Transient vibrations of a cantilever bar with an attachedabsorber in case of pre-set initial conditions Переходные режимы колебаний консольного стержня с присоединенным гасителем при заданных начальных условиях

The authors consider decaying flexural vibrations of a cantilever bar having a permanent cross section. The mass is concentrated at the free end, and the impact absorber is attached to the mass. Initial conditions are pre-set by the authors. Properties of the bar and the damper are considered in pur...
Ausführliche Beschreibung

The authors consider decaying flexural vibrations of a cantilever bar having a permanent cross section. The mass is concentrated at the free end, and the impact absorber is attached to the mass. Initial conditions are pre-set by the authors. Properties of the bar and the damper are considered in pursuance of the Е.S. Sorokin theory of frequency independent friction whereby it is accepted that the initial system demonstrates disproportionate friction.The effect of impacts is assessed using the restitution coefficient. It is assumed that vibrations of the system are described by linear differential equalizations. The Fourier method of division of variables in combination with the method of initial parameters is employed, and motion of the mass of the bar and absorber is presented in an explicit form.The solution is used to study the system behaviour exposed to the instantaneous single impulse applied to the concentrated mass at the end of the bar. The influence of parameters of dynamic and impact absorbers onto transient vibrations of the system is studied. In addition, the impact of higher modes of vibrations on overall results is estimated.<br<Рассмотрены затухающие изгибные колебания консольного стержня постоянного сечения с сосредоточенной массой на свободном конце и присоединенным к ней осциллятором с трением при заданных начальных условиях. Принимается, что исходная система обладает непропорциональным трением, которое учитывается по гипотезе Е.С. Сорокина. Приведенные соотношения используются для анализа влияния параметров динамического и ударного гасителей на переходные режимы движения стержня и гасителя. Ausführliche Beschreibung