Vibration and buckling characteristics of weld-bonded rectangular plates using the flexibility function approach

Abstract

Structures with a combination of spot welds and adhesive bonding, often referred to as weld-bonded structures, are likely to see increasing usage in automotive and other engineering structures. The present study considers a representative weld-bonded rectangular plate having simple supports on two opposite edges and weld-bonded support conditions with periodic spot welds along the other two edges. The study shows that the flexibility function approach for modeling free edges with point supports [Bapat AV, Venkatramani N, Suryanarayan S. Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates. Journal of Sound and Vibration 1988;120(1):127–40; Bapat AV, Venkatramani N, Suryanarayan S. A new approach for the representation of a point support in the analysis of plates. Journal of Sound and Vibration 1988;120(1):107–25; Bapat AV, Venkatramani N, Suryanarayan S. The use of flexibility functions with negative domains in the vibration analysis of asymmetrically point-supported rectangular plates. Journal of Sound and Vibration 1988;124(3):555–76; Bapat AV, Suryanarayan S. Free vibrations of periodically point-supported rectangular plates. Journal of Sound and Vibration 1989;132(3):491–509; Bapat AV, Suryanarayan S. The flexibility function approach to vibration analysis of rectangular plates with arbitrary multiple point supports on the edges. Journal of Sound and Vibration 1989;128(2):203–33; Bapat AV, Suryanarayan S. Free vibrations of rectangular plates with interior point supports. Journal of Sound and Vibration 1989;134(2):291–313; Bapat AV, Suryanarayan S. Importance of satisfaction of point-support compatibility conditions in the simulation of point supports by the flexibility function approach. Journal of Sound and Vibration 1990;137(2):191–207; Bapat AV, Suryanarayan S. A fictitious foundation approach to vibration analysis of plates with interior point. Journal of Sound and Vibration 1992;155(2):325–41; Bapat AV, Suryanarayan S. A theoretical basis for the experimental realization of boundary conditions in the vibration analysis of plates. Journal of Sound and Vibration 1993;163(3):463–78], used in the direct series solution of the governing differential equations, can be employed very effectively to study the vibration and buckling characteristics of the weld-bonded rectangular plates. This is done by using a flexibility function constructed in terms of Fourier components to model the weld-bonded edge that represents the finite uniform flexibility of the adhesively bonded segment of the weld-bonded edge along with zero flexibility at the spot welds modeled as discrete point supports. A detailed convergence study shows that by a proper choice of the number of terms used to represent the flexibility function and the number of terms in the Levy sine series for the solution of the plate displacement, accurate results can be obtained for vibration and buckling characteristics. This paper also includes a parametric study undertaken to show the effect of plate geometry, number of spot welds and adhesive joint parameters. The paper also discusses how such parametric studies can be of use to the designer in arriving at an optimal joint configuration of weld-bonded rectangular plates from linear elastic buckling and free vibration considerations.