Free vibration of plate structures of various material systems has been vastly studied. Transverse shear can play an important role even in thin laminated structures and therefore must be included in the analysis. A method applicable to the study of generally laminated, thick, skew, trapezoidal plates is developed as there appears to be limited information available in this area. Using Chebychev polynomials as displacement functions in the Rayleigh-Ritz method, the first-order shear deformation theory is utilized to account for the transverse shear effects. All appropriate inertia terms are retained. Boundary conditions are enforced by the appropriate use of distributed linear and rotational springs along the edges. Thus, the method is applicable to any supported quadrilateral plate but is applied to cantilever plates in this study. After the validity of the method is established through comparison to published results, an extensive study is made of thick, symmetrically laminated and unsymmetrically laminated, cantilever, skew, trapezoidal plates.

Free vibration of thick generally laminated cantilever quadrilateral plates

Plates of variable thickness are widely used in modern technology nowadays in various engineering fields, such as marine engineering, aeronautical fields, nuclear reactors etc. The present paper is...

Effect of linear thermal gradient on vibrations of trapezoidal plates whose thickness varies parabolically

The main objective of the present investigation is to study linear temperature behaviour of a non-homogeneous trapezoidal plate of variable thickness. The non-homogeneity of the plate material is mainly raise due to variation in Young’s modulus and mass density. The thickness of the plate and mass density assumed to vary linearly. Rayleigh-Ritz technique has been employs to obtain fundamental frequencies for the first two modes of vibration. The effect of structural parameters such as taper constant, thermal gradient, non-homogeneity constant and aspect ratio with clamped-simply supported-clamped-simply supported boundary condition has considered. Numerical results thus obtained are tabulate. Excellent agreement is noted when comparison is made with previous available experimental data.

Thermal effect on vibration of non-homogeneous trapezoidal plate of linearly varying thickness

In this paper, effect of thermal gradient on vibration of trapezoidal plate of varying thickness is studied. Thermal effect and thickness variation is taken as linearly in x-direction. Rayleigh Ritz technique is used to calculate the fundamental frequencies. The frequencies corresponding to the first two modes of vibrations are obtained for a trapezoidal plate for different values of taper constant, thermal gradient and aspect ratio. Results are presented in graphical form.

https://file.scirp.org/pdf/AM20100500002_63936481.pdf

A. Krishnan

Papers

A study on free vibration of trapezoidal plates