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For a mechanical engineer working in the field of design of new technolo- gies the principal thing is his know-how in developing the sophisticated math- ematical models in which all specific features of operation of the objects under design in real conditions are meticulously taken into account. So, the main emphasis in this book is made on the methods of derivation of equations and on the algorithms of solving them (exactly or approximately) taking into con- sideration all features of actual behavior of the forces acting upon elastic rod elements. 'The eigen value and eigen vector problems are considered at vibrations of curvilinear rods (including the rods with concentrated masses). Also consid- ered are the problems with forced vibrations. When investigating into these problems an approximate method of numerical solution of the systems of lin- ear differential equations in partial derivatives is described, which uses the principle of virtual displacements. 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Problems related to parametric vibrations and statistical dynamics of mechanical systems, as well as to determination of critical parameters and of dy- namic stability are also analyzed. As a rule, problems presented in the monograph are associated with particular mechanical systems and can be applied for current studies in vibration theory. 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Ancient Babylonian inscription X Preface Preface to the English Edition The book you are reading is a translation from Russian into English. Within a pretty short term this book saw two editions in Russian. The authors received in- spiring responses from readers that both stimulated our continuing and improving this work and made sure it would not be in vain of us to try to multiply our readers by covering the English-speaking engineering community. When we prepared the present edition, we took into account interests of the Western readers, so we had to make some changes to our text published earlier. These changes include the following aspects. First, we excluded a lot of references and discussions regarding Russian engi- neering codes. 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The principal subjects of creep mechanics are the formulation of constitutive equations for creep in structural materials under multi-axial stress states; the application of structural mechanics models of beams, plates, shells and three-dimensional solids and the utilization of procedures for the solution of non-linear initial-boundary value problems. The objective of this book is to review some of the classical and recently proposed approaches to the modeling of creep for structural analysis applications as well as to extend the collection of available solutions of creep problems by new, more sophisticated examples.   In Chapter 1, the book discusses basic features of the creep behavior in materials and structures and presents an overview of various approaches to the modeling of creep. Chapter 2 collects constitutive models that describe creep and damage processes under multi-axial stress states. 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