Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Discerning heat transfer in building materials

The function of a building is to ensure safety and thermal comfort for healthy living conditions. Buildings primarily comprise an envelope, which acts as an interface separating the external environment from the indoors environment. The building envelope is primarily responsible for regulating indoor thermal comfort in response to external climatic conditions. It usually comprises a configuration of building materials to thus far provide requisite structural performance. However, studies into building-envelope configurations to provide a particular thermal performance are limited. As the building envelope is exposed to the external environment there will be heat and moisture transfer to the indoor environment through it. The overall phenomenon of heat and moisture transfer depends on the microstructure and configuration within the building material. Further, thermal property of a material is generally dependent on its microstructure, which comprises a network of pores and particles arranged in a definite structure. Thermal behaviour of a building material thus depends on the thermal conductivities of the solid particles, pore micro-structure and its constituent fluid (air and/or moisture). The thermal response of a building envelope is determined by the thermal characteristics of the individual building materials and its configuration. Understanding the heat transfer influenced by the complex networks of pores and particles is a relatively new study in the area of building climatic-response. The current study reviews the heat-transfer mechanisms that determine the thermal performance of a building material attributed to its micro-structure. A theoretical basis for the same is being evolved and its relevance in regulating heat-transfer through building envelopes, walls in particular, is reviewed in this paper. (C) 2014 N.C. Balaji. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).