Time Period Analysis of Orthotropic Skew Plate with 2-D Circular Thickness and 1-D Circular Density

Abstract

In the present study, the time period of vibration of an orthotropic parallelogram plate with 2 − D (two-dimensional) circular thickness under the effect of 2 − D parabolic temperature is investigated for the first time. The different edge conditions are C C C C , C C C F , C F C F , C S C F , and S F S F boundary conditions, where C, S, and F stands for clamped, simply supported, and free edges of the plate, respectively. The variation in density of plate material is considered to be 1 − D (one-dimensional) circular. The Rayleigh–Ritz technique is used to solve the differential equation and evaluate the time period for the first two modes of vibration. A convergence study of an orthotropic parallelogram, rectangle plate, and square plate for modes of frequency at various edge conditions is also carried out. The authors performed a comparative analysis of the time period and modes of frequency of orthotropic parallelogram, rectangle plate, and isotropic square plate with the available published results at various edge conditions. The main conclusion which we made from this study is that by choosing the above-mentioned plate parameters, we obtained fewer modes of frequency in comparison to other variations mentioned in the literature. Also, the study suggests that the variation in modes of frequency is less in comparison to other variations.

Thermal Vibration of Nonhomogeneous Orthotropic Tapered Skew Plate

“…• Variation in frequency mode  due to linear temperature variation (current research) was less as compared to parabolic temperature variation [14] for CCCC, CSCF, SFSF edge condition but variation in frequency mode  was higher in current research as compared to [14] at CFCF boundary condition mentioned in table 4.…”

“…The authors have considered an orthotropic skew (parallelogram) plate made having variables l (thickness),  (angle of skewness), a (length), b (breadth),  (density) and  (Poisson's ratio). Two skew coordinates Plate's thickness ( l ) was taken as circular in two dimension where as density (  ) was considered to be circular in one dimension only (as done in [14]):…”

“…• Frequency modes of orthotropic skew plate achieved in [14] for CFCF, CSCF, CCCC and SFSF boundary conditions with respect to thermal gradient  mentioned in Table 4.…”

“…In table 4, a comparison study of frequency modes  attained by present research (orthotropic parallelogram plate) and achieved in [14]  is varied from 0.0 to 1.0. From the comparison, it is observed that the frequency modes  attained by present research was higher as compared to [14] for the increasing value of  at all edge condition but variation in frequency mode was less as compared to [14] for CCCC, CSCF, SFSF edge conditions.…”

Vibrational frequency of triangular plate having circular thickness

“…Chebyshevs Ritz method is applied in [2] to the free in plane vibration of arbitrary shaped laminated triangular plates with elastic boundary conditions. Time period analysis of isotropic and orthotropic visco skew plate having circular variation in thickness and density at different edge conditions is discussed in [3] and [4]. Two dimensional temperature effect on the vibration is computed in [5] for the first time for a clamped triangular plate with two dimensional thickness by using the Rayleigh Ritz method.…”