Large amplitude free vibration analysis of isotropic curved nano/micro beams using a nonlocal sinusoidal shear deformation theory-based finite element method

2021 ◽  
Author(s):  
G. Prateek ◽  
De Sarthak ◽  
R. Vasudevan ◽  
M. Haboussi ◽  
M. Ganapathi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Sinusoidal Shear Deformation Theory

scholarly journals Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite element method

2016 ◽  
Vol 54 (3) ◽  
pp. 402 ◽  
Author(s):  
Tran Huu Quoc ◽  
Tran Minh Tu ◽  
Nguyen Van Long
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates

In this paper, a new eight-unknown shear deformation theory is developed for bending and free vibration analysis of functionally graded plates by finite element method. The theory based on full twelve-unknown higher order shear deformation theory, simultaneously satisfy zeros transverse stresses at top and bottom surface of FG plates. A four-node rectangular element with sixteen degrees of freedom per node is used. Poisson’s ratios, Young’s moduli and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as power law functions. Results are verified with available results in the literature. Parametric studies are performed for different power law index, side-to-thickness ratios.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

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