Showing papers by "M. Ganapathi published in 1999"

Flexural loss factors of sandwich and laminated composite beams using linear and nonlinear dynamic analysis

Abstract: The purpose of the article presented here is to analyze the flexural loss factors of beams with sandwich or constrained layer damping arrangements and laminated composite beams using a C 1 continuous, three-noded beam element. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects, and is applicable for both flexural and torsional studies. The geometric nonlinearity based on von Karman’s assumptions is incorporated in the formulation while retaining the linear behavior for the material. The finite element employed here is based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam. The transverse shear deformation in the form of trigonometric sine function is introduced in the formulation to define the transverse shear strain. The governing equations of motion for the dynamic analysis are obtained using Lagrange’s equation of motion. The solution for nonlinear equations is sought by using an algorithmdirect iteration technique suitably modified for eigenvalue problems, based on the QR algorithm. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear modulus and thickness of the core of the sandwich beam, aspect ratios, boundary conditions, and lay-up in the case of laminates on the system loss factors. q 1999 Elsevier Science Ltd. All rights reserved.

AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams

Abstract: A new three-noded C1 beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three-dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three-dimensional solu-tions available for laminates under bending, and the elasticity three-dimensional solution deduced from the de Saint-Venant solution including both torsion with warping and bending. In addition, three-dimensional solid finite elements using 27 noded-brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, free (de Saint-Venant) and constrained torsion. Copyright © 1999 John Wiley & Sons, Ltd.

Parametric Dynamic Instability Analysis of Laminated Composite Conical Shells

Abstract: The dynamic instability analysis of parametrically excited truncated conical shells subjected to periodic in-plane loads is investigated using C 0 two-noded shear flexible shell element. The present model accounts for in-plane and rotary inertia effects. The boundaries of the principal instability region obtained here are conveniently represented in the non-dimensional excitation frequency-non-dimensional load amplitude plane. The influences of various parameters such as cone orthotropicity, cone angle, ply-angle and elastic edge restraint on dynamic stability are brought out.

Free Vibrations Analysis of Laminated Composite Rotating Beam using C' Shear Flexible Element

Abstract: The free flexural vibrations of rotating beam made of anisotropic laminated composite beam are investigated using a new three noded finite element. The governing equations for the free vibration of rotating beam are derived using Lagrange's equation of motion. The element employed is based on shear flexible theory. It also includes inplane and rotary inertia terms. The formulation takes care of continuity conditions for stresses and displacements at the interfaces between the layers of a laminated beam. Numerical results for uniform rotating cantilever beam are presented by considering various parameters like slenderness ratio, modular ratio and rotational speed, etc.

Torsional Vibration and Damping Analysis of Sandwich Beams

Abstract: The objective of the paper presented here is to investigate the torsional vibration and damping analysis of beams with sandwich or constrained layer damping arrangements using finite element procedure. Finite element based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam, is employed. The element is capable of simulating free as well as constrained torsion. The transverse shear deformation in the form of trigonometric sine function is incorporated to define the transverse shear strain. The inertia effects due to in-plane, rotary and torsional motion have been included in the formulation. The governing equations of motion for the dynamic analysis are obtained using Lagrange's equation of motion. The solutions are evaluated by QR algorithm. Numerical results are presented for both free-free and cantilever beams. A detailed parametric study is carried out to highlight the influence of shear modulus of the core or constrained layer in beams, thickness ratio, and boundary condition on the torsional resonance frequencies and its associated system loss factors.