Layered identity

The solution that has been adopted by makers of composite soundboards is to fabricate a sandwich structure where a layer of high-quality cardboard is glued between two identical layers of CFRP (Fig. 28.22). The philosophy of this design modification is to replace some CFRP by a much lighter material in those regions that contribute least to the overall stiffness of the section. 

This design study has shown that it is possible to design a sectional composite that will reproduce both the vibrational frequencies and the mass of a traditional wooden soundboard. For a soundboard made out of spruce the equivalent composite is a sandwich of cardboard glued between two identical layers of aligned CFRP with a fibre volume fraction of 0.13. If the wooden soundboard is 3 mm thick the replacement composite must be 1.98 mm thick with a cardboard core of 1.25 mm. 

Figure 3.11 Cubic close-packed structure of face-centered cubic crystals such as copper as a packing of atom layers (a) a single close-packed layer of copper atoms (b) two identical layers, layer B sits in dimples in layer A (c) three identical layers, layer C sits in dimples in layer B that are not over atoms in layer A. The direction normal to these layers is the cubic [111] direction.

A wall is constructed of a section of stainless steel [k = 16 W/m - °C] 4.0 mm thick with identical layers of plastic on both sides of the steel. The overall heat-transfer coefficient, considering convection on both sides of the plastic, is 120 W/m2 °C. If the overall temperature difference across the arrangement is 60°C, calculate the temperature difference across the stainless steel. 

Mica particles coated with a metal oxide film have three layers with different refractive indices (layer 1 and 3 are identical, layer 2 is mica) and four interfaces (see chapter 16.2). Interference of light is generated by reflections of all six possible combinations of the four interfaces. Some of them lead to equal effects. The thickness of the mica platelets varies according to a statistical distribution. As a con-... 

Several studies of multiple layer treatments have been made 23., 22., 21, 21. For such treatment comprising identical layers, there does not appear to be a strong performance advantage over a single constrained-layer treatment of equal weight 23., 22). ... 

In all of the above combinations, reagents of identical layers (primary and secondary) may be applied simultaneously in the same incubation steps. Only the chromogenic-enzyme reactions, if relevant, need to be carried out consecutively, (e.g., alkaline phosphatase activity revealed first followed by peroxidase development). 

The simplest lattice structure is the so-called simple cubic packing (sc). This structure consists of identical layers of atoms placed exactly above and below each other. The structure is sketched in Figure 2- 20. 

The atoms in a metal can also be packed according the so-called body-centered cubic packing structure (bcc). In this structure identical layers of atoms are placed above and below each other so that every second layer is... 

The term poly type implies that there is a family of structures to which the polytype belongs. The original idea of Baumhauer (1912, 1915), who introduced the term polytypism, was that the individual members of a family consist of identical layers and differ only in their stacking mode. 

Consider a normal light transmission through a finite isotropic three-layer periodical structure, made of identical layers indicated by numbers 1, 2 and 3 with a thickness c/, and and refraction indexes , and, respectively. Let this SPS with N periods to be surrounded by isotropic dielectric media with refraction indexes and (Fig. 1). 

Arrangement (d). Arrangement (c) places each sphere in the second layer directly above a sphere in the first layer. That is, (c) has identical layers placed one above the other. Arrangement (d) places the spheres of the top layer in the depressions of the bottom layer. It therefore uses the space available most effectively and brings the spheres in closer contact to one another. 

Figure 2.9 The brownmillerite structure (a) identical layers of tetrahedra, space group I2bm (46) (b) alternating layers of tetrahedra, space group Pnma (62)...

Layers deposited on PP films display different behaviour. Layers obtained at highest gun powers remain amorphous. At identical layer deposition parameters the materials characterises with higher SE than the nonwoven fabric. It stems from continuous structure of layers deposited on film as opposed to conductive mesh formed on the surface of nonwoven fabrics. As in case of Ni, Fe or At layers, SE of film is 10 dB higher. 

Figure 1.13 Monoclinic (blue) and triclinic (red) variants of the BARNUD structure. The actual structures shown are MTPHEP01 (space group P2i/c) and BONLEV (after inversion of its published coordinates). The two structures comprise identical layers (in the ab-plane of the monoclinic unit cell). In the view along the a-axis of the monoclinic cell (right), the top layers overlay exactly while the bottom layers are offset from each other along the b-axis of the monoclinic cell, (see colour plate section)...

Taking into account the length of the amine molecule (2.35-2.65 nm) and the size of dicarboxylic acids molecules equal to 0.8-1.0 nm (GA) and 0.7-0.9 nm (MA) as well as calculated values for the interplanar distance d shown in Figure one can conclude that one layered stmcture (a) as well as double layered structure (b) are not realized. The most realistic model corresponds to double layered ordering with overlapped aliphatic tails and acids residues (c). It shows also that both 2 1 (c) and 1 1 complexes (d) of GA have to form the identical layered structure with the same interplanar distance. This model permits to suppose that in complexes containing an excess acid its molecules are displaced between complex molecules within the domains enriched by acid residues. In this case the layered stmcture with the similar interplanar distance has to be preserved. 

If ti,ri, and at represent the known properties of a sample that contains a number i of identical layers, each of which is described by t, n, and ai, the properties of a sample containing i such layers is given by Benford as... 

All laminates should be balanced to achieve in-plane orthotropic behavior. To achieve balance, for every layer centered at some positive angle +0, there must exist an identical layer oriented at -9 with the same thickness and material properties. If the laminate contains only 0° and/or 90° layers, it satisfies the requirements for balance. Laminates may be midplane symmetric but not balanced, and vice versa. Figure 4.1 le is symmetric and balanced, whereas Fig. 4.1 Ig is balanced but unsymmetric. 

Peeling. One of the simplest and most widely used methods of measuring adhesion is by peeling a thin adhering layer away from a rigid substrate (Fig. 14a) or from an identical layer (Fig. 14b). The peel force is a direct measure of fracture energy, at least in the simplest cases, as the following analysis shows. 

Interdiffusion. When two identical layers are brought into contact, molecules from each surface may diffuse across the interface. This process is hastened when the molecular weight is low. It has been proposedas a necessary condition for strong autohesion, whereas others consider that intimate molecular contact at the interface is sufficient to give good... 

A FIGURE 13.7 Sublimation When a layer of particles sublimes, another identical layer is just below it. Consequently, the number of particles available to sublime at any one time does not change with the total number of particles in the sample, and the process is zero order. 

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