Stacking Sequence Effects on Natural Frequency of Laminated Composite Beams

Abstract

INTRODUCTION Composite materials made up of combining two or more materials are being used increasingly in the industry throughout the world. Applications include marine, aircraft and automotive industries as well as domestic appliance, electrical and chemical industries. Composite materials are very popular as they are lightweight, anti-corrosive and low in cost. Many analytical methods of analysis have been used to study the vibration of plates and shells. Analytical difficulties in solving equations in the closed form have been overcome only in some special cases. In other words, the general case has not yet received a satisfactory treatment. The finite element approach has proved to be a powerful and widely applicable method for the vibration analysis of complex problems for which analytical solutions are nearly impossible to find [1]. Vibrating systems can be characterized as linear or non-linear. There exists a wide range of mathematical tools that may be used to describe linear systems' behaviours. On the contrary, there are few techniques for non-linear system analysis and they Letter

Free Vibration and Buckling Analysis of the Laminated Composite Beams by Using GDQM

“…As seen from the Fig.s The natural frequencies of composite laminated beams are calculated in order to compare with Ref. [18] and [22]. C-F and SS-SS boundary conditions were used in References [18] and [22] respectively.…”

“…[18] and [22]. C-F and SS-SS boundary conditions were used in References [18] and [22] respectively. Material properties and geometries of the laminated beams used present work, [18] and [22] are given in Table 1.…”

“…The bending moment M on a composite laminated beam is shown in Fig. 1 and can be written as [18]: where b is width of the beam, ρ is curvature of the beam, m is the number of layer and z j is distance between the outer face of jth layer and the neutral plane, respectively. The relationship between the bending moment and the curvature can be written as follow:…”

“…A sin cos t L Gökmen Atlıhan, Ersin Demir, Zekeriya Girgin and Hasan Çallıoğlu following characteristic problem as below: (18) where λ 2 = ρ m Αω 2 n L 4 / E ef I yy is the dimensionless frequency parameter and X = x / L is the normalized form of x. Since Eq.…”

Analyses of Laminated Cantilever Composite Beams by Model Order Reduction Techniques

“…Kisa et al (1998) analyzed the vibrational characteristics of a cracked Timoshenko beam by integrating the FEM and CMS. Topcu et al (2008) investigated the effects of stacking sequences of composite laminated beams on natural frequencies by using experimental, theoretical, and numerical approaches. Numayr et al (2006) examined free vibration of symmetrically laminated fiber-reinforced composite beams with different boundary conditions.…”