Vibrations of Elastic Systems Having Hereditary Characteristics

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Abstract
Results of experiments carried out on plastics and rubberlike materials at high rate of straining are given. It is shown that the dynamic stress-strain (σ, ϵ) relationship for those materials can be expressed by the formula σ = f ( ϵ ) + ∫ 0 t ϕ ( t - τ ) d ϵ ( τ ) d τ d τ The first term represents the static stress-strain relationship, while the second depends on the rate of straining de dt . As a first approximation it is supposed that the materials follow Hooke’s law when statically stressed. Equation [1] then becomes σ = E ϵ + ∫ 0 t ϕ ( t - τ ) d ϵ ( τ ) d τ d τ Materials which follow the second equation are called materials with “hereditary characteristics.” Vibrations of single-degree-of-freedom systems having hereditary characteristics are considered. Methods of finding the hereditary function ϕ(t) from forced vibrations are given. Free and forced vibrations of simply supported beams having hereditary characteristics are studied.

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