Y. C. Das

A refined model for beams on elastic foundations

Abstract The concept of a beam or slab on an elastic foundation has been one of the convenient tools for obtaining solutions to several geotechnical engineering problems. While it is easy to establish quite accurately the stiffness characteristics of the beam or the slab, the parameters which govern the behavior of the subsoil or the elastic foundation are indeed hard to model. This difficulty remains true even if one assumes that the soil has linear, isotropic, and homogeneous properties. Using the Vlasov model. Vallabhan and Das (1988, J. Engng Mech. Div., ASCE 114 (2). 2072–2082) have developed an effective iterative technique to solve the beam-on-elastic-foundation problem where the soil is assumed to have a uniform depth with a rigid base at the bottom. Geotechnical engineers usually encounter subsoil of finite depth, and normally the elastic properties are considered to remain constant or vary linearly with depth. In this paper, the authors have extended their model to incorporate numerically this physical characteristic of the soil. Even though the derivations may look laborious, the numerical model is quite simple and can be programmed on a desktop computer.

Nonlinear dynamic response of window glass units

Abstract For glazing of modern buildings, rectangular window glass units are being used extensively. When these glass units are subjected to lateral wind pressures, they respond dynamically; a simple quasi-static analysis may lead to less conservative design procedures. Since window glass units undergo large displacements when subjected to lateral pressures, a nonlinear dynamic analysis is necessary. Using von Karman nonlinear plate equations, Vallabhan and Selvam (1986) have developed a finite differencemodel for computing the dynamic response of a thin rectangular plate. Here, the maximum amplitudes along with the corresponding periods of vibration and the maximum tensile stresses due to uniform lateral pressures applied suddenly on simply supported thin rectangular plates, are presented using nondimensional parameters. Also, results are presented for various aspect ratios of plates.

Free vibration analysis of insulating glass units

Abstract Modern insulating glass (IG) units consist of two glass plates, normally rectangular, placed parallel to each other. The plates are joined by a perimeter spacer and the unit is sealed so as to be air tight. Such IG units are widely used for thermal and sound insulation in modern buildings. An IG unit responds dynamically when exposed to wind loading. Fluctuating winds induce vibrations in the exterior glass plate and, in turn, this plate induces motion of the air enclosed between the plates and vibration of the interior plate. Hence, there is dynamic interaction between the two plates and the air trapped between them. A rigorous dynamic analysis is needed to determine the response of IG units to wind loading. As a first step, it is essential to study the periods of the fluid-plate system. In the present work, the two plates are assumed to satisfy small deflection plate theory. The air trapped between the plates is assumed to be irrotational and inviscid, but compressible, and it is assumed to satisfy the small amplitude equations of gas dynamics. A mathematical model is developed to study the interaction between the plates and the enclosed air. Assuming all edges of the plates to be simply supported and the perimeter spacer to provide a rigid boundary on the air space, the governing dynamic equations of the fluid-plate system are solved for free vibration response of the system. It is found that even plates modes are coupled with add fluid modes and vice versa. The coupled frequencies of the fluid-plate system exhibit decreased magnitudes compared with the corresponding uncoupled plate frequencies. The information obtained concerning the frequencies of IG units will be useful in further dynamic analysis of these units when subjected to fluctuating winds.