Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation

Abstract

The present study is concerned with the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Continuous gradation of the fiber volume fraction is modeled in the form of an m-th power polynomial of the coordinate axis in the thickness direction of the beam. By varying the fiber volume fraction within the symmetric composite beam to create a functionally graded material (FGM), certain vibration characteristics are affected. Results are presented to demonstrate the effects of shear deformation, fiber volume fraction, and boundary conditions on the natural frequencies and mode shapes of composite beams.

A New Approach for Adhesive Stress Analysis of a Beam Bonded with Composite Plate Having Variable Fiber Spacing

“…Substituting equations (18) and (19) into the fourth derivative of the interfacial normal stress obtainable from equation (4) gives the following governing differential equation for the interfacial normal stress…”

“…By varying the fiber volume fraction within a symmetric laminated beam to create a functionally graded material (FGM), certain thermal deformations can be controlled or tailored. Bedjilili et al [18] presented exact solutions for shear flexible symmetric composite beams with a variable fiber volume fraction through thickness. The laminates with variable fiber spacing along the thickness direction have been investigated recently by Fu et al [19].…”

A design of laminated composite plates using graded orthotropic fiber-reinforced composite plies

“…Bedjilili et al [26] presented free vibration characteristics of a symmetric composite beam with variable FVF along the thickness direction. Han et al [27] considered sigmoid distributions of FVF across the thickness of composite plates and shells.…”

Free Vibration Analysis of Generally Layered Composite Beams with Arbitrary Boundary Conditions

“…The importance of shear deformation in the description of the dynamic responses of laminated beams is well documented and the first-order shear deformation theory is developed, which extends the kinematics of the classical lamination theory by including a gross transverse shear deformation in its kinematic assumption. Bedjilili et al [1] performed the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness using the first-order shear deformation theory. Li and Hua [2] gave the developments in the Address correspondence to Jun Li, School of Transportation, Wuhan University of Technology, Wuhan, China.…”