Sessions 2022-2023

10.04.2023, Session 270

Man is a slow, sloppy, and brilliant thinker;
computers are fast, accurate, and stupid.

November 28, 2023

Piskun N.V., Lukin A. V., Popov I. A., Shtukin L. V. (Peter the Great SPbPU, IPME RAS)

On the measurement of ultra-low mass of deposited particles with micromechanical mode-localized detectors

The report is devoted to methods for measuring ultra-low mass of deposited particles using micromechanical sensors based on the phenomenon of mode localization. Two types of sensitive elements of a mass detector are considered – a beam with an initial curvature and a system of two mechanically weakly coupled beams. In the first case, mass detection is supposed to be carried out by the amplitude ratio of beam vibrations on different natural modes. It is shown that with the correct choice of geometric parameters in the system, an exchange of energy is observed between the first asymmetric and second symmetric modes of vibration. The work proposes a system of electrodes that makes it possible to excite and detect vibrations in selected forms. In the case of a system of two weakly coupled beams, it is shown that in the presence of a disturbance in the form of a deposited particle, an oscillation mode with different amplitudes is observed in the system, the ratio of which is the output signal of the device. A comparison is made of the output characteristics of the devices, primarily sensitivity, with known mass detectors presented in the literature.

Piskun N. V. – graduate student of the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute, research engineer at the Digital Engineering School of the Peter the Great St. Petersburg Polytechnic University. Area of scientific interests: Nonlinear dynamics, mechanics of deformable solids, computational mechanics, nano/microelectromechanical systems, bifurcation theory. Scientific suppervizor - Asso. Prof. A.V. Lukin.

Lukin A. V. – Associate Professor of the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute of Peter the Great St. Petersburg Polytechnic University.

Popov I. A. – Research Engineer at the Advanced Engineering School “Digital Engineering” of the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute of Peter the Great St. Petersburg Polytechnic University.

Shtukin L. V. – Associate Professor at the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute of Peter the Great St. Petersburg Polytechnic University.

October 10, 2023

A. S. Smirnov, S. A. Kravchinskiy (Peter the Great SPbPU, IPME RAS)

Oscillations of a double pendulum with a weak nonlinearity

The report considers nonlinear oscillations of a double mathematical pendulum with identical parameters of links and end weights. Exact nonlinear equations of motion of the system are derived, from which a classical linear model of small oscillations is obtained, as well as a weakly nonlinear oscillation model that takes into account cubic nonlinearity. A well-known solution of the problem of small oscillations of a double pendulum is given, which serves as a basis for further research. With the help of asymptotic methods of nonlinear mechanics, an approximate solution is constructed for a weakly nonlinear model under arbitrary initial conditions of motion. It is shown that the found solution has a nontrivial structure and represents polyharmonic oscillations on eight different frequencies. The resulting approximate formulas are accompanied by graphical illustrations that compare the behavior of the angles of deviation of the links of a double pendulum from the vertical when using linear and weakly nonlinear models, as well as the original nonlinear model, which is calculated using numerical integration. The conclusions drawn are of interest for analytical mechanics and theory of oscillations, and they can also be used in practice in applied problems of robotics and biomechatronics.

Smirnov Alexey S. – Assistant Professor at the Higher School of Mechanics and Control Processes (Peter the Great St. Petersburg Polytechnic University), Junior Researcher at the Laboratory of Mechatronics (Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences). Research interests: analytical mechanics, theory of mechanical oscillations, rigid body dynamics, stability of equilibrium and motion, control of mechanical systems, optimization in mechanics.

Kravchinskiy Sergey A. – Master's Student at the Higher School of Mechanics and Control Processes (Peter the Great St. Petersburg Polytechnic University). Research interests: analytical mechanics, theory of mechanical oscillations, computational mechanics, computer engineering. Scientific supervisor - Assistant Professor A. S. Smirnov.