Constantly increasing attention is paid in the course 'Vibration
'Theory' to vibration of mechanical systems with distributed parameters,
since the real elements of machines, devices, and constructions are made
of materials that are not perfectly rigid. 'Therefore, vibrations of the
objects including, for ex- ample, rod elastic elements excite the
vibrations of these elements, which can produce a substantial effect on
dynamic characteristics of moving objects and on readings of
instruments. 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. Some problems are more complicated than others and can be
used for practical works of students and their graduation theses.
