scholarly journals Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Arun Kumar Gupta ◽  
Shanu Sharma
Keyword(s):  
Temperature Distribution ◽  
Aspect Ratio ◽  
Transverse Vibration ◽  
Thermal Gradient ◽  
Ritz Method ◽  
Linear Temperature ◽  
Varying Thickness ◽  
Free Transverse Vibration ◽  
Trapezoidal Plate ◽  
Taper Constant

The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness inx-direction subjected to linear temperature distribution inx-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations.

Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Panels

1975 ◽  
Vol 26 (3) ◽  
pp. 211-218 ◽  
Author(s):  
P K Sinha ◽  
A K Rath
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Shear Deformation ◽  
Transverse Vibration ◽  
Arbitrary Sequence ◽  
Composite Panels ◽  
Simply Supported ◽  
Cylindrical Panels ◽  
Free Transverse Vibration

SummaryThe paper deals with the free transverse vibration and stability analysis of circular cylindrical composite panels. The panels are assumed to be composed of an arbitrary sequence of 0° and 90° layers. The non-dimensional vibration and buckling parameters are computed for simply-supported panels consisting of antisymmetric crossply graphite-epoxy laminates. The influence of the coupling between bending and extension, shear deformation, the panel curvature, and the aspect ratio are then discussed.

Calculation of Curvature Using Linear Thermal Gradient

2012 ◽  
Author(s):  
Sungjin Bae
Keyword(s):  
Temperature Distribution ◽  
Thermal Effects ◽  
Thermal Gradient ◽  
Nuclear Power ◽  
Power Plants ◽  
Transient Temperature ◽  
Element Analysis ◽  
Linear Temperature ◽  
Equivalent Linear ◽  
Nonlinear Temperature

Reinforced concrete structures for nuclear power plants are designed for thermal effects. When a structure is subject to transient temperature rise, the temperature distribution in a member becomes nonlinear. Commentary of ACI 349 code provides a method of converting a nonlinear temperature distribution to an equivalent linear temperature distribution in order to facilitate calculating curvature due to temperature change. However, the accuracy of estimated thermal curvatures for concrete sections with a liner plate needs to be examined because the ACI 349 method is based on a pure concrete section. The objective of this paper is to investigate the accuracy of thermal curvatures calculated using the equivalent linear temperature distribution for concrete sections with a liner. Temperature distributions across concrete sections are obtained from heat transfer analyses. Free thermal curvatures are calculated by converting temperature distribution to the equivalent linear temperatures and compared with those from a finite element analysis. Based on the study, the modified expression for linear thermal gradient is proposed which includes the effect of liner on curvatures.

scholarly journals Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

2021 ◽  
Vol 15 (4) ◽  
pp. 15-28
Author(s):  
Tran Quang Hung ◽  
Tran Minh Tu ◽  
Do Minh Duc
Keyword(s):  
Temperature Distribution ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Thermal Environment ◽  
Ritz Method ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Lagrange Equations ◽  
Linear Temperature

This paper aims to present thermo-electrical free vibration characteristics of functionally graded material (FGM) sandwich beam placed on the two-parameter elastic foundation. The beam is constructed of a foam core, two middle FGM layers, and two outer piezoelectric layers. It is assumed that the beam is subjected to a constant voltage and a uniform/linear temperature distribution. Physical properties of the core and two middle layers vary smoothly through the thickness according to the cosine and power-law forms, respectively. Lagrange equations in conjunction with the Reddy third-order beam theory is employed to derive the governing equations of motion. A simple polynomial trial function-based Ritz method is adopted for the approximation of the displacement field to obtain the vibration response. The correctness of the study is verified by comparisons with other authors’ published results. Influences of geometry parameters, material property distribution, applied voltage, elastic foundation, temperature distribution, temperature change, porosity coefficient, span-to-height ratio, and boundary conditions are investigated through parametric studies.

scholarly journals Time Period of the Vibration of the Circular Plate with Circular Variation Both in Thickness and Density

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Reeta Bhardwaj ◽  
Amit Sharma ◽  
Sudeshna Ghosh ◽  
Naveen Mani ◽  
Kamal Kumar
Keyword(s):  
Thermal Gradient ◽  
Ritz Method ◽  
The Other ◽  
Circular Plates ◽  
Linear Quadratic ◽  
Linear Temperature ◽  
Thermally Induced ◽  
Time Period ◽  
Modes Of Vibration ◽  
Convergence Study

An analysis was carried out to investigate the time period of the thermally induced vibration of clamped and simply supported circular plates with circular variation both in thickness and density. Prior to this study, the variations considered were either linear, quadratic, parabolic, or exponential in nature. To study thermal effect, one-dimensional linear temperature variation on the plates is taken into consideration. Rayleigh–Ritz method is applied to compute the time period of the first three modes of vibration for both plates by varying tapering parameter, thermal gradient, and density. Convergence study of frequency modes for both plates conducted suggests that the convergence rate in case of circular variation is faster than the other studies done. A comparison of time period with the available published results is done. The comparison done concludes that time period obtained in the present study by varying thermal gradient and tapering parameter is found to be less than the other studies done for the same set of parameters. This study helped to establish the fact that, by using circular variation in plate parameters, we can get less time period of frequency modes in comparison to other variations considered till date.

Transverse Vibration Analysis of Axially Moving Trapezoidal Plates

2021 ◽  
Vol 16 (6) ◽  
pp. 978-986
Author(s):  
Man Zhang ◽  
Ji-Xian Dong
Keyword(s):  
Aspect Ratio ◽  
Transverse Vibration ◽  
Differential Quadrature Method ◽  
Eigenvalue Equation ◽  
Parameter Method ◽  
Complex Eigenvalue ◽  
Complex Frequency ◽  
Discrete Method ◽  
Axially Moving ◽  
Trapezoidal Plate

Transverse vibration of axially moving trapezoidal plates is investigated. The differential equation of transverse vibration for a axially moving trapezoidal plate is established by D'Alembert principle. The original trapezoid region can be replaced by regular square region by the medium parameter method for the convenience of calculation. A generalized complex eigenvalue equation is derived by a discrete method (the differential quadrature method). The complex frequency curve of trapezoidal plate is obtained by calculating the eigenvalue equation. The change of the complex frequencies of the axially moving trapezoidal plates with the dimensionless axially moving speed is analyzed. The effects of the aspect ratio and the trapezoidal angle on instability type of the trapezoidal plate are discussed under different boundary conditions. The results of numerical analysis show that there are two main instability types of axially moving trapezoidal plate: divergence and flutter. The modal orders of the two types of instability are also different, which is related to the trapezoidal angle, aspect ratio and boundary condition of the trapezoidal plate.

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