Standard linear solid model for dynamic and time dependent behaviour of building materials

Vibrations in building structures are almost always undesirable. Whether in the form of low frequency oscillations, or droning of the structure, or as audible noise, they may effect the comfort of the user. They may even effect the safety and the integrity of (parts of) the structure. Damping of mechanical vibrations has always been a point of consideration for the engineer. Presently, it is of increasing interest and importance for the building industry. There are several reasons for this: increasing use of high quality materials which exhibit very low material damping; tendency towards 'slender' designing requiring a lower volume of (high quality) materials, thus offering less capacity for absorption of vibration energy; excessive noise and vibration hindrance and interference in highly populated area's (particularly city centers), due to high concentration of structures including high rise buildings, surface- or underground infrastructure, combined with replacement of natural soil between them by low damping solid material; necessity to meet higher performance standards and environmental requirements as to vibration hindrance and noise; necessity to apply high vibration-absorbing materials and systems. Study and careful description of various sources and forms of damping, including the internal damping of materials, is a requirement for meeting these developments. This paper discusses the merits of a three parameter rheological model for modeling time dependent behaviour of materials in general and dynamic behaviour in particular, with emphasis on damping of free vibrations. This model is known in litterature as the standard linear solid (SLS). Damping of vibrations in materials is normally anticipated on the basis of the damping modes of the standard mechanical model for damping: viscous damping element parallel with a elastic element (spring). It is shown that these modes are not the general free damping modes for linear materials. When the three-parameter (SLS) model is adopted, the general damping modes do appear. The agreement between model and actual time-dependent material behaviour is acceptable for a wide range of materials with low as well as high damping under both free and forced vibration, over a wide frequency (or time) domain. Parameters can be adapted according to specific materials, including composite materials. The standard (spring-damper) model retains its applicability for low-damping materials.