Free Vibration of Elliptical Plates in Uniform Temperature Field

2005 ◽  
Author(s):  
Xiaohu Yao ◽  
Qiang Han ◽  
Liming Dai
Keyword(s):  
Temperature Field ◽  
Differential Equations ◽  
Free Vibration ◽  
Nonlinear Differential Equations ◽  
Stress Fields ◽  
Elastic Coupling ◽  
Uniform Temperature ◽  
Elliptical Plate ◽  
Uniform Temperature Field ◽  
Fundamental Equations

The free vibration of clamped elliptical plate, when temperature and stress fields are coupled, is analyzed based on the fundamental equations of nonlinear thermo-elastic vibrations. A system of nonlinear differential equations of time is obtained with utilization of Galerkin’s method. The vibration states are compared with respect to different coefficients. The effects of thermo-elastic coupling on the amplitude and frequency are also presented.

scholarly journals Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130473 ◽  
Author(s):  
Yingli Li ◽  
S. A. Meguid ◽  
Yiming Fu ◽  
Daolin Xu
Keyword(s):  
Temperature Field ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Thermal Loading ◽  
Electrostatic Force ◽  
Nonlinear Differential Equations ◽  
Functionally Graded ◽  
Uniform Temperature ◽  
Graded Material ◽  
Uniform Temperature Field

In this paper, we provide a unified and self-consistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The non-uniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam. For the clamped-clamped case, care must be taken to account for the effective use of thermal loading in the design of microbeams. It is also observed that uniform thermal loading will lead to a reduction in the pull-in voltage of a FGM microbeam for all the three boundary conditions considered.

Non-uniform temperature distribution of the main reflector of a large radio telescope under solar radiation

2021 ◽  
Vol 21 (11) ◽  
pp. 293
Author(s):  
Shan-Xiang Wei ◽  
De-Qing Kong ◽  
Qi-Ming Wang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Solar Radiation ◽  
Radio Telescope ◽  
Thermal Imaging ◽  
Uniform Temperature ◽  
Large Radio Telescope ◽  
Uniform Temperature Distribution ◽  
Uniform Temperature Field ◽  
Main Reflector

Abstract The non-uniform temperature distribution of the main reflector of a large radio telescope may cause serious deformation of the main reflector, which will dramatically reduce the aperture efficiency of a radio telescope. To study the non-uniform temperature field of the main reflector of a large radio telescope, numerical calculations including thermal environment factors, the coefficients on convection and radiation, and the shadow boundary of the main reflector are first discussed. In addition, the shadow coverage and the non-uniform temperature field of the main reflector of a 70-m radio telescope under solar radiation are simulated by finite element analysis. The simulation results show that the temperature distribution of the main reflector under solar radiation is very uneven, and the maximum of the root mean square temperature is 12.3°C. To verify the simulation results, an optical camera and a thermal imaging camera are used to measure the shadow coverage and the non-uniform temperature distribution of the main reflector on a clear day. At the same time, some temperature sensors are used to measure the temperature at some points close to the main reflector on the backup structure. It has been verified that the simulation and measurement results of the shadow coverage on the main reflector are in good agreement, and the cosine similarity between the simulation and the measurement is above 90%. Despite the inevitable thermal imaging errors caused by large viewing angles, the simulated temperature field is similar to the measured temperature distribution of the main reflector to a large extent. The temperature trend measured at the test points on the backup structure close to the main reflector without direct solar radiation is consistent with the simulated temperature trend of the corresponding points on the main reflector with the solar radiation. It is credible to calculate the temperature field of the main reflector through the finite element method. This work can provide valuable references for studying the thermal deformation and the surface accuracy of the main reflector of a large radio telescope.

scholarly journals Polarizing effect in natural polymer cellulose

2019 ◽  
pp. 45-46
Author(s):  
N. N. Matveev ◽  
V. V. Saushkin ◽  
N. Yu. Evsikova ◽  
N. S. Kamalova ◽  
V. I. Lisitsyn
Keyword(s):  
Temperature Field ◽  
Low Temperature ◽  
Natural Polymer ◽  
Uniform Temperature ◽  
Polarization Mechanism ◽  
Uniform Temperature Field ◽  
First Time

For the first time, a method based on the registration of polarization and depolarization currents arising in wood in a non-uniform temperature field was used to study the properties of cellulose. The purpose of the method used is to record the relaxation of bound charges with a change in the temperature of the sample under study. It is shown that the detected low-temperature transitions have a crystal-crystal polarization mechanism, and the natural polymer cellulose is an active dielectric.

scholarly journals Repeated alternating loading of a elastoplastic three-layer plate in a temperature field

2021 ◽  
Vol 21 (1) ◽  
pp. 60-75
Author(s):  
Eduard I. Starovoitov ◽  
◽  
Denis V. Leonenko ◽  
Keyword(s):  
Temperature Field ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Plastic Region ◽  
Local Load ◽  
Natural State ◽  
Elastic Plastic

Axisymmetric deformation of a three-layer circular plate under repeated alternating loading from the plastic region by a local load is considered. To describe kinematics of asymmetrical on the thickness of the plate pack is adopted the hypothesis of a broken line. In a thin elastic-plastic load-bearing layers are used the hypothesis of Kirchhoff. A non-linearly elastic relatively thick filler is incompressible in thickness. It is taken to be a hypothesis of Tymoshenko regarding the straightness and the incompressibility of the deformed normals with linear approximation of the displacements through the thickness layer. The work of the filler in the tangential direction is taken into account. The physical relations of stress-strain relations correspond to the theory of small elastic-plastic deformations. The effect of heat flow is taken into account. The temperature field in the plate was calculated by the formula obtained by averaging the thermophysical parameters over the thickness of the package. The system of differential equations of equilibrium under loading of the plate from the natural state is obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution of the corresponding boundary value problem is reduced to finding the three desired functions: deflection, shear and radial displacement of the shear surface of the filler. A non-uniform system of ordinary nonlinear differential equations is written for these functions. Its analytical iterative solution is obtained in Bessel functions by the method of elastic solutions of Ilyushin. In case of repeated alternating loading of the plate, the solution of the boundary value problem is constructed using the theory of variable loading of Moskvitin. In this case, the hypothesis of similarity of plasticity functions at each loading step is used. Their analytical form is taken independent of the point of unloading. However, the material constants included in the approximation formulas will be different. The cyclic hardening of the material of the bearing layers is taken into account. The parametric analysis of the obtained solutions under different boundary conditions in the case of a local load distributed in a circle is carried out. The influence of temperature and nonlinearity of layer materials on the displacements in the plate is numerically investigated.

Non-uniform temperature field and effects of Shanghai 65 m radio telescope

2014 ◽  
Vol 22 (4) ◽  
pp. 970-978 ◽  
Author(s):  
钱宏亮 QIAN Hong-liang ◽  
柳叶 LIU Ye ◽  
范峰 FAN Feng ◽  
金晓飞 JIN Xiao-fei
Keyword(s):  
Temperature Field ◽  
Radio Telescope ◽  
Uniform Temperature ◽  
Uniform Temperature Field

The Composite Tool Design Technologies of Aircraft Composite Parts in Autoclave Forming

2012 ◽  
Vol 426 ◽  
pp. 330-334 ◽  
Author(s):  
Ying Guang Li ◽  
C.Y. Fu ◽  
D.S. Li ◽  
S.M. Wan
Keyword(s):  
Temperature Field ◽  
Fiber Reinforced Composites ◽  
Field Analysis ◽  
Reinforced Composites ◽  
Uniform Temperature ◽  
Composite Component ◽  
Cure Process ◽  
Design Flexibility ◽  
Composite Tool ◽  
Uniform Temperature Field

Aiming at the problems of composites of anisotropic, poor in dimensional and uneven temperature field in the designing of composite tool in autoclave, the techniques of designing the composite tool of aircraft components were constructed, involving in the following aspects: Taking advantage of design flexibility of composites, the thermal expansion coefficient between the moulding board and composite components matched. By analyzing the cure process curve of fiber-reinforced composites, the result that the crisis point without stress between component and tool, which the shape of composite component decided was concluded. By the temperature field analysis, and contrasted with the experimental results, the maximum difference was 4.95°C，after analysis, optimized the structure of the tool, obtaining the relatively uniform temperature field of the board.

Sign in / Sign up

Export Citation Format

Share Document