scholarly journals Free Vibration Analysis of Spinning Spindles: A Calibrated Dynamic Stiffness Matrix Method

10.5772/51174 ◽  
2012 ◽  
Author(s):  
Seyed M. ◽  
Omar Gaber
Keyword(s):  
Free Vibration ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Dynamic Stiffness Matrix

Free vibration analysis of multistepped nonlocal Bernoulli–Euler beams using dynamic stiffness matrix method

2020 ◽  
pp. 107754632093347
Author(s):  
Moustafa S Taima ◽  
Tamer A El-Sayed ◽  
Said H Farghaly
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Dynamic Stiffness ◽  
Nonlocal Parameter ◽  
Free Vibration Analysis ◽  
Nonlocal Elasticity Theory ◽  
Dynamic Stiffness Matrix

The free vibration of multistepped nanobeams is studied using the dynamic stiffness matrix method. The beam analysis is based on the Bernoulli–Euler theory, and the nanoscale analysis is based on the Eringen’s nonlocal elasticity theory. The nanobeam is attached to linear and rotational elastic supports at the start, end, and intermediate boundary conditions. The effect of the nonlocal parameter, boundary conditions, and step ratios on the nanobeam natural frequency is investigated. The results of the dynamic stiffness matrix methods are validated by comparing selected cases with the literature, which give excellent agreement with those literatures. The results show that the dimensionless natural frequency parameter is inversely proportional to the nonlocal parameters except in the first mode for clamped-free boundary conditions. Also, the gap between every two consecutive modes decreases with the increasing of the nonlocal parameter.

COUPLED FREE VIBRATION ANALYSIS OF SHEAR-FLEXIBLE LAMINATED COMPOSITE I-BEAMS

2013 ◽  
Vol 21 (01) ◽  
pp. 1250024
Author(s):  
NAM-IL KIM
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Dynamic Stiffness Matrix ◽  
Analytical Technique

The coupled free vibration analysis of the thin-walled laminated composite I-beams with bisymmetric and monosymmetric cross sections considering shear effects is developed. The laminated composite beam takes into account the transverse shear and the restrained warping induced shear deformation based on the first-order shear deformation beam theory. The analytical technique is used to derive the constitutive equations and the equations of motion of the beam in a systematic manner considering all deformations and their mutual couplings. The explicit expressions for displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the dynamic stiffness matrix is determined using the force–displacement relationships. In addition, for comparison, a finite beam element with two-nodes and fourteen-degrees-of-freedom is presented to solve the equations of motion. The performance of the dynamic stiffness matrix developed by study is tested through the solutions of numerical examples and the obtained results are compared with results available in literature and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The vibrational behavior and the effect of shear deformation are investigated with respect to the modulus ratios and the fiber angle change.

scholarly journals Free Vibration Analysis of Axially Moving Track Using Stiffness Matrix Method.

1997 ◽  
Vol 63 (614) ◽  
pp. 3396-3401
Author(s):  
Keiji WATANABE ◽  
Kouetsu TAKANO ◽  
Osami MATSUSHITA ◽  
Masanori KITANO ◽  
Daisaku SATO
Keyword(s):  
Free Vibration ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Axially Moving
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