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Modelling of casings
Published in Marek Pawelczyk, Stanislaw Wrona, Noise-Controlling Casings, 2023
Marek Pawelczyk, Stanislaw Wrona, C. W. Isaac, J. Klamka, J. Wyrwal
A plate is a structural element with a small thickness compared to the planar dimensions. In most cases, the thickness is no greater than one-tenth of the smaller in-plane dimension [147]. The theory of plates is an approximation of the three-dimensional elasticity theory to two dimensions, which assumes that a mid-surface plane can be used to represent deformation of every point of the plate. The aim of the plate theory is to study the deformation and stresses in plate structures subjected to loads.
Combining direct and flanking transmission
Published in Carl Hopkins, Sound Insulation, 2020
The plates are assumed to be solid, homogeneous, and isotropic, and are modelled using thin plate theory. The model uses a junction beam to connect the plates together, but it does not represent a physical part of the real junction. The junction beam has no mass, does not support wave motion and has a rigid cross-section. This beam is free to rotate and to undergo displacement in the three coordinate directions; this allows generation of in-plane waves at the junction. With each plate there is an offset, ep, from the junction beam. For rigid junctions this offset can be set to zero; note that masonry/concrete walls or floors can be rigidly connected together in more than one way, and there is no clear way of exactly defining any offset. However, it is included here because the offset does have a physical meaning when altering this basic model to account for a junction beam with mass and stiffness that supports wave motion, resilient layers between one or more plates and the junction beam, or a hinged junction (see Bosmans, 1998; Mees and Vermeir, 1993).
A high order Newton method to solve vibration problem of composite structures considering fractional derivative Zener model
Published in Mechanics of Advanced Materials and Structures, 2022
Mathias Ziapkoff, Laetitia Duigou, Guillaume Robin, Jean-Marc Cadou, El Mostafa Daya
The present numerical procedure is applied to the vibration analysis of different composite structures. For each layer, we consider the Fractional derivative Zener model. The finite element method is used. The structures have been discretized using an eight-nodded quadrilateral C0 isoparametric flat shell element with eight degrees of freedom per node. In order to describe the kinematics of the structure, the Third-Order Shear Deformation Theory (TSDT) is used [28, 29]. This theory is more accurate than the Classical Laminate plate Theory (CLT) and the First order Shear Deformation Theory (FSDT) as the TSDT theory takes the shear stress deformation into account. In order to validate the proposed High-Order Newton method, we propose to compare its results to examples from the literature [5, 6, 21]. In a first time, we consider an isotropic material plate with one layer. E and G follow Fractional derivative Zener model. In a second time, fiber-reinforced composite structures with several layers are studied. Each layer has three moduli EL, ET, GLT defined by Fractional derivative Zener model. In all cases, the tolerance for relative residual (21) is set to
Flexural analysis of laminated plates based on trigonometric layerwise shear deformation theory
Published in Mechanics of Advanced Materials and Structures, 2018
Suganyadevi Sarangan, B. N. Singh
For a long period several shear deformation theories have been proposed and developed by several research workers. Pagano [1] gave an exact three-dimensional (3D) elasticity solution for laminated plates. Noor [2] developed a 3D elasticity analytical solution for a laminated plate. Herein, each lamina is considered as a 3D solid and, hence, the computational cost is becoming a major consideration. Further, Srinivas [3] has given a layerwise (LW) theory. To ensure the interlaminar shear stress continuity, Toledano and Murakami [4] presented a layerwise theory using a mixed formulation. Ambartsumyan [5] presented a plate theory with shear stress continuity effects. To enhance the free vibration response of laminated plates, Cho et al. [6] developed a model with 3rd- and 2nd-order of thickness coordinate in in-plane and normal displacement components respectively. Further, remarkable works can be found based on layerwise theories in [7, 8]. These theories evaluate the structural responses of laminated plates with sufficient precision. However, these models required high computational efforts because the unknowns strongly depend on each layer.
A refined sinusoidal theory for laminated composite and sandwich plates
Published in Mechanics of Advanced Materials and Structures, 2020
In order to consider the shear deformation effects, the five-unknown shear deformation theories have been proposed by adding the certain functions in the in-plane displacement field of classical laminated plate theory (CLPT). By using the sinusoidal function, Touratier [33] proposed a sinusoidal shear deformation plate theory (SPT) which can describe a cosine-law distribution of transverse shear deformation through the thickness of plate. The displacement field of the sinusoidal shear deformation plate theory can be written as [33] where u0, v0, and w0 are respectively the middle surface displacements in the x, y, and z direction.