Viscoelasticity

No mathematical theory can completely describe the complex world around us. Every theory is aimed at a certain class of phenomena, formulates their essential features, and disregards what is of minor importance. The theory meets its limits of applicability where a dis­ regarded influence becomes important. Thus, rigid-body dynamics describes in many cases the motion of actual bodies with high accu­ racy, but it fails to produce more than a few general statements in the case of impact, because elastic or anelastic deformation, no matter how local or how small, attains a dominating influence. For a long time mechanics of deformable bodies has been based upon Hooke's law - that is, upon thE" assumption of linear elasticity. It was well known that most engineering materials like metals, con­ crde, wood, soil, are not linearly elastic or, are so within limits too narrow to cover tne range of pl'actical intcrest. Nevertheless, almost all routine stress analysis is still based on Hooke T s law be­ cause of its simplicity. In the course of time engineers have become increasingly con­ scious of the importance of the anelastic behavior of many materials, and mathematical formulations have been attempted and applied to practical problems. Outstanding among them are the theories of ide­ ally plastic and of viscoelastic materials. While plastic behavior is essentially nonlinear (piecewise linear at best), viscoelasticity, like elasticity, permits a linear theory. This theory of linear visco­ elasticity is the subject of tbe present book. No mathematical theory can completely describe the complex world around us. Every theory is aimed at a certain class of phenomena, formulates their essential features, and disregards what is of minor importance. The theory meets its limits of applicability where a disƯ regarded influence becomes important. Thus, rigid-body dynamics describes in many cases the motion of actual bodies with high accuƯ racy, but it fails to produce more than a few general statements in the case of impact, because elastic or anelastic deformation, no matter how local or how small, attains a dominating influence. For a long time mechanics of deformable bodies has been based upon Hooke's law - that is, upon thE" assumption of linear elasticity. It was well known that most engineering materials like metals, conƯ crde, wood, soil, are not linearly elastic or, are so within limits too narrow to cover tne range of pl'actical intcrest. Nevertheless, almost all routine stress analysis is still based on Hooke T s law beƯ cause of its simplicity. In the course of time engineers have become increasingly conƯ scious of the importance of the anelastic behavior of many materials, and mathematical formulations have been attempted and applied to practical problems. Outstanding among them are the theories of ideƯ ally plastic and of viscoelastic materials. While plastic behavior is essentially nonlinear (piecewise linear at best), viscoelasticity, like elasticity, permits a linear theory. This theory of linear viscoƯ elasticity is the subject of tbe present book Front Matter....Pages N1-VII Introduction....Pages 1-3 Viscoelastic Models....Pages 4-33 Hereditary Integrals....Pages 34-45 Viscoelastic Beams....Pages 46-72 Beam on Continuous Support....Pages 73-94 Vibrations....Pages 95-120 Wave Propagation....Pages 121-146 Buckling of Columns....Pages 147-158 Viscoelasticity in Three Dimensions....Pages 159-187 Back Matter....Pages 188-194