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Research Papers

# Importance of Higher Order Modes and Refined Theories in Free Vibration Analysis of Composite Plates

[+] Author and Article Information
S. Brischetto1

Department of Aeronautics and Space Engineering, Politecnico di Torino, Turin 10129, Italysalvatore.brischetto@polito.it

E. Carrera

Department of Aeronautics and Space Engineering, Politecnico di Torino, Turin 10129, Italy

1

Corresponding author.

J. Appl. Mech 77(1), 011013 (Oct 05, 2009) (14 pages) doi:10.1115/1.3173605 History: Received March 12, 2008; Revised April 14, 2009; Published October 05, 2009

## Abstract

This paper evaluates frequencies of higher-order modes in the free vibration response of simply-supported multilayered orthotropic composite plates. Closed-form solutions in harmonic forms are given for the governing equations related to classical and refined plate theories. Typical cross-ply (0 deg/90 deg) laminated panels (10 and 20 layers) are considered in the numerical investigation (these were suggested by European Aeronautic Defence and Space Company (EADS) in the framework of the “Composites and Adaptive Structures: Simulation, Experimentation and Modeling” (CASSEM) European Union (EU) project. The Carrera unified formulation has been employed to implement the considered theories: the classical lamination theory, the first-order shear deformation theory, the equivalent single layer model with fourth-order of expansion in the thickness direction $z$, and the layerwise model with linear order of expansion in $z$ for each layer. Higher-order frequencies and the related harmonic modes are computed by varying the number of wavelengths $(m,n)$ in the two-plate directions and the degrees of freedom in the plate theories. It can be concluded above all that—refined plate models lead to higher-order frequencies, which cannot be computed by simplified plate theories—frequencies related to high values of wavelengths, even the fundamental ones, can be wrongly predicted when using classical plate theories, even though thin plate geometries are analyzed.

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## Figures

Figure 2

Displacements distribution in thickness direction in case of CLT and FSDT

Figure 4

Displacements distribution in thickness direction in case of LW(N=1)

Figure 6

Multilayer stiffness matrix for FSDT

Figure 7

Multilayer stiffness matrix for ESL(N=4)

Figure 8

Multilayer stiffness matrix for LW(N=1) in case of a three-layered plate

Figure 9

Examples of in-plane modes

Figure 10

Benchmark 1, ten-layered plate, m=n=50. Through the thickness z distribution of CLT modes.

Figure 11

Benchmark 1, ten-layered plate, m=n=50. Through the thickness z distribution of FSDT modes.

Figure 1

Geometry and notations for the considered multilayered plates

Figure 3

Displacements distribution in thickness direction in case of ESL(N=4)

Figure 5

Multilayer stiffness matrix for CLT

Figure 12

Benchmark 1, ten-layered plate, m=n=50. Through the thickness z distribution of first six ESL(N=4) modes (the total number of modes is 15).

Figure 13

Benchmark 1, ten-layered plate, m=n=50. Through the thickness z distribution of first six LW(N=1) modes (the total number of modes is 33).

Figure 14

Benchmark 1, fundamental frequencies in Hz for the ten-layered plate. Comparison between CLT, ESL(N=4), and LW(N=1) results. The figure on the right is a zoom of the figure on the left side.

Figure 15

Benchmark 2, fundamental frequencies in Hz for the 20-layered plate. Comparison between CLT, ESL(N=4), and LW(N=1) results. The figure on the right is a zoom of the figure on the left side.

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