1.4.3 Vibration of a cable under tension

Product: ABAQUS/Standard  

This “violin string” problem is a simple case in which a structure's frequencies depend on the state of prestress existing when the vibrations occur. In such cases the analysis is done by preloading the structure in one (or several) static steps and then requesting eigenvalue extraction. In some cases the static preload may involve considerable nonlinearity, although this is not the case in this simple problem. The basic concept is to obtain frequencies of small vibrations about a prestressed, predeformed configuration.

Problem description

Results and discussion

Input files

Reference

Table

Table 1.4.3–1 Natural frequencies for preloaded cable, Hz.

ModeExactABAQUS Error ABAQUSError
(Thomson, 1965)T2D2T2D2B21B21
174.774.3–0.5%74.3–0.5%
2149.148.–1.2%148.–1.2%
3224.219.–2.4%219.–2.4%
4299.287.–4.1%287.–4.1%


Figure

Figure 1.4.3–1 Preloaded cable vibration example.