An exact analytical approach for in-plane and out-of-plane free vibration analysis of thick laminated transversely isotropic plates

2011 ◽  
Vol 82 (5) ◽  
pp. 677-698 ◽  
Author(s):  
Sh. Hosseini Hashemi ◽  
S. R. Atashipour ◽  
M. Fadaee
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Free Vibration Analysis ◽  
Transversely Isotropic ◽  
Isotropic Plates ◽  
Out Of Plane

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.

scholarly journals Free Vibration Analysis of Rings via Wave Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Wang Zhipeng ◽  
Liu Wei ◽  
Yuan Yunbo ◽  
Shuai Zhijun ◽  
Guo Yibin ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Classical Method ◽  
Free Vibration Analysis ◽  
Material Parameters ◽  
Wave Approach ◽  
Out Of Plane ◽  
Vibration Transmissibility ◽  
Ring Structures

Free vibration of rings is presented via wave approach theoretically. Firstly, based on the solutions of out-of-plane vibration, propagation, reflection, and coordination matrices are derived for the case of a fixed boundary at inner surface and a free boundary at outer surface. Then, assembling these matrices, characteristic equation of natural frequency is obtained. Wave approach is employed to study the free vibration of these ring structures. Natural frequencies calculated by wave approach are compared with those obtained by classical method and Finite Element Method (FEM). Afterwards natural frequencies of four type boundaries are calculated. Transverse vibration transmissibility of rings propagating from outer to inner and from inner to outer is investigated. Finally, the effects of structural and material parameters on free vibration are discussed in detail.

An Exact Analytical Approach for Free Vibration Analysis of Built-Up Space Frames

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
C. Mei ◽  
H. Sha
Keyword(s):  
Free Vibration ◽  
Analytical Approach ◽  
Free Vibration Analysis ◽  
Structural Elements ◽  
Space Frames ◽  
Out Of Plane ◽  
Vibration Responses ◽  
Numerical Tools ◽  
Classical Vibration ◽  
Exact Analytical Method

Coupled in- and out-of-plane bending, axial, and torsional vibrations exist in a built-up space frame, which greatly challenges the conventional modal approach. A wave-based exact analytical method is applied to study vibrations in built-up multistory space frames. From the wave vibration standpoint, vibrations are described as waves propagating along uniform structural elements and being reflected and transmitted at structural discontinuities. Free vibration responses are studied based on classical vibration theories. Numerical examples are given with comparison to results available in the literature. Good agreements have been reached. This study not only provides an exact analytical approach to complex vibration problems in built-up multistory space frames that have mostly been studied numerically but also provides a benchmark to existing numerical tools.

An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using an Analytical Approach

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Closed Form ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Mass System

This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam using an analytical approach, a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems, as well as that of spring-mass systems, was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.

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