ipmash@ipme.ru | +7-812-321-47-78
пн-пт 10.00-17.00
Институт Проблем Машиноведения РАН ( ИПМаш РАН ) Институт Проблем Машиноведения РАН ( ИПМаш РАН )

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences

Academic council


Contributions of the Academic Council

We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative stiffness). In such a system with constant parameters (the string tension), under certain conditions a trapped mode of oscillation exists and is unique. Therefore, applying a non-stationary external excitation to this system can lead to the emergence of the string oscillations localized near the inhomogeneity. We provide an analytical description of non-stationary localized oscillations of the string with slowly time-varying tension using the asymptotic procedure based on successive application of two asymptotic methods, namely the method of stationary phase and the method of multiple scales. The obtained analytical results were verified by independent numerical calculations based on the finite difference method. The applicability of the analytical formulas was demonstrated for various types of external excitation and laws governing the varying tension. In particular, we have shown that in the case when the trapped mode frequency approaches zero, localized low-frequency oscillations with increasing amplitude precede the localized string buckling. The dependence of the amplitude of such oscillations on its frequency is more complicated in comparison with the case of a one-degree-of-freedom system with time-varying stiffness.

Members of the Academic Council
Полянский В.А.
Полянский В.А.
Position:
Director of the Institute
Academic degree:
Doctor of Technical Sciences
Индейцев Д.А.
Индейцев Д.А.
Position:
Scientific Director
Academic title:
Professor , RAS Corresponding Member
Academic degree:
Doctor of Physical and Mathematical Sciences
Мочалова Юлия Алексеевна
Мочалова Юлия Алексеевна
Position:
Scientific Secretary of the Institute , Leading Researcher
Academic degree:
Candidate of Physical and Mathematical Sciences
Alexey Porubov
Alexey Porubov
Position:
Head of Department
Academic degree:
Doctor of Physical and Mathematical Sciences
Yuriy Alekseevich
Yuriy Alekseevich
Position:
Head of Department
Academic degree:
Candidate of Physical and Mathematical Sciences
Кукушкин С.А.
Кукушкин С.А.
Position:
Head of Department
Academic title:
Professor
Academic degree:
Doctor of Physical and Mathematical Sciences
A.B. Freidin
A.B. Freidin
Position:
Head of Department , Principal Researcher
Academic title:
Senior Researcher
Academic degree:
Doctor of Physical and Mathematical Sciences
Nikolay V. Kuznetsov
Nikolay V. Kuznetsov
Position:
Head of Department , Leading Researcher
Academic title:
Professor , RAS Corresponding Member
Academic degree:
Doctor of Physical and Mathematical Sciences
Furtat I.B.
Furtat I.B.
Position:
Head of Department , Principal Researcher
Academic title:
Professor
Academic degree:
Doctor of Technical Sciences
Dr. Sedakova Elena B.
Dr. Sedakova Elena B.
Position:
Head of Department
Academic title:
Docent
Academic degree:
Doctor of Technical Sciences
Используя этот сайт, вы соглашаетесь с тем, что мы используем файлы cookie.