Vibration Analysis Of Multilayered Plates Research Articles

Equivalent Single Layer Models in Free Vibration Analysis of Laminated Multi-Layered Plates

The performance of selected equivalent single-layer (ESL) models is evaluated within several classical benchmark tests for small amplitude free vibration analysis of multi-layered plates. The authors elaborated their own Finite Element software based on the first-order shear deformation (FOSD) theory with some modifications incorporated including a correction of the transverse shear stiffness and an application of zigzag type functions. Seven different ESL models were considered in the study; beside the classical FOSD model, there were three FOSD models with various transverse shear corrections and three ESL models enhanced by the application of zigzag functions and based on Reissner’s Mixed Variational Theorem.

Analytical solution for free vibration analysis of composite plates with layer-wise displacement assumptions

This paper presents an analytical closed form solution for free vibration analysis of multilayered plates by using a layer-wise displacement assumption based on Carrera’s Unified Formulation. A wide range of boundary conditions are analysed by using a Levy type solution. By using such a solution, the number of the differential equations of motion depends on the number of plies. This means that for plates with different number of plies the equations of motion need to be re-derived and re-solved. In this paper, a procedure has been devised to overcame this problem and the equation of motions can be automatically obtained and solved to obtain natural frequencies and mode shapes for plates with any number of layers. This procedure has been called “L-matrix method”. The novel solutions have been validated by analytical 3D and 2D Navier type solutions for plates simply supported at all edges. A comparison of the results with 2D and 3D NASTRAN finite element models is also carried out showing the superiority of the analytical solution. Furthermore, benchmark solutions have been obtained for plates with different boundary conditions. The presented Levy type solution can be easily extended to static, buckling and response analysis.

Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory

Bending and free vibration analysis of multilayered plates and shells by using a new accurate higher order shear deformation theory (HSDT) is presented. It is one of the most accurate HSDT available in the literature, mainly because new non-polynomial shear strain shape functions (combination of exponential and trigonometric) used in the present theory are richer than polynomial functions, and free surface boundary conditions can be guaranteed a priori. The present HSDT is able to reproduce Touratier’s HSDT as special case. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are then solved via Navier-type, closed form solutions. Bending and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Panels are subjected to sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The present results are compared with the exact three-dimensional elasticity theory and with several other well-known HSDT theories. The present HSDT is found to be more precise than other several existing ones for analyzing the bending and free vibration of isotropic and multilayered composite shell and plate structures.