Vibration analysis of 3-D composite beam elements including warping and shear deformation effects

In this Paper, the analysis of simply supported laminated composite beam having uniformly distributed load is performed. The solutions obtained in the form of the displacements and stresses for different layered cross ply laminated composite simply supported beams subjected uniformly distributed to load. Different aspect ratio consider for different results in terms of displacement, bending stress and shear stresses. The shear stresses are calculated with the help of equilibrium equation and constitutive relationship. Using displacement field including trigonometric function of laminated composite beams are derived from virtual displacement principle. There are axial displacement, transverse displacement, bending stress and shear stresses. In addition, Euler-Bernoulli (ETB), First order shear deformation beam theory (FSDT), Higher order shear deformation beam theory (HSDT) and Hyperbolic shear deformation beam theory (HYSDT) solution have been made for comparison and better accuracy of solutions and results of static analyses of laminated composite beams for simply supported laminated composite beam.

Download Full-text

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

Progress in Civil and Structural Engineering ◽

10.38208/pcse.v1i1.2 ◽

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.

Download Full-text

Second Order Shear Deformation Theory (SSDT) for Free Vibration Analysis on a Functionally Graded Quadrangle Plate

Recent Advances in Vibrations Analysis ◽

10.5772/22245 ◽

2011 ◽

Cited By ~ 1

Author(s):

A. Shahrjerdi ◽

F. Mustaph

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Vibration Analysis ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Free Vibration Analysis ◽

Second Order ◽

Functionally Graded

Download Full-text

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

Volume 1: Acoustics, Vibration, and Phononics ◽

10.1115/imece2020-23098 ◽

2020 ◽

Author(s):

Yichi Zhang ◽

Bingen Yang

Keyword(s):

Shear Deformation ◽

Timoshenko Beam ◽

Vibration Analysis ◽

Beam Theory ◽

Timoshenko Beam Theory ◽

Bernoulli Beam ◽

Beam Structure ◽

Medium Frequency ◽

Beam Structures ◽

Euler Bernoulli Beam

Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

Download Full-text