An investigation of free vibrations of a strain gradient Timoshenko beams with the method of initial values

2019 ◽  
Vol 26 (3) ◽  
pp. 835-852
Author(s):  
Ceyda Nur ◽  
Reha Artan
Keyword(s):  
Strain Gradient ◽  
Free Vibrations ◽  
Timoshenko Beams ◽  
Initial Values

Free vibrations of a strain gradient beam by the method of initial values

2012 ◽  
Vol 223 (11) ◽  
pp. 2393-2409 ◽  
Author(s):  
R. Artan ◽  
R. C. Batra
Keyword(s):  
Strain Gradient ◽  
Free Vibrations ◽  
Initial Values

Free Vibrations of Timoshenko Beams Carrying Elastically Mounted, Concentrated Masses

1993 ◽  
Vol 165 (2) ◽  
pp. 209-223 ◽  
Author(s):  
R.E. Rossi ◽  
P.A.A. Laura ◽  
D.R. Avalos ◽  
H. Larrondo
Keyword(s):  
Free Vibrations ◽  
Timoshenko Beams ◽  
Concentrated Masses

Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress-driven nonlocal models

2018 ◽  
Vol 154 ◽  
pp. 20-32 ◽  
Author(s):  
R. Barretta ◽  
S. Ali Faghidian ◽  
R. Luciano ◽  
C.M. Medaglia ◽  
R. Penna
Keyword(s):  
Strain Gradient ◽  
Free Vibrations ◽  
Nonlocal Models

An accurate solution method for the vibration analysis of Timoshenko beams with general elastic supports

2014 ◽  
Vol 229 (13) ◽  
pp. 2327-2340 ◽  
Author(s):  
Dongyan Shi ◽  
Qingshan Wang ◽  
Xianjie Shi ◽  
Fuzhan Pang
Keyword(s):  
Boundary Conditions ◽  
Series Expansion ◽  
Solution Method ◽  
Free Vibrations ◽  
Accurate Solution ◽  
Fourier Series Expansion ◽  
Timoshenko Beams ◽  
End Points ◽  
Solution Algorithms ◽  
Wide Range

In this investigation, an accurate solution method is presented for the free vibrations of Timoshenko beams with general elastic restraints at the end points, a class of problems which are rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the displacement and rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions introduced to remove the potential discontinuities with the displacement components and its derivatives at the end points and accelerated the series expansion. Mathematically, the current Fourier series expansion is an exact solution for a class of problems with the Timoshenko beam such that both the governing equations and the boundary conditions simultaneously satisfy any specified degree of accuracy. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in literatures and finite element method data, and numerous new results for beams with elastic boundary restraints is presented, which may serve as benchmark solution for future researches.

Forced Vibrations of Viscoelastic Timoshenko Beams

1976 ◽  
Vol 98 (3) ◽  
pp. 820-826 ◽  
Author(s):  
C. C. Huang ◽  
T. C. Huang
Keyword(s):  
Boundary Conditions ◽  
Laplace Transform ◽  
Attenuation Factor ◽  
Equations Of Motion ◽  
Bending Moment ◽  
Expansion Method ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Mode Shapes ◽  
Timoshenko Beams

In a previous paper, the correspondence principle has been applied to derive the differential equations of motion of viscoelastic Timoshenko beams with or without external viscous damping. To study free vibrations these equations are solved by Laplace transform and boundary conditions are applied to obtain the attenuation factor and the frequency of the damped free vibrations and mode shapes. The present paper continues to analyze this subject and deals with the responses in deflection, bending slope, bending moment and shear for forced vibrations. Laplace transform and appropriate boundary conditions have been applied. Examples are given and results are plotted. The solution of forced vibrations of elastic Timoshenko beams obtained as a result of reduction from viscoelastic case and by eigenfunction expansion method concludes the paper.

FREE VIBRATIONS OF UNIFORM TIMOSHENKO BEAMS WITH ATTACHMENTS

1997 ◽  
Vol 204 (2) ◽  
pp. 359-369 ◽  
Author(s):  
B. Posiadała
Keyword(s):  
Free Vibrations ◽  
Timoshenko Beams

Free vibrations of elastic beams by modified nonlocal strain gradient theory

2018 ◽  
Vol 133 ◽  
pp. 99-108 ◽  
Author(s):  
A. Apuzzo ◽  
R. Barretta ◽  
S.A. Faghidian ◽  
R. Luciano ◽  
F. Marotti de Sciarra
Keyword(s):  
Strain Gradient ◽  
Free Vibrations ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Elastic Beams ◽  
Nonlocal Strain Gradient
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