An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

Abstract

Abstract:The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.

Experimental Identification and Vibration Control of A Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

“…The time response signals for chirp excitation are plotted in Figure 3a To find the transfer function of the system in the frequency domain, Fourier transform is performed on the chirp excitation signal u(t) and sensor output signal y(t). The frequency response function (FRF) of the open loop system is given by Equation (6) …”

“…In addition, the introduction of piezoelectric actuators/sensors adds complexity to the analytical modeling. Numerical approaches based on finite element method (FEM) are developed to obtain equivalent finite-dimensional models of smart structures, and yield fairly accurate results [6]. However, these approaches always require intensive mathematical derivations, which are usually labor intensive and time consuming.…”

An Improved Differential Quadrature Time Element Method

“…In solid mechanics, DQM is usually used for plate or shell [23,24] structure analysis; many examples refer to mechanical behavior of a plate or panel [25,26], vibration of composite laminated plate [27,28] considering lower-order shear deformation, nonlinear bending problems of an orthotropic plate [29], nonlinear vibrations of a plate and nonlinear dynamics of viscoelastic beams [27,30], etc. In fluid mechanics, typical applications include incompressible viscous fluid flow analysis together with hydrodynamics and heat transfer [3], circulation around a circular cylinder at Reynold's number problems for incompressible viscous fluid flow [3,31], boundary layer equations solutions [32,33] and coupled heat transfer problems [2,34,35].…”

Experimental Identification and Vibration Control of A Non-Collocated Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

“…In some cases, it is intractable, even impossible to find the system differential equations. Numerical approaches based on finite element method (FEM) are developed to obtain equivalent finite-dimensional models of smart structures, and yield fairly accurate results [6]. However, these approaches always require intensive mathematical derivations, which are usually labor intensive and time consuming.…”