary conditions for the coupled flexural-torsional vibration of beams subjected to axial loads and end moments

1989 ◽  
Vol 129 (2) ◽  
pp. 313-326 ◽  
Author(s):  
A. Joshi ◽  
S. Suryanarayan
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Torsional Vibration ◽  
Axial Loads ◽  
Various Boundary Conditions

Vibration and Frequency Analysis of Non-Uniform Timoshenko Beams Subjected to Axial Forces

2003 ◽  
Author(s):  
A. R. Ohadi ◽  
H. Mehdigholi ◽  
E. Esmailzadeh
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Axial Force ◽  
Frequency Equation ◽  
Axial Loads ◽  
Various Boundary Conditions ◽  
Axial Forces ◽  
First Case ◽  
The Stability ◽  
Elastically Supported

Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been presented. The stability analysis, for the variation of the natural frequencies of the uniform and non-uniform beams with the axial force, has also been investigated.

Critical Spin Rate of Rotating Beams by Liapunov’s Direct Method

1986 ◽  
Vol 108 (4) ◽  
pp. 389-393 ◽  
Author(s):  
D. C. Kammer ◽  
A. L. Schlack
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Equations Of Motion ◽  
Axial Loads ◽  
System Parameters ◽  
Various Boundary Conditions ◽  
Out Of Plane ◽  
Steady Rotation ◽  
Stability Results ◽  
Liapunov's Direct Method

The in-plane and out-of-plane buckling of a beam subjected to axial loads due to steady rotation are investigated for various boundary conditions. The critical spin rate which will cause the beam to buckle is derived as a function of system parameters using Liapunov’s direct method. A significant advantage is offered by this method in that the equations of motion do not have to be solved in order to determine stability. Results are compared with those found in the literature.

Torsional Vibration of Cracked Nanobeam Based on Nonlocal Stress Theory with Various Boundary Conditions: An Analytical Study

2015 ◽  
Vol 07 (03) ◽  
pp. 1550036 ◽  
Author(s):  
Omid Rahmani ◽  
S. A. H. Hosseini ◽  
M. H. Noroozi Moghaddam ◽  
I. Fakhari Golpayegani
Keyword(s):  
Boundary Conditions ◽  
Torsional Vibration ◽  
Analytical Study ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Stress Theory ◽  
Various Boundary Conditions ◽  
Crack Location ◽  
Nonlocal Stress ◽  
Torsional Spring

In this paper, the torsional vibration of cracked nanobeam was studied based on a nonlocal elasticity theory. The location of the crack is simulated by a torsional spring which links segments of nanobeam together. Also, different boundary conditions, including clamped–free, clamped–clamped and clamped–torsional spring, were considered. Furthermore, a detailed parametric study was conducted to investigate the influence of crack location, nonlocal parameter, length of nanobeam, spring constant and end supports on the torsional vibration.

scholarly journals ANALYTICAL SOLUTION OF THE EQUATION OF CONDUCTIVITY FOR VARIOUS BOUNDARY CONDITIONS

2019 ◽  
Vol 2019 (4) ◽  
pp. 33-37
Author(s):  
Vadim Krys'ko ◽  
Olga Saltykova ◽  
Alexey Tebyakin
Keyword(s):  
Analytical Solution ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Solution Method ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Two Dimensional ◽  
Various Boundary Conditions ◽  
The Finite Difference Method

The aim of the work is to obtain an analytical solution of the heat equation for various boundary conditions in the case of a two-dimensional body. As a solution method, the method of variational iterations is used. In the work, both an analytical and a numerical solution of the problem are obtained for the boundary conditions of various types and taking into account the internal heat source. To obtain a numerical solution, the finite difference method was used. The results are compared and the conclusion is made on the reliability of the decisions.

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