scholarly journals On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
M. Tahmaseb Towliat Kashani ◽  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Axial Load ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Elastic Beam ◽  
Axial Compressive Force ◽  
Various Boundary Conditions ◽  
Linear Eigenvalue Problem ◽  
The Moment

The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MATLAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

scholarly journals On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

2021 ◽  
Author(s):  
M. Tahmaseb Towliat Kashani ◽  
Supun Jayasinghe Jayashinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Axial Load ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Elastic Beam ◽  
Axial Compressive Force ◽  
Various Boundary Conditions ◽  
Linear Eigenvalue Problem ◽  
The Moment

The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MAT LAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

scholarly journals On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment

2021 ◽  
Author(s):  
M. Tahmaseb Towliat Kashani ◽  
Supun Jayasinghe Jayashinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Axial Load ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Elastic Beam ◽  
Axial Compressive Force ◽  
Various Boundary Conditions ◽  
Linear Eigenvalue Problem ◽  
The Moment

The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MAT LAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

Node Control of Uniform Beams Subject to Various Boundary Conditions

1992 ◽  
Vol 59 (4) ◽  
pp. 983-990 ◽  
Author(s):  
L. Weaver ◽  
L. Silverberg
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Controlled System ◽  
Free Boundary Conditions ◽  
Various Boundary Conditions ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Control Forces ◽  
Direct Feedback

This paper introduces node control, whereby discrete direct feedback control forces are placed at the nodes of the N+1th mode (the lowest N modes participate in the response). Node control is motivated by the node control theorem which states, under certain conditions, that node control preserves the natural frequencies and natural modes of vibration of the controlled system while achieving uniform damping. The node control theorem is verified for uniform beams with pinned-pinned, cantilevered, and free-free boundary conditions, and two cases of beams with springs on the boundaries. A general proof of the node control theorem remains elusive.

An efficient GDQ model for vibration analysis of a multiwall carbon nanotube on Pasternak foundation with general boundary conditions

2011 ◽  
Vol 225 (7) ◽  
pp. 1730-1741 ◽  
Author(s):  
P Soltani ◽  
P Bahar ◽  
A Farshidianfar
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Differential Quadrature Method ◽  
Elastic Beam ◽  
Beam Theory ◽  
Multiwall Carbon Nanotube ◽  
Various Boundary Conditions ◽  
Aspect Ratios ◽  
Multiwall Carbon

In this article, the free transverse vibrational behaviour of a multiwall carbon nanotube (MWNT) surrounded by a Pasternak-type elastic medium has been determined using a very generalized model. The model has been made on the basis of Timoshenko elastic beam theory which allows the effects of shear deformation and rotary inertia and supports non-coaxial vibration of the adjacent layers of MWNT using interlayer van der Waals forces. The boundary conditions used in this simulation are such that not only standard and conventional kinds, but also all possible forms, of end conditions are applicable. A generalized differential quadrature method is utilized to solve the governing equations with assorted aspect ratios, various boundary conditions, and different foundation stiffnesses. This study shows that the resonant frequencies of MWNTs are strongly dependent on the stiffness of the elastic medium, aspect ratios, and number of walls in carbon nanotubes and, for short nanotubes, the boundary stiffness plays a significant role on the natural frequencies.

Free vibration of high-speed rotating Timoshenko shaft with various boundary conditions: effect of centrifugally induced axial force

2014 ◽  
Vol 84 (12) ◽  
pp. 1691-1700 ◽  
Author(s):  
Benyamin Gholami Bazehhour ◽  
Seyed Mahmoud Mousavi ◽  
Anoushiravan Farshidianfar
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Axial Force ◽  
High Speed ◽  
Various Boundary Conditions

EFFECTS OF THE INITIAL DEFLECTION SHAPE ON THE MOMENT AMPLIFICATION FACTOR OF BEAM-COLUMNS

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Haruna Utsunomiya ◽  
Masayuki Haraguchi ◽  
Masae Kido ◽  
Keigo Tsuda
Keyword(s):  
Amplification Factor ◽  
Slenderness Ratio ◽  
Compressive Force ◽  
Bending Moment ◽  
Load Ratio ◽  
Longitudinal Direction ◽  
Initial Deflection ◽  
Axial Compressive Force ◽  
Beam Columns ◽  
The Moment

In the design of slender steel beam-columns, the moment amplification factor is used to estimate the maximum moment along with the longitudinal direction. While formulas for evaluating the factor have been presented on the basis of elastic or elastic-plastic analysis, the initial deflection of the column is not considered. The effect that the initial deflection on the strength and behavior of the column has been shown only when the initial deflection shape is half sine wave. This paper discusses the effect of the initial deflection shape on the value of the moment amplification factor by performing the analytical work. The analytical model is the hinged-end beam-column subjected to constant axial compressive force and end moments. First of all, the equilibrium differential equation which governs the problem is solved and the formula for calculating the bending moment is presented. In the parametric study, magnitude of initial deflection, initial deflection shape, axial load ratio, slenderness ratio and end moment ratio are selected as the parameters. In this paper, we discuss the effects of the amount of the initial deflection and the initial deflection shape.

FREE VIBRATION ANALYSIS OF DISCRETELY STIFFENED SKEW PLATES

2001 ◽  
Vol 01 (01) ◽  
pp. 125-144 ◽  
Author(s):  
HUAN ZENG ◽  
CHARLES W. BERT
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Skew Angle ◽  
Various Boundary Conditions ◽  
Skew Plate ◽  
Convergence Study

Stiffened skew plates find application in various engineering fields. The free vibration characteristics of such plates have been studied by various methods. An orthogonally stiffened skew plate is a skew plate with stiffeners running orthogonal to two opposite edges. To the best knowledge of the present investigators, no previous work has been done for free vibration characteristics of skew plates of such stiffening geometry. The present work studies the free vibration of such plates. The pb-2 Rayleigh–Ritz method was employed due to its accuracy and computational efficiency. The conventional finite element method was also used as a comparative check. A convergence study was first performed for various boundary conditions. Then the vibration of orthogonally stiffened skew plates with different boundary conditions was studied. Close agreement was found between these two methods. The variations of natural frequencies with different parameters, including skew angle ϕ, edge ratio b/a, and height-thickness ratio f/h, were investigated for three types of boundary conditions.

scholarly journals Vibration frequency of prestress slender beams resting on Winkler elastic foundation

2006 ◽  
Vol 28 (4) ◽  
pp. 241-251
Author(s):  
Nguyen Dinh Kien
Keyword(s):  
Axial Force ◽  
Vibration Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Winkler Foundation ◽  
The Finite Element Method ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation ◽  
Mass Matrices ◽  
Slender Beams

The present paper investigates the vibration frequency of slender beams prestressing by axial force and resting on an elastic Winkler foundation by the finite element method. A beam element taking the effects of both the prestress and foundation support into account is formulated using the expression of strain energy. Using the developed element, the natural frequencies of beams having various boundary conditions are computed for different values of the axial force and foundation stiffness. The influence of the axial force and the foundation stiffness on the frequency of the beams is investigated. The effect of partial support by the foundation and the type of mass matrices on the vibration frequency of the beam is also studied and highlighted.

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