Cross-coupling stiffness

Bearing Load and Cross-Coupling Stiffness Measurements... 

Fig. 4 Dimensionless cross coupled stiffness and damping C versus...

The aerodynamic cross-coupling effect has been quantified into equivalent stiffness. For instance, in axial-flow machines... 

A regular antisymmetric cross-ply laminate is delined to have laminae all of equal thickness and is common because of simplicity of fabrication. As the number of layers increases, the bending-extension coupling stiffness B.,., can be shown to approach zero. 

Bending-Extension Coupling Stiffness, versus Cross-Ply Ratio, M (After Tsai [4-6])... 

Derive the bending-extension coupling stiffnesses for regular special antisymmetric cross-ply laminates, that is, derive Equation (4.83) for the special case in which odd = v n = f/N (for which also M = 1). 

Antisymmetric cross-ply laminates were described in Section 4.3.3 and found to have extensional stiffnesses A. , A. 2, A22 = A.. , and Agg bending-extension coupling stiffnesses B., and 822 =-Bn and bending stiffnesses D., D.,2, 822 = and Dgg. The new terms here in comparison to a speciaily orthotro Dic iaminate are B.,and 822- Because of this coupiing, the three equiiibrium differentiai equations are coupied ... 

Discrepancies between numerical values of the estimated damping coefficients is shown in Table I. The frequency domain approach invariably produced an indication of strong cross-coupling terms which was not confirmed either by the time-domain results or by direct observation of the damper ring response. The authors believe that the squeeze-film was probably over-excited during the frequency domain tests and consequently driven out of the linear regime. The presence of significant nonlinear stiffness effects in the squeeze-film could account for the discrepancies which have been observed. 

As stated by Remark 6.4, the wall thickness of the considered beams is small in comparison to the cross-sectional dimensions, being reflected in r (s) and rs(s), and to the radius of curvature R s). These geometric orders of magnitude also enter the constitutive description of the laminated beam wall in Eq. (6.4b). The plate stiffness coefficients 613(5) and 633(5) and coupling stiffnesses 831(5) and 633(5) essentially depend upon the difference of cubed, respectively squared, laminae positions in the thickness direction, while the membrane stiffness kss s) is a function of the laminae thicknesses. To comply with Remark 6.4, it is necessary to revise the formulation of the warping... 

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

Bend-twist coupling is a totally different animal. The governing stiffnesses, D g and D2g, simply are never zero for any laminate that is more complicated than a cross-ply laminate. You cannot force those stiffnesses to go to zero unless you do something else to the laminate. You can make them go to zero if you let the laminate be unsymmetric, but that is robbing Peter to pay Paul. In fact, it is not very difficult in most contemporary analyses to include the influence of those bend-twist cou-... 

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