0000000000652861
AUTHOR
Alexis Castel
Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations
Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functio…
Vibroacoustic Simulation of Heterogeneous Multilayer Composite Plates Involving Low Young's Modulus Viscoelastic Material
The vibroacoustic behavior of composite multilayered plates involving high Young’s modulus ratios between adjacent layers, like sandwich panels and passive constrained layer damped plates, is studied. As classical plate models give poor results with such structures, a specific model has been used. It is an equivalent single layer model, with a five unknown displacement field which takes into account a variation of transverse shear strains into the thickness. A classical sandwich structure is simulated, its natural frequencies are compared to those given by other models and a 3D finite element simulation which is taken as reference. A second study concerns a composite plate with a damping pa…
Complex power distribution analysis in plates covered with passive constrained layer damping patches
International audience; The vibration of a plate partially covered with a passive constrained layer damping (PCLD) patch is studied from an energetic point of view. The damped plate is excited by an acoustic plane wave. The study is done with a numerical two-dimensional multilayer plate model. Results of the present model are compared to those obtained with three-dimensional finite element models. It is shown that the present model gives accurate results, even for the layer's inner behavior. It is less expansive in terms of computational cost; hence, it can simulate efficiently the structure for higher frequencies. Mathematical formulas for complex mechanical power are presented, and the li…
Vibro-acoustocal behavior of composite structures with damping elements
This work is on the subject of modelization of structures treated with passive damping elements. A generic "equivalent single layer" plate model using transverse shear warping functions is presented. Several methods to obtain these functions are described, allowing the implementation of classical models and others issued from the litterature. Two new methods for obtaining these functions are also presented.Several discretization methods adapted to the generic plate model are studied. Navier's procedure allows the testing of the quality of each model associated with a set of transverse shear warping functions. Rayleigh-Ritz method allows the study of the vibrational behavior of a rectangular…
A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work
Abstract In this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10×10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2×2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios be…