A New Concept in Mechanics Based on the Notions of Space, Time, and Energy

Alyushin, Yu. A.

doi:10.1134/s1029959919060109

Cited by 2 publications

(11 citation statements)

References 2 publications

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“…Because the condition (6) must be performed in any frame of reference velocity, movement (1) must satisfy the differential equation [9][10][11] , 0 ,…”

Section: Fundamentals Of the Energy Model Of Mechanicsmentioning

confidence: 99%

“…The purpose of the work is to describe the mechanism of natural oscillations and resonance, considering the peculiarities of the transformation of elastic and kinetic energy in the implementation of the law of conservation of energy in local and integral volumes of the body, using the concept of mechanics based on the concepts of space, time, and energy [9][10].…”

Section: Introductionmentioning

confidence: 99%

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Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

Alyushin¹

2021

Preprint

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The mechanisms of natural oscillations and resonance are described, considering the peculiarities of the transformation of elastic and kinetic energy in the implementation of the law of conservation of energy in local and integral volumes of the body, using the concept of mechanics based on the concepts of space, time and energy. When describing the motion in the Lagrange form, the elastic deformation energy of the particles is determined by the quadratic invariant of the tensor, whose components are the partial derivatives of Euler variables with respect to Lagrange variables. The increment of the invariant due to elastic deformation is represented as the sum of two scalars, one of which depends on the average value of the relative lengths of the edges of the particles in the form of an infinitesimal parallelepiped, the second is equal to the standard deviation of these lengths from the average value. It is shown that each of the scalars can be represented in the form of two dimensionless kinematic parameters of elastic energy, which participate in different ways in the implementation of the law of conservation of energy. One part of the elastic energy passes into kinetic energy and participates in the implementation of the law of conservation of energy for the body as a whole, considering external forces. The second part is not converted into kinetic energy but changes the deformed state of the particles in accordance with the equations of motion while maintaining the same level of the part of the elastic energy of the particles used for this. The kinematic parameters differ from the volume density of the corresponding types of energy by a factor equal to the elastic modulus, which is directly proportional to the density and heat capacity of the material and inversely proportional to the volume compression coefficient. Transverse, torsional, and longitudinal vibrations are considered free and under resonance conditions. The mechanisms of transformation of forced vibrations into their own after the termination of external influences and resonance at the superposition of free and forced vibrations with the same or similar frequency are considered. The formation of a new free wave at each cycle with an increase in the amplitude, which occurs mainly due to internal energy sources, and not external forces, is justified.

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“…Because the condition (6) must be performed in any frame of reference velocity, movement (1) must satisfy the differential equation [9][10][11] , 0 ,…”

Section: Fundamentals Of the Energy Model Of Mechanicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

Alyushin¹

2021

Preprint

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“…The stresses τ pi are similar to the Kirchhoff stresses [10] but differ in the range of the arguments (Lagrange variables) and the possibility of arbitrary selection of the reference point of the average stress scale.…”

Section: Fundamentals Of the Energy Model Of Mechanicsmentioning

confidence: 99%

“…The energy model of mechanics should use a description of motion of material particles in the form of Lagrange, since only Lagrange variables allow us to consider the change in the energy state of particles at any time interval, and also to consider the transformation of some types of energy into others, including due to deformation and temperature. Let us use the notations [8][9][10] x i = x i (α p , t),…”

Section: Fundamentals Of the Energy Model Of Mechanicsmentioning

confidence: 99%

“…The purpose of this work is: using a new concept in mechanics based on the concepts of space, time and energy [9,10], to analyze the change in the deformed and energetic state of particles; comparing their phase changes with changes in kinetic energy and energy of external forces, to substantiate the essential role of additional types of internal energy, providing a change only in the deformed state of particles determined by their equations of motion; check the fulfillment of the law of conservation of energy for local volumes and for the body as a whole.…”

Section: Introductionmentioning

confidence: 99%

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Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

Alyushin

2021

Physics

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The scientific novelty of this work is determined by the rationale for the participation in transformations, along with the kinetic energy of particles, of four types of elastic energy, identified by the peculiarities of their phase changes in the oscillation process. Two types are converted into kinetic energy, while the other two types change the deformed state of particles in accordance with the equations of motion due to internal sources. The result is obtained based on the use of the superposition principle in the space of Lagrange variables with the imposition of forced and free oscillations, as well as a new model of mechanics based on the concepts of space, time, and energy with a new scale of average stresses that takes into account the energy of particles in the initial state. In such a model of mechanics, a generalized measure of the elastic energy of particles is a quadratic invariant of asymmetric tensor whose components are partial derivatives of Euler variables with respect to Lagrange variables. The concept of kinematic energy parameters is introduced, which differ from the corresponding volumetric energy densities by a multiplier equal to the modulus of elasticity, which is directly proportional to the density and heat capacity of the material, and inversely proportional to the volumetric compression coefficient. Comparison of the values of kinematic parameters shows that most of the energy required for oscillations is associated with the deformation of particles and comes from internal sources. The mechanisms of transformation of forced vibrations into their own for transverse, torsional, and longitudinal vibrations are considered, as well as the occurrence of resonance when free and forced vibrations are superimposed with the same or a similar frequency. The formation of a new free wave after each cycle of external influences with an increase in amplitude, which occurs mainly due to internal, and not external, energy sources is justified.

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A New Concept in Mechanics Based on the Notions of Space, Time, and Energy

Cited by 2 publications

References 2 publications

Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

Energy Mechanisms of Free Vibrations and Resonance in Elastic Bodies

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