Abstract
Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.
Highlights
Many of mechanics’ problems involve the action of dissipative forces and the problem is to be dealt with the laws of thermodynamics [1] in addition to Newton’s laws of motion
In this study we present a novel and practically feasible approach to introduce friction as a thermodynamic dissipative process, and solve one-dimensional free vibration problems, using the unified mechanics’ theory
The unified mechanics theory-based model involves Thermodynamics State Index (TSI), which evolves with the thermodynamics of dissipative mechanisms that are associated with friction
Summary
Many of mechanics’ problems involve the action of dissipative forces and the problem is to be dealt with the laws of thermodynamics [1] in addition to Newton’s laws of motion. In the context of thermodynamics, the work done by dissipative forces is known as pseudo-works [2]. These pseudo-works are treated as the equivalent heat dissipated, to explain the irreversibility of the process [3,4]. None of the real systems are conservative and the dissipation process is essential to explain the irreversibility in mechanics. Ludwig Boltzmann attempted to reduce thermodynamics to the time-reversible laws of Newton’s mechanics [6]. Boltzmann postulated that a transition from one configuration or microstate to another configuration or microstate is probable [7]
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