Corrigendum to “Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice” [ J. Sound Vib. 333 (11) (2014) 2359–2377]

2015 ◽  
Vol 339 ◽  
pp. 433
Author(s):  
M. Attar ◽  
A. Karrech ◽  
K. Regenauer-Lieb
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Shear Deformable Beam ◽  
Shear Deformable ◽  
Two Parameter

Analytical and Experimental Free Vibration Analysis of Uniform Cracked Thick Beam on Two-Parameter Elastic Partial Foundation

Volume 1 ◽  
2004 ◽  
Author(s):  
Ali Bahc¸ıvan ◽  
Vedat Karadag˘
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Element ◽  
Thick Beam ◽  
Two Parameter

In this study, the analytical and experimental free vibration analysis of rectangular cross-section uniform cracked thick beam on two-parameter vibration and noise isolating elastic foundation, considering shear deformation and rotatory inertia is made by the finite element method. The beam element in our study is a recently introduced 4 degrees of freedom thick beam element and has two nodes with two degrees of freedom at each node such as transverse displacements and cross-section rotations. Two kinds of end conditions, i.e. clamped-clamped and clamped-free ends are considered in this study. Axial displacement of the beam is also considered. For axial displacement of the beam, linear finite elements are used. The elastic foundation is idealized as a constant two-parameter model characterized by two moduli, i.e. the Winkler foundation modulus k and the shear foundation modulus kG. In the case kG = 0, this model reduces to the Winkler model, i.e. the elastic foundation is idealized as a constant one-parameter model. The effects of foundation stiffness parameters, partial elastic foundation and crack changing its depth on the natural frequencies of the beam are examined. The effect of partial elastic foundation on the natural frequencies of the beam is examined for only half of the beam length. The crack is in the middle of the beam and only on one side of the beam having a form of open crack. In the analytical analysis, the spring coefficients of the crack are calculated in the computer program and then directly added to the stiffness matrix. The crack model used in this study is mentioned as a linear spring model in the literature. The crack modeled is in the middle of the beam and the related spring constants of rotational and extensional springs, which will be used, are added to the global matrix in the process. In the experimental analysis, steel and hard plastic beam are used as the beam material. Moreover, sponge and glass wool, which are manufactured by Petkim Ltd., are used as the isolating elastic foundation material. The results obtained from the analytical and experimental studies are presented by showing in tables and graphs and their importance in design is discussed. The analytical and experimental results and comparisons show the efficiency and effectiveness of the proposed method.

scholarly journals Free Vibration Analysis Of The Moderately Thick Laminated Composite Rectangular Plate On Two-Parameter Elastic Foundation With Elastic Boundary Conditions

2016 ◽  
Vol 1 (1) ◽  
pp. 190 ◽  
Author(s):  
H. Zhang ◽  
D.Y. Shi ◽  
Q.S. Wang
Keyword(s):  
Fourier Series ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Two Parameter

<p>An improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with general elastic supports and point supports resting on an elastic foundation. The approach is based on the first order shear deformation theory and foundation effect using two-parameter Pasternak foundation model. The displacement and rotation functions are generally sought, regardless of boundary conditions, as Fourier series and supplementary functions. All the series expansion coefficients are determined using the Rayleigh-Ritz technique. The excellent accuracy of the current results is validated by comparing them with existing results.</p>

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