Free Vibration Analysis of Laminated Composite Box Sections

Free Vibration Analysis of Laminated Composite Box Sections

Clydin P A

Dept. of Civil Engineering METS School of Engineering Thrissur, India

Abstract Laminated composite box sections may be subjected to vibrations. Their thin walled configuration makes them more prone to damages during such conditions. In the present paper, the free vibration characteristics of laminated composite box sections are studied and a design parameter is proposed. Finite Element Software ANSYS 15 is used for the purpose and natural frequencies determined. The variation of natural frequency with the proposed design parameter is studied.

Keywords Laminated composites, Box section, Free vibration, Orthotropic Stiffness, Natural frequency

1. INTRODUCTION

   Laminated composites consist of layers of fibrous composite materials. The individual layers consist of high modulus, high strength fibers in a polymeric, metallic or ceramic matrix material. They may or may not exhibit the properties of individual components. However, they are found to be stronger, lighter and more efficient than their individual counterparts. The major advantage is that they can be tailored as per requirement to achieve maximum performance. They find applications in automobile, aerospace, civil, mechanical and athletics industry. Their popularity is also evident in structural applications such as long span bridge decks, ship deck hulls and superstructure of offshore oil platforms. They are found to exhibit high strength to weight and stiffness to weight ratios, long fatigue life and excellent corrosion resistance. Some typical examples include carbon fiber epoxy, graphite epoxy and boron epoxies.

   Thin walled laminated composite box sections used in bridges, ship decks, helicopter blades and other applications are subjected to vibrations. Since they are thin structures they are more vulnerable to these effects and hence there is a need to understand the vibration characteristics and need to identify criteria to design sections which are more effective against vibrations.

2. METHODOLOGY

   Modelling of laminated composite box beams have been implemented using Finite Element Package ANSYS 15. ANSYS can carry out advanced engineering analyses quickly, safely and practically by variety of contact algorithms. Modelling of laminated composite box sections requires defining the properties of laminated composite, number of layers, thickness of laminate, type of layup and fiber orientations. Element used is Shell 281, with 8 nodes and 6 degrees of freedom at each node, preferred for modelling thin plates and shells.

   Nithin Mohan

   Dept. of Civil Engineering

   Vidya Academy of Science & Technology Thrissur, India

   1. Orthotropic Stiffness Parameter

      Vibration characteristic is highly influenced by the stiffness of the laminated composite box section which in turn depends on the fiber orientation of the layers. Several arbitrary layup configurations were considered. Their stiffness evaluated and layups with constant values of extension stiffness A12 were chosen. A design parameter was able to be identified, referred in this paper as the Orthotropic Stiffness parameter. Close examination of various arbitrary layups and their stiffness helped in identifying this parameter. Further, study of this parameter and its variation with natural frequency was carried out.

      Orthotropic Stiffness Parameter, C

      =1/2 {(A11/A66)web + (A11/A66)flange}

   2. Finite Element Modelling

      Laminated composite box section of Graphite Epoxy material is modelled. The material and geometric properties are as in Table 1.The layup considered is symmetric with angle combinations of angles 0, 15, 30, 45, 60, 75 and 90 The model was analyzed for same lay up configuration in web and flanges. A total of 27 lay up configurations were considered for the study. A 3-D finite element model of the laminated composite box beam is developed in ANSYS 15 as in Figure 1.

   3. Free Vibration Analysis

   Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force. Modal Analysis is carried out in ANSYS 15 to determine natural frequencies. The laminated composite box section of 4000 mm X 300 mm X 200 mm and 2mm thickness consisting of 6 layers were analyzed for about 27 layup configurations. The layup configurations were chosen such that their A12 is constant.

   Fig 1 The 3 D Laminated Composite Box Section from ANSYS 15

3. RESULTS

   For the box section of graphite epoxy material with geometric properties as in Table 1, orthotropic stiffness parameter is evaluated. First lowest natural frequency is also determined. This is done for sections, with same layup in web and flange.

   From Table 2, it can be seen that lowest natural frequency is attained for an A12 value of 27337.9377, with orthotropic stiffness parameter value of 1.3132. This stands out to be 12.652 Hz. From Figure 2, it is evident that natural frequency reduces with reduction in orthotropic stiffness parameter.

   TABLE 1. GEOMETRIC AND MATERIAL PROPERTIES

   Material properties		Geometric properties
   Longitudinal modulus of elasticity, E1(N/mm2)	14500 0	Length (mm)	4000
   Transverse modulus of elasticity, E2(N/mm2)	16500	Breadth (mm)	300
   Longitudinal Poissons ratio,1	0.314	Depth (mm)	200
   Transverse Poissons ratio, 2	0.0357	Thickness (mm)	2
   Shear Modulus, G (N/mm2)	4480	Number of layers	6
   Density, (Kg/m3)	1520	Ply thickness(mm)	0.33333

4. CONCLUSION

A design parameter that help in proposing sections with least natural frequency was identified by studying stiffness of various layup configurations. The variation of this parameter with natural frequency was depicted.

• Design Parameter, called orthotropic stiffness parameter was identified.

• As Orthotropic stiffness parameter reduces natural frequency reduces, for sections of same lay up

  configurations in web and flange of box sections for a constant value of A12.

• For any constant A12, if orthotropic stiffness parameter is kept low then natural frequency can be reduced.

TABLE 2. RESULTS OF MODAL ANALYSIS

30

25

20

15

10

5

A12=16092.8931 A12=27337.9377 A12=32960.4601 A12=44205.5047 A12=49828.0271

0

0

Orthotro5pic Stiffness P1a0rameter

15

35

Natural Frequency (Hz)

Fig 2. The variation of Orthotropic Stiffness and Natural Frequencies for various values of A12

REFERENCES

MODALANALYSIS

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