Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method

Meccanica ◽  
2015 ◽  
Vol 50 (5) ◽  
pp. 1331-1342 ◽  
Author(s):  
Nuttawit Wattanasakulpong ◽  
Arisara Chaikittiratana
Keyword(s):  
Collocation Method ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Timoshenko Beam Theory ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation

Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Jihong Wen ◽  
Honggang Zhao ◽  
Yaozong Liu ◽  
Xisen Wen
Keyword(s):  
Finite Element Method ◽  
Band Gap ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Beam Theory ◽  
Flexural Wave ◽  
Vibration Band ◽  
Frequency Range ◽  
Pipe System

The flexural vibration band gap in a periodic fluid-conveying pipe system is studied based on the Timoshenko beam theory. The band structure of the flexural wave is calculated with a transfer matrix method to investigate the gap frequency range. The effects of the rotary inertia and shear deformation on the gap frequency range are considered. The frequency response of finite periodic pipe is calculated with a finite element method to validate the gap frequency ranges.

Vibration Analysis of Third-Order Shear Deformable FGM Beams with Elastic Support by Chebyshev Collocation Method

2018 ◽  
Vol 18 (05) ◽  
pp. 1850071 ◽  
Author(s):  
Nuttawit Wattanasakulpong ◽  
Tinh Quoc Bui
Keyword(s):  
Collocation Method ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Constant Factor ◽  
Functionally Graded ◽  
Spring Constant ◽  
Chebyshev Collocation Method ◽  
Third Order ◽  
Chebyshev Collocation

In this paper, we present new results of natural frequencies for the functionally graded beams based on Chebyshev collocation method and the third-order shear deformation theory (TSDT), without requiring any shear correction factors. The beams are assumed to be elastically supported by translational and rotational springs, or simply known as elastically restrained ends. The material compositions of the beams across the gradient direction are described by different mathematical models including the simple power law, exponential and Mori–Tanaka models, and their effects on the response of beams are analyzed. We first present the Chebyshev collocation formulation of the coupled differential equations of motion for free vibration of FGM beams considering different boundary conditions, and then verify the results obtained by the proposed approach against reference ones. A parametric study is also performed for parameters such as thickness, spring constant factor, material volume fraction index, etc. The present numerical results reveal that the proposed method can offer accurate frequency results for the FGM beams as compared with those available in the literature. The results also indicate that the spring constant factors have a significant effect on the frequencies of the beams.

Vibration Analysis of Bidirectional Functionally Graded Timoshenko Beams Using Chebyshev Collocation Method

2020 ◽  
pp. 2150009 ◽  
Author(s):  
Wei-Ren Chen ◽  
Heng Chang
Keyword(s):  
Collocation Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Proposed Model ◽  
Good Agreement

This paper studies the vibration behaviors of bidirectional functionally graded (BDFG) Timoshenko beams based on the Chebyshev collocation method. The material properties of the beam are assumed to vary simultaneously in the beam length and thickness directions. The Chebyshev differentiation matrices are used to reduce the ordinary differential equations into a set of algebraic equations to form the eigenvalue problem for free vibration analysis. To validate the accuracy of the proposed model, some calculated results are compared with those obtained by other investigators. Good agreement has been achieved. Then the effects of slenderness ratios, material distribution types, gradient indexes, and restraint types on the natural frequency of BDFG beams are examined. Through the parametric study, the influences of the various geometric and material parameters on the vibration characteristics of BDFG beams are evaluated.

scholarly journals Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

Vibration ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 201-221 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Ali Farajpour ◽  
Hamed Farokhi
Keyword(s):  
Timoshenko Beam ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Timoshenko Beam Theory ◽  
Cross Sectional ◽  
Stress Theory ◽  
Size Dependent ◽  
Modified Couple Stress

A nonlinear vibration analysis is conducted on the mechanical behavior of axially functionally graded (AFG) microscale Timoshenko nonuniform beams. Asymmetry is due to both the nonuniform material mixture and geometric nonuniformity. Using the Timoshenko beam theory, the continuous models for translation/rotation are developed via an energy balance. Size-dependence is incorporated via the modified couple stress theory and the rotation via the Timoshenko beam theory. Galerkin’s method of discretization is applied and numerical simulations are conducted for a size-dependent vibration of the AFG microscale beam. Effects of material gradient index and axial change in the cross-sectional area on the force and frequency diagrams are investigated.

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