This paper attempts to investigate experimentally the influence of base conditions on the mobility of a stratum on a rigid base. The results are compared with the theoretical results as presented by the author in a previous publication. It is shown that the obtained measurement results reasonably agree with the theory and that the base conditions of stratum on a rigid base do have a significant influence on the force mobility, particularly at resonance.

2.

Hassan, Osama

Umea universitet, Department of Applied Physics and Electronics,Sweden .

An approximate approach to derive the input mobility of an infinite elastic stratum on a rigid base is investigated. The excitation is due to a vertical force, which is applied via a small massless indenter with a circular base, fixed to the stratum. Two cases are investigated: a stratum with a fixed base and a stratum with a frictionless base. General expressions for the mobilities are derived from the equations of motion of an isotropic elastic medium. Using a numerical approach, the analytical results are evaluated up to a Helmholtz number k(L)d = 10, where k(L) is the wave number of the P- wave and d is the stratum depth. For small Helmholtz numbers, asymptotic expressions are derived analytically; the two evaluations agree well up to a Helmholtz number of 0.2 for the frictionless base and to 0.5 for the fixed base. It is shown that the mobilities for the two cases differ significantly at small Helmholtz numbers. This is mainly due to the influence of a propagating wave, which can exist only in the case of a frictionless base. It is also shown that the local deformations in the vicinity of the indenter are built up by low-frequency, non-propagating Lamb modes. Finally, the dispersion relations are evaluated up to a Helmholtz number k(L)d = 16.

3.

Hassan, Osama

Umea universitet, Department of Applied Physics and Electronics, Sweden .

The second part of this paper deals with the exact solution for the force mobility of an infinite elastic stratum with respect to a vertical force. The stratum rests on a rigid and frictionless foundation. The upper surface of the stratum is excited by a circular weightless indenter with a prescribed velocity; otherwise this surface is stress-free. The mixed boundary conditions result in dual integral equations, which are solved using analytical and numerical techniques. An exact analytical solution for the force mobility of the stratum is determined by using the method of resolvent kernel together with the residue theorem. The results are validated by comparisons with the results from a numerical solution using the quadrature method. It is shown that the results from an approximate solution as presented in the first part, where the prescribed velocity is exchanged for a presumed stress distribution, agrees well with the present results for low frequencies up to approximately the first thickness resonance, but not for higher frequencies.

4.

Hassan, Osama

KTH, Tidigare Institutioner, Byggnader och installationer.

The decision of selecting building structures with respect to the environmental demand is an issue commonly addressed in environmental management. In this paper, the importance of considering the decision analysis technique value-focused thinking in the environmental selection of wall structures is investigated. In this context, a qualitative value model is developed in which the external and internal environmental factors are considered. The model is applied on a case study in which a decision should be made on three categories of exterior wall structures: wood, masonry and concrete. It is found that the wall structure made of wood is the most compatible option with respect to the external and internal environmental requirements of building structures.

The effect of an elastic stratum in reducing ground-borne sound transmission in buildings to be built above railway tunnels is investigated, by considering a sand layer between the bedrock and load bearing elements of the building. It is assumed that the initial vibrational energy that propagates from the foundation is in the form of quasi-longitudinal waves. The complete model as presented by the author in a previous paper is considered. Calculated results are compared with previous results for a typical building and it is shown that a sand layer can considerably reduce upward sound transmission in the building. The results of a parametric study to investigate the influence of the type of load-bearing elements and the thickness of the layer, on transmission of structure-borne sound in the building, are presented.

An analytical model for predicting the sound reduction index of a single plate is presented. The plate is assumed to be excited by a diffuse sound field and the velocity distribution of the plate is derived from the Kirchoff plate equation in the frequency domain. The resulting Fourier transform is evaluated using residue calculus and the solution is verified numerically. The analytical model is valid for a wide frequency range, both below, above and at the critical frequency. Special interest is paid to the area dependency of the sound reduction index. Calculated results are presented for a 0.5 m(2), 1.7 m(2) and 4.4 m(2) plate of 16 rum chipboard. These results, which agree well with measured values, show that the sound reduction index decreases with increasing area in the whole frequency range.