Thermal Effect on Vibration of Tapered Rectangular Plate

Abstract

A mathematical model is constructed to help the engineers in designing various mechanical structures mostly used in satellite and aeronautical engineering. In the present model, vibration of rectangular plate with nonuniform thickness is discussed. Temperature variations are considered biparabolic, that is, parabolic in x-direction and parabolic in y-direction. The fourth-order differential equation of the motion is solved by Rayleigh Ritz method for three different boundary conditions around the boundary of plate. Numerical values of frequencies for the first two modes of vibration are presented in tabular form for different values of thermal gradient, taper constants, and aspect ratio.

Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

“…In order to validate the findings of the present study as well as to present the objective of the study, a comparison of frequency modes obtained in the present study was done with the following: (i) Frequency modes of parallelogram plate obtained in [11] on CCCC and CSCS edge condition corresponding to tapering parameters ϖ 1 , ϖ 2 and aspect ratio (a/b) (ii) Frequency modes of rectangle plate obtained in [17,18] on CCCC, SSSS, and CSCS edge condition corresponding to tapering parameters ϖ 1 , ϖ 2 and on CCCC, SSSS, CSSS, CSCS, and CCCS edge conditions corresponding to a thermal gradient κ e results are reported in tabular form (refer Tables 6 and 7 for parallelogram plate and refer Tables 8 and 9 for rectangle plate). For comparison of frequency modes of rectangle plate and obtained in [17,18], the authors exclude the nonhomogeneity φ in the present study as it was not considered in [17,18].…”

“…A comparison of frequency modes of rectangle plate (by taking skew angle θ � 0 °in the present study) and obtained in [18] on CCCC, SSSS, CSSS, CSCS and CCCS edge conditions corresponding to thermal gradient κ for fixed value Bold font values are obtained in [17].…”

“…Here also, the frequency modes obtained in the present study (parallelogram plate) are less when compared with the frequency modes obtained in [11] with the increasing value of aspect ratio (a/b) and tapering parameters ϖ 1 , ϖ 2 on both CCCC and CSCS edge conditions. Table 8 shows the comparison of frequency modes of rectangle plate (by taking skew angle θ � 0 °in the present study) and obtained in [17] on CCCC, SSSS, and CSCS edge conditions corresponding to tapering parameters ϖ 1 , ϖ 2 for a fixed value of κ � 0.0 and aspect ratio (a/b) � 1.5. Table 8 enlightens the fact that frequency modes of rectangle plate are very less in comparison to the frequency modes obtained in [17] on all the above edge conditions with the increasing value of tapering parameters ϖ 1 , ϖ 2 .…”

“…Table 8 shows the comparison of frequency modes of rectangle plate (by taking skew angle θ � 0 °in the present study) and obtained in [17] on CCCC, SSSS, and CSCS edge conditions corresponding to tapering parameters ϖ 1 , ϖ 2 for a fixed value of κ � 0.0 and aspect ratio (a/b) � 1.5. Table 8 enlightens the fact that frequency modes of rectangle plate are very less in comparison to the frequency modes obtained in [17] on all the above edge conditions with the increasing value of tapering parameters ϖ 1 , ϖ 2 .…”

“…Comparison of frequency modes of the present study (rectangle plate) and obtained in[17] corresponding to tapering parameters ϖ 1 , ϖ 2 for a fixed value of thermal gradient κ � 0.0 and aspect ratio (a/b) � 1.5.…”