Frictionless plane

Abstract: PURPOSE:To make it possible to execute an accurate and quantitative test inexpensively and very precisely by a method wherein an IC card placed on a plane is made to collide with a wall facing it by applying an acceleration equivalent to that of gravity. CONSTITUTION:An IC card 1 is placed on a frictionless plane 3, and separated from a wall 4 by a distance desired for dropping, and a force 5 being equal to the gravity is applied to the IC card 1 to make it collide with a specified spot of the wall 4. In this way, an accurate and quantitative test can be executed inexpensively and very precisely.

Abstract: In this paper we discuss the effect of neglecting relative tangential surface displacements in forming the boundary conditions of elastic contact problems between dissimilar materials. This is one of the known approximations made by Hertz in his original theory. Attempts have been made only recently to build up procedures to take this `convective' effect into account, for simple plane problems (Soldatenkov, 1996). However, before questioning all the existing solutions for elastically dissimilar contact problems, it is considered important to estimate quantitatively the order of the possible correction. Here a simple iterative procedure is set up to solve frictionless plane contact problems taking into account the `convective effect'. Attention is focused on the problem of wedge indentation, as this provides a reasonably tractable problem, and on the parabolic indenter, to discuss the Hertzian case. The correction introduced is shown not to be negligible, but is of practical significance only in extreme conditions, viz. frictionless contact and large Dundurs' constant, β. In these extreme cases, the maximum correction to the contact are dimension may be of the order of an increase of 10% for the contact area dimension. The effect tends to be more significant for Hertzian indenter and higher order profiles.

Abstract: An exact formulation is presented for the problem of a rigid circular body performing harmonic vibrations on an elastic half-space whose shear modulus increases linearly with depth and is interrupted at some finite depth by a frictionless horizontal plane The static case is derived in the limit of zero frequency vibrations while the known result for the uninterrupted half-space is recovered in either extreme limit of the horizontal frictionless plane coinciding with the surface or when it is pushed down to an infinite depth It is shown that the maximum effect of the interruption occurs when the frictionless plane is at a depth where the shear modulus is about 1·6 times the surface shear modulus Furthermore, this maximum effect is equivalent to a reduction of about 5 per cent of the surface shear modulus or a reduction of about 2½ per cent in the natural frequency of the rigid body on an uninterrupted half-space The important conclusion, therefore, is that irrespective of the depth at which a half-space isso interrupted, the surface shear modulus is still the dominant parameter and that both the increase in shear modulus with depth and the interruption are not only secondary but also opposing effects