A study on vibration and acoustic radiation characters of an isotropic rectangular thin plate under thermal environments is presented in this paper. It is assumed that thermal loads caused by thermal environments just change the structure stress state. Thermal stresses induced by uniform temperature rise of the plate are determined with the thermo-elastic theory. Then the stress state is used in the following dynamic analysis as a pre-stressed factor. It is observed that thermal loads influence the natural frequencies evidently, especially the fundamental natural frequency. The order of mode shapes stays the same. Dynamic response peaks float to lower frequency range with the increment of structure temperature. Acoustic radiation efficiency of the plate subjected to thermal loads decreases in the mid-frequency band. For validation, numerical simulations are also carried out. It can be found that the combined approach of finite element method (FEM) and boundary element method (BEM) is more appropriate for radiation problems.

Analysis of Dynamic and Acoustic Radiation Characters for a Flat Plate Under Thermal Environments

This paper presents a new approach to characterize the conditions that can possibly lead to chaotic motion for a simply supported large deflection rectangular plate of thermo-mechanical coupling by utilizing the criteria of the fractal dimension and the maximum Lyapunov exponent. The governing partial differential equation of the simply supported rectangular plate of thermo-mechanical coupling is first derived and simplified to a set of three ordinary differential equations by the Galerkin method. Several different features including power spectra, phase plot, Poincare map and bifurcation diagram are then numerically computed. These features are used to characterize the dynamic behavior of the plate subjected to various excitation conditions. Numerical examples are presented to verify the validity of the conditions that lead to chaotic motion and the effectiveness of the proposed modeling approach. The numerical results indicate that large deflection motion of the thermo-mechanical coupling rectangular plate possesses many bifurcation points, chaotic motions and period-double phenomena under various lateral loads, bi-axial loads, thermo-mechanical coupling factors and aspect ratios. The modeling results of numerical simulation indicate that the chaotic motion may occur in the range of lateral loads Q =1.25 to 3.35 and near the bi-axial load η2=1.5. The dynamic motion of the thermal-couple plate is periodic if the aspect ratio is within a specific range or the thermo-mechanical coupling factor is within a specific range. The modeling result thus obtained by using the method proposed in this paper can be employed to predict the instability induced by the dynamics of the thermo-mechanical coupling plate in large deflection.

Chaotic and bifurcation dynamics for a simply supported rectangular plate of thermo-mechanical coupling in large deflection

This paper is presented for the analysis of the large amplitude thermo-mechanically coupled vibration of the simply supported orthotropic rectangular thin plate. The governing partial differential equation of the large deflection orthotropic rectangular thin plate of thermo-mechanical coupling is derived and simplified to a set of three non-linear ordinary differential equations by the Galerkin method. The modeling result of numerical simulation indicated that the amplitude of the simply supported orthotropic rectangular thin plate decays under the various parameters of orthotropic materials. As these thermo-mechanical coupling factor, percentage of the Poisson ratio, percentage of the thermal conductance of the plate, percentage of the coefficient of thermal expansion, external in-plane force are decreased, the thermo mechanical damping of plate would be increased. The different thermal damping of the simply supported orthotropic plate can be controlled in the special range of the parameter.

The effect of thermo-mechanical coupling for a simply supported orthotropic rectangular plate on non-linear dynamics

An analysis on nonlinear dynamic characteristics of a simply supported functionally graded materials (FGMs) rectangular plate subjected to the transversal and in-plane excitations is presented in the time dependent thermal environment. Here we look the FGM Plates as isotropic materials which is assumed to be temperature dependent and graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents. The geometrical nonlinearity using Von Karman’s assumption is introduced. The formulation also includes in-plane and rotary inertia effects. In the framework of Reddy’s third-order shear deformation plate theory, the governing equations of motion for the FGM plate are derived by the Hamilton’s principle. Then the equations of motion with two-degree-of-freedom under combined the time-dependent thermomechanical loads can be obtained by using Galerkin’s method. Using numerical method, the control equations are analyzed to obtain the response curves. Under certain conditions the periodic and chaotic motions of the FGM plate are found. It is found that because of the existence of the temperature which relate to the time the motions of the FGM plate show the great difference. A period motion can be changed into the chaotic motions which are affected by the time dependent temperature.

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Nonlinear dynamic response of a simply supported rectangular functionally graded material plate under the time-dependent thermalmechanical loads

The nonlinear free vibration of a conductive rotating thin circular plate subjected to static loads in magnetic field was investigated The nonlinear vibration equations of the motion on a spinning circular thin plate were derived According to the set of a displacement function, the approximate solution of the static problem and the magneto elastic axisymmetric vibration differential equation of the round plate were obtained through the application of Galerkin integral method The characteristic formula between nonlinear frequency and amplitude using the static load as a parameter was obtained by the method of multiple scales According to the numerical calculation, the characteristic curves of the relationship between frequency and the parameter such as the static load, the magnetic induction intensity and the speed of rotation were obtained The nonlinear vibration characteristics of a spinning plate with clamped boundary condition were described according to the curves drawn by Matlab We also showed that different parameters (including magnetic induction intensity, static load, time and spinning velocity) have effect on the frequency of the plate

Nonlinear free vibration of a rotating circular plate under the static load in magnetic field

An analysis was given for the free vibration of clamped circular plate when temperature and stress fields were coupled. A nonlinear differential equation about time was obtained by using Galerkin's method. The numerical results of vibration amplitude vs time were compared with the uncoupled case. It is found that if the given initial displacement is small, the effect of thermoelastical coupling will make the natural frequency increase; if the given initial displacement is large, it will be the opposite case. Effects of some different vibration factors are also discussed.

Zhang Jinxiang

Papers

Thermoelastic free vibration of clampe circular plate