Mathematical Model of the Car Shock Absorber Based on Viscous Friction

The study objective is to find a mechanical analogue of cyclotron motion and to determine the structure of the corresponding device, which is appropriately called a stabilized rotator. The topic of speed stabilization is relevant. With cyclotron motion, the Lagrangian of an electron is twice as large as its kinetic energy. In terms of macromechanics, this corresponds to the equality of kinetic and potential energies. This condition is key to the possibility of generalizing cyclotron motion to mechanics. It follows from this that the composition of a stabilized rotator should include elements that are able to store both of these energy types. Such elements are the load and the spring. The natural rotation frequency of the stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the angular momentum) and remarkably coincides with the natural frequency of the pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). At zero torque moment in stationary mode, the rotation frequency of the stabilized rotator cannot be arbitrary and takes a single value. Just as when the pendulum is forced to swing, the frequency does not coincide with its own frequency, the rotation frequency of the stabilized rotator does not coincide with its own rotation frequency when loaded. A stabilized rotor can be used to control the natural oscillation frequency of a radial oscillator, although in this case it may have strong competition with mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and determined by the extremely simple design.

Mechanical Rotation Stabilizer

Pavlov¹

2022

Mechanical Oscillator Without Potential Energy Storage

Popov

2022

In a monoreactive harmonic oscillator, inert elements can make free sinusoidal oscillations, which are accompanied by the transformation of one inert element kinetic energy into the kinetic energy of another inert element. In this condition the energy of the first inert element is zero. At the same time, the energy of the second element has the maximum value. At the next moment of time, the first element acquires acceleration due to the kinetic energy of the second element, the speed of which begins to decrease. In a classical oscillator, free sinusoidal oscillations are accompanied by an exchange of energy between its elements having the opposite reactivity character. In a spring pendulum, the potential energy of an elastic element is transformed into the kinetic energy of an inert element and vice versa. These elements have the opposite character of reactivity. In an electric oscillatory circuit, the energy of the coil magnetic field is transformed into the energy of the condenser electric field and vice versa. These elements also have the opposite character of reactivity. There are also oscillators in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element or the potential energy of an elastic element into the energy of the coil magnetic field or the energy of the capacitor electric field and vice versa. Free sinusoidal oscillations can occur during the mutual transformation of any physical types of energy.This circumstance is the motive to make an oscillator, in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element into the kinetic energy of another inert element. There are no elements with a different reactivity character in such an oscillator. This type of an oscillator is essentially monoreactive.

Inertial Properties of a Disperse Material in the Mode of Forced Oscillations

Pavlov

2023

It is noted that the modes of forced and natural oscillations are taken into account to calculate strength of structural elements of transport vehicles and mechanisms. In this regard, the dynamic properties of the transported cargo are considered, and they are significantly different for solid and disperse materials. The study objective is to define the dynamic properties of a disperse material under harmonic vibrations. The research method is to present the status of the system under study in the form of a combination of its diametrically opposite maximum statuses. A common example of such a representation is the composition of a dry construction mixture – a combination of sand and cement (100% sand in the mixture is one maximum status, 100% cement is the diametrically opposite maximum status). A disperse material located on a platform performing harmonic oscillations is considered. To assess the instability (or stability) of the disperse material relative to the platform, a dimensionless quantity ξ is introduced. The main problem in determining the dynamic properties of a disperse material is the impossibility of calculating the average coefficient of dynamic friction, since its value is influenced by the interaction of dispersed particles with each other in the entire mass of the material, and not only with the surface of the platform. The description of the dynamic status of a disperse material as a composition of its unstable and stable statuses provides the key to solving this and similar problems. The opposite maximum statuses of the system under study may be comparable and incomparable in terms of quantitative assessment. The subject of the study are systems with equal maximum statuses. This method is universal and applicable to a wide variety of systems with different statuses and parameters.