Buckling and vibro-acoustic response of the clamped composite laminated plate in thermal environment

Highlights

• Vibro-acoustic responses of laminated plate in thermal environment are studied.

• An analytical method for fully clamped laminated plate is presented.

• Classical laminate theory and first order shear deformation theory are utilized

• The theory is validated by numerical simulations.

• The vibro-acoustic responses affected by the thermal load are investigated.

Abstract

Composite structures are extensively applied in aircraft and marine industries because of their high stiffness-to-weight ratios and other advantages. The composite structures in the hypersonic aircraft are usually exposed to the thermal and noise environment. The paper is focused on the buckling and vibro-acoustic response of the clamped composite laminated plate excited by a concentrated harmonic force in the thermal environment. The analytical solution of vibration and acoustic response for fully clamped boundary condition is derived in the paper. Meanwhile, the natural frequencies and buckling temperatures of the plate in uniform temperature environment are also derived by applying the classical laminate theory (CLT) and first order shear deformation theory (FOSDT). The vibration response is obtained by applying the mode superposition method, while the sound pressure and radiation efficiency are calculated by Rayleigh integral in sequence. The accuracy of the presented method is verified by the numerical simulations. The structural and acoustic response affected by the thermal load is demonstrated through a numerical example.

Introduction

The high temperature is a crucial environment for the hypersonic aircraft due to serious aerodynamic heating. The thermal stresses may lead to buckling and dynamic instability because the stiffness of the structures is significantly changed in thermal environment.

Jadeja and Loo [1] investigated the vibration of a rectangular plate with one edge fixed and the other edges simply supported under a sinusoidal heat input. It was found that the inertia term was of great importance for thermal plate during the dynamic analysis. Yeh [2] presented for the analysis of the large amplitude thermo-mechanically coupled vibration of the simply supported orthotropic rectangular thin plate. The results indicated that the coupling effect should not be ignored when the initial deflection was large. Chen [3] studied the thermal buckling of laminated composite plate by using Galerkin's method. Kant and Babu [4] studied the elastic buckling of skew fiber-reinforced composite and sandwich plates subjected to thermal loads by using the finite element model. Vangipuram and Ganesan [5] investigated the free vibration and damping characteristics of plates consisting of composite stiff-layers and an isotropic viscoelastic core in thermal loads using finite element method. Then they [6] studied the thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates. Zhen et al. [7] proposed a new efficient global–local higher-order model for the thermoelastic analysis of laminated composite and sandwich plates taking account of the contribution of thermal expansion in the transverse displacement component. Matsunaga [8] presented the vibration and stability problems of angle-ply laminated composite and sandwich plates subjected to thermal loading by global higher-order deformation theory. Jabbari et al. [9] presented the thermal buckling of radially solid circular plate made of porous material with piezoelectric actuator layers based on the first order shear deformation theory. Chen et al. [10] studied the buckling and vibration of simple supported composite plates with temperature-dependent material properties in thermal environments. Nasihatgozar et al. [11] studied the buckling response of piezoelectric cylindrical composite panels reinforced with carbon nano-tubes subjected to axial load using classical laminated plate theory.

Together with the vibration analysis in thermal environment, the sound radiation of the vibration structures is studied simultaneously. The object of the sound radiation from vibration structures is very significant. It is important that designers understand the mechanism of sound radiation and take effective and economic measures to eliminate or suppress the noise since it can destroy the facilities and injure human beings [12].

Wallace [13] studied the radiation resistance corresponding to the natural modes of a finite simple supported rectangular plate from the total energy. Atalla et al. [14] investigated the sound radiation of a plane with finite dimensions and general elastic boundary conditions. Xie et al. [15] studied the average radiation efficiency of point-excited rectangular plates, with a modal summation method. Remillieux and Burdisso [16] investigated the vibration and sound radiation from an infinite, fluid loaded, thick plate assembly stiffened periodically with ribs using finite-element method. Ma et al. [17] proposed an analytical study of active control of sound radiation from a rib stiffened plate using the well-known modal expansion method.

Many literatures about the dynamic characteristics in thermal environment can be found so far. Meanwhile, lots of researchers have devoted to the study of acoustic of the vibration structures. However, the literatures about the vibration and acoustic responses in thermal environment of the composite structures are rare.

Jeyaraj et al. [18] presented the numerical simulation studies on the vibration and acoustic characteristics of an isotropic rectangular plate in thermal environment by applying commercial software ANSYS and SYSNOISE. It was observed that the natural frequencies decrease with the increment of the temperature for different boundary conditions. Then they addressed numerical method [19] on fiber-reinforced single layer composite plate in thermal environment. The effect of damping on the structure was also considered in their work. Later, they presented numerical simulation studies on a multilayered viscoelastic sandwich plate [20] in thermal environment. Geng and Li [21] utilized the analytical method to investigate the vibration and acoustic responses of an isotropic rectangular simply supported thin plate in a uniform temperature environment. It was found that the natural frequencies descend with the increment of the temperature. Furthermore, the fundamental frequency was much more sensitive to the temperature changes than other frequencies. Later, they [22] investigated the characters of clamped isotropic plate in thermal environment. They [23] performed the experiment to investigate the vibration and acoustic response of a clamped rectangular aluminum plate in the thermal environments. They got the modal damping ratio of the plate in different temperature environment, and they also found that the initial deflection was of significance to the natural frequencies. Liu and Li [24], [25] researched the vibration and acoustic characters of the isotropic sandwich plate which was subjected to a concentrated harmonic force or acoustic excitation in thermal environment. They utilized the equivalent non-classical theory [26] which considered the shear deformation and rotation inertia of the sandwich plate. Li et al.[27], [28] investigated the vibration and acoustic response of the simple supported sandwich panels constituted of orthotropic materials using the piecewise shear deformation theory.

Lots of machinery systems work in thermal environment. As a typical example, hypersonic aircraft are frequently exposed to the thermal and noise environment for aerodynamic heating [29], [30], [31], [32]. Composite laminated plates have been extensively applied in these aircraft because of its specific strength and good designability.

As a rule of thumb, for simple supported boundary condition, the analytical solution of the plate can be written in form of double trigonometric series. Most of the analytical solutions are specific to the simple supported boundary condition. But for complex boundary condition e.g. fully clamped condition, it is difficult to derive the analytical solutions. The analytical solution has higher computation efficiency, can reveal the physical mechanism of the problem and provide a reference for the experiment and numerical methods. Additionally, it is more convenient to discuss the influence of various parameters on the vibro-acoustic responses of the plate. Therefore, the paper focuses on the analytical solution of the buckling and vibro-acoustic responses for fully clamped composite laminated plate in thermal environment. The structure of the remainder is as follows. In Section 2, analytical solutions of the buckling temperatures, natural frequencies and modal shapes of the clamped plate are firstly obtained in thermal environment by applying the CLT. Then the presented theory is extended to the more accurate method of FOSDT. Finally, the vibration and acoustic responses are analyzed. In Section 3, the numerical simulations are carried out to validate the accuracy of the theory. In Section 4, the influence of the temperature on the laminated plates is discussed in depth. In Section 5, some conclusions are presented.