Linear and nonlinear vibrations of variable cross‐section beams using shear deformation theory

2021 ◽  
Author(s):  
Fatemeh Sohani ◽  
Hamidreza Eipakchi
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Shear Deformation Theory ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Linear And Nonlinear

A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

2010 ◽  
Author(s):  
M. Amabili ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Curvilinear Coordinates ◽  
Geometrically Nonlinear ◽  
Geometric Imperfections ◽  
Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

Blast loads and nonlinear vibrations of laminated glass plates in an enhanced shear deformation theory

2020 ◽  
Vol 252 ◽  
pp. 112720 ◽  
Author(s):  
Marco Amabili ◽  
Prabakaran Balasubramanian ◽  
Rinaldo Garziera ◽  
Gianni Royer-Carfagni
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Shear Deformation Theory ◽  
Laminated Glass ◽  
Blast Loads ◽  
Glass Plates

scholarly journals Vibration and Stability of Variable Cross Section Thin-Walled Composite Shafts with Transverse Shear

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Ma Jing-min ◽  
Ren Yong-sheng
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Transverse Shear ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Rotating Speed ◽  
Composite Shaft ◽  
Variational Asymptotic ◽  
Finite Element Package ◽  
Thin Walled

A dynamic model of composite shaft with variable cross section is presented. Free vibration equations of the variable cross section thin-walled composite shaft considering the effect of shear deformation are established based on a refined variational asymptotic method and Hamilton’s principle. The numerical results calculated by Galerkin method are analyzed to indicate the effects of ply angle, taper ratio, and transverse shear deformation on the first natural frequency and critical rotating speed. The results are compared with those obtained by using finite element package ANSYS and available in the literature using other models.

An accurate modeling of piezoelectric smart beams with first-order shear deformation theory

2015 ◽  
Vol 06 (02) ◽  
pp. 1550022
Author(s):  
Litesh N. Sulbhewar ◽  
P. Raveendranath
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Cross Section ◽  
Electric Potential ◽  
Deformation Theory ◽  
Thickness Distribution ◽  
Shear Deformation Theory ◽  
Beam Cross Section ◽  
Present Formulation ◽  
First Order

A finite element model for piezoelectric smart beam in extension mode based on First-order Shear Deformation Theory (FSDT) with an appropriate through-thickness distribution of electric potential is presented. Accuracy of piezoelectric finite element formulations depends on the selection of assumed mechanical and electrical fields. Most of the conventional FSDT-based piezoelectric beam formulations available in the literature use linear through-thickness distribution of electric potential which is actually nonlinear. Here, a novel quadratic profile of the through-thickness electric potential is proposed to include the nonlinear effects. The results obtained show that the accuracy of conventional formulations with linear through-thickness potential approximation is affected by the material configuration, especially when the piezoelectric material dominates the beam cross section. It is shown that the present formulation gives the same level of accuracy for all regimes of material configurations in the beam cross section. Also, a modified form of the FSDT displacements is employed, which utilizes the shear angle as a degree of freedom instead of section rotation. Such a FSDT displacement field shows improved performance compared to the conventional field. The present formulation is validated by comparing the results with ANSYS 2D simulation. The comparison of results proves the improved efficiency and accuracy of the present formulation over the conventional formulations.

A simple single variable shear deformation theory for a rectangular beam

2016 ◽  
Vol 231 (24) ◽  
pp. 4576-4591 ◽  
Author(s):  
Rameshchandra P Shimpi ◽  
Rajesh A Shetty ◽  
Anirban Guha
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Governing Equation ◽  
Deformation Theory ◽  
Rectangular Cross Section ◽  
Shear Deformation Theory ◽  
Beam Theory ◽  
Single Variable ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

This paper proposes a simple single variable shear deformation theory for an isotropic beam of rectangular cross-section. The theory involves only one fourth-order governing differential equation. For beam bending problems, the governing equation and the expressions for the bending moment and shear force of the theory are strikingly similar to those of Euler–Bernoulli beam theory. For vibration and buckling problems, the Euler–Bernoulli beam theory governing equation comes out as a special case when terms pertaining to the effects of shear deformation are ignored from the governing equation of present theory. The chosen displacement functions of the theory give rise to a realistic parabolic distribution of transverse shear stress across the beam cross-section. The theory does not require a shear correction factor. Efficacy of the proposed theory is demonstrated through illustrative examples for bending, free vibrations and buckling of isotropic beams of rectangular cross-section. The numerical results obtained are compared with those of exact theory (two-dimensional theory of elasticity) and other first-order and higher-order shear deformation beam theory results. The results obtained are found to be accurate.

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