А PENDULUM SUSPENDED ON AN ELASTIC BEAM

Anastas Ivanov Ivanov

Scientific paper ID 2121 : 2021/3

А PENDULUM SUSPENDED ON AN ELASTIC BEAM

Anastas Ivanov Ivanov

The oscillations of a pendulum suspended on an elastic beam are examined.

The mathematical pendulum is a material point suspended on an ideal rigid and massless rod.

The upper end of the rod is connected by a joint with an elastic beam on two supports. The

beam is considered to be perfectly elastic and massless. The system has two degrees of

freedom. The nonlinearity is due only to a geometric nature. A nonlinear system of two

differential equations is derived. A numerical solution was made with the mathematical

package MatLab. The laws of motion, generalized velocities, generalized accelerations, and

phase trajectories are obtained. The internal force in the rod as a time function is also

determined. The dynamical coefficient for the rod is calculated. In order to continue the task

by preparing an actual model and conducting experimental research, the projections of the

velocity and acceleration of the material point along the horizontal and vertical axes, as well

as their magnitudes, are determined. The obtained results are presented graphically and

analyzed in detail. The research has a theoretical and applied character.

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махало еластична греда геометрична нелинейност нелинейни трептения симулация MatLabpendulum elastic beam geometric nonlinearity nonlinear oscillations simulation MatLabAnastas Ivanov Ivanov

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