Material characterization of structural adhesives in the lap shear mode

A general method for characterizing structual adhesives in the bonded lap shear mode is proposed. Two approaches in the form of semiempirical and theoretical approaches are used. The semiempirical approach includes Ludwik's and Zhurkov's equations to describe respectively, the failure stresses in the constant strain rate and constant stress loading modes with the inclusion of the temperature effects. The theoretical approach is used to describe adhesive shear stress-strain behavior with the use of viscoelastic or nonlinear elastic constitutive equations. Two different model adhesives are used in the single lap shear mode with titanium adherends. These adhesives (one of which was developed at NASA Langley Research Center) are currently considered by NASA for possible aerospace applications. Use of different model adhesives helps in assessment of the generality of the method

Free vibration analysis of symmetric cross-ply laminated composite beams with the help of the transfer matrix approach

The transfer matrix method is used for the numerical solution of both in-plane and out-of-plane free vibration problems of symmetric cross-ply laminated composite beams. The rotary inertia, and both shear and extensional deformation effects, are considered in the analysis. A distributed parameter model is used in the mathematical formulation of the free vibration problem. The overall transfer matrix of the beam is obtained making use of the series solution of a set of differential equations. All the effects of the boundary conditions, the slenderness ratio, the ratio of the height to the width of the rectangular cross-section, the number of plies, and material types on the free vibration frequencies are studied. Comparison of the exact natural frequencies obtained in this study with the existing results is quite good. Copyright ©1999 John Wiley & Sons, Ltd

Linear free vibration analysis of cross-ply laminated cylindrical helical springs

A linear free vibration analysis of symmetric cross-ply laminated cylindrical helical springs is performed based on the first-order shear deformation theory. Considering the rotary inertia, the shear and axial deformation effects, governing equations of symmetric laminated helical springs made of a linear, homogeneous, and orthotropic material are presented in a straightforward manner based on the classical beam theory. The free vibration equations consisting of 12 scalar ordinary differential equations are solved by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy. The soundness of the present results are verified with the reported values which were obtained theoretically and experimentally. After presenting the non-dimensional graphical forms of the free vibrational characteristics of (0°/90°/90°/0°) laminated helical spring made of graphite-epoxy material (AS4/3501-6) with fixed-fixed ends, a non-dimensional parametric study is worked out to examine the effects of the number of active turns, the shear modulus in the 1-2 plane (G12), the ratio of the cylinder diameter to the thickness (D/d), and Young's moduli ratio in 1 and 2 directions (E1/E2) on the first six natural frequencies of a uniaxial composite helical spring with clamped-free, clamped-simple, and clamped-clamped ends.This study was sponsored by the Scientific and Technical Research Council of Turkey (TUBITAK). The first author gratefully acknowledges the TUBITAK. Appendix

Effect of the material types on the fundamental frequencies of uniaxial composite conical springs

ASMEReliability, Stress Analysis, and Failure Prevention Issues in Adhesive and Bolted Connections - 1999 (The ASME International Mechanical Engineering Congress and Exposition) --14 November 1999 through 19 November 1999 -- Nashville, TN, USA --This paper deals with the effect of the material types (Graphite-Epoxies and Kevlar-Epoxy) on the fundamental frequencies of uniaxial constant-pitch composite conical helical springs with solid circle section and fixed-fixed ends. The transfer matrix method is used for the determination of the fundamental natural frequencies. The rotary inertia, the shear and axial deformation effects are taken into account in the solution. The free vibrational charts for each material presented in this study cover the following vibrational parameters: n (number of active turns) =5-10, ?= (helix pitch angle)=5° and 25°, R2/R1 (minimum to maximum radii of the cylinder)= 0.1 and 0.9, and Dmax/d (maximum cylinder to wire diameters)=5 and 15. These charts can be used for the design of uniaxial composite conical springs

Fundamental frequencies of uniaxial composite barrel and hyperboloidal springs

ASMEReliability, Stress Analysis, and Failure Prevention Issues in Adhesive and Bolted Connections - 1999 (The ASME International Mechanical Engineering Congress and Exposition) --14 November 1999 through 19 November 1999 -- Nashville, TN, USA --The fundamental natural frequencies of uniaxial composite non-cylindrical helical springs (barrel and hyperboloidal types) are determined theoretically based on the transfer matrix method. The rotary inertia, shear and axial deformation effects are considered with the first order shear deformation theory. The overall transfer matrix is obtained by integrating the twelve scalar ordinary differential equations with variable coefficients governing the free vibration behavior of non-cylindrical helical springs made of an anisotropic material. Numerical results are verified with the reported values for isotropic non-cylindrical helices. A parametric study is performed to investigate the effects of the number of active coils (n=5-10), the helix pitch angle (?=5° and 25°), the ratio of the minimum to maximum cylinder radii (Rmin/Rmax), and the ratio of the maximum cylinder diameter to the wire diameter (Dmax/d) on the fundamental free vibration frequencies of constant-pitch composite barrel and hyperboloidal helical springs with circular section and fixed-fixed ends

Comparison of the in-plane natural frequencies of symmetric cross-ply laminated beams based on the bernoulli- euler and timoshenko beam theories

The in-plane free vibration problem of symmetric cross-ply laminated beams is studied based on the transfer matrix method. Distributed parameter model is used in the mathematical formulation. The rotary inertia, the shear and extensional deJormation effects, are considered for the Timoshenko’s beam analysis. These effects are neglected in the Bernoulli-Euler analysis. The exact overall dynamic transfer matrix of the beam is obtained by making use of the numerical algorithm available in the literature. In order to obtain detailed knowledge about the effects of the rotary inertia, shear and axial deformations on the first six non-dimensional frequencies, the results of Timoshenko and Bernoulli-Euler theories are compared with each other for length-to-thickness ratios from ranging 3 to 20. Fixed-fixed, fixed-simple, and fixedfree boundary conditions are considered for three values of the thickness-to-width ratios of a rectangular section (2, 1, 0.5). © 1999 ASME

The effect of the longitudinal to transverse ivioduli ratio on the natural frequencies of symmetric cross-ply laminated cylindrical helical springs

The first six free vibration frequencies of symmetric cross-ply laminated cylindrical helical springs with fixed-fixed ends are theoretically computed based on the transfer matrix method. The rotary inertia, shear and axial deformation effects are taken into account in the solution. Considering different values for the helix pitch angles and the number of active turns, a parametric study is performed to analyze the effects of the ratio of the longitudinal Young's modulus to the transverse Young's modulus on the natural frequencies of such springs with square section. The results are given in dimensionless graphical forms © 1999 by ASME