Photoacoustic effect in micro- and nanostructures: numerical simulations of Lagrange equations

The work provides the description of theoretical and numerical modeling techniques of thermomechanical effects that take place in absorbing micro- and nanostructures of different materials under the action of pulsed laser radiation. A proposed technique of the numerical simulation is based on the solution of equations of motion of continuous media in the form of Lagrange for spatially inhomogeneous media. This model allows calculating fields of temperature, pressure, density, and velocity of the medium depending on the parameters of laser pulses and the characteristics of micro- and nanostructures.

Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

Forced Vibration Analysis of Laminated Composite Plates under the Action of a Moving Vehicle

This paper provides a finite element analysis of laminated composite plates under the action of a moving vehicle. The vehicle is modeled as a rigid body with four suspension systems, each consisting of a spring-dashpot. Overall, the vehicle possesses three degrees of freedom: vertical, rolling, and pitching motions. The equations of motion of the plate are deduced based on first-order shear deformation theory. Using the Euler-Lagrange equations, the system of coupled equations of motion is extracted and solved by using the Newmark time discretization scheme. The algorithm is validated through the comparison of both the free and forced vibration results provided by the present model and exact or numerical results reported in the literature. The effects are investigated of several system parameters on the dynamic response.

Rotational nonlinear double-beam energy harvesting

This paper presents an investigation of the performance of a coupled rotational double-beam energy harvester (DBEH) with magnetic nonlinearity. Two spring-connected cantilever beams are fixed on a rotating disc. Repelling magnets are attached to the frame and to the lower beam tip, and an equal-mass block is attached to the tip of the upper beam. To describe the dynamic response, a theoretical model related to the rotational motion of the coupled cantilever beam is derived from the Lagrange equations. In addition, the harmonic balance method, together with the arc-length continuation method, is applied to obtain the frequency response functions (FRFs). Parametric studies are then conducted to analyze the effect of varying the parameters on the energy harvesting performance, and numerical analysis is performed to validate the analytical solutions. Finally, the theoretical model is verified by forward- and reverse-frequency-sweeping experiments. The DBEH in rotational motion can perform effective energy harvesting over a wide range of rotational frequencies (10 to 35 rad/s). The upper beam is found to exhibit better energy harvesting efficiency than the lower beam around the resonant frequency. This study effectively broadens the energy harvesting bandwidth and provides a theoretical model for the design of nonlinear magnet-coupled double-beam structure in rotational energy harvesting.

A cohomological obstruction in higher-dimensional Chern–Simons gauge theories

We study a set of cohomology classes which emerge in the cohomological formulations of the calculus of variations as obstructions to the existence of (global) solutions of the Euler–Lagrange equations of Chern–Simons gauge theories in higher dimensions [Formula: see text].

Inflation from the Symmetry of the Generalized Cosmological Model

It is shown that the inflationary model is the result of the symmetry of the generalized F(R,T,X,φ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R,X,φ) and F(T,X,φ) the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field φ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with R2 or X2. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term.

Substantiation of amplitude-frequency characteristics and design parameters of vibration exciter in volume oscillation separator

The main effects of the developed design for vibratory separator: the increased driving force in the process of bulk material separation in this work, achieved by providing the working cylindrical-conical container with vibrational motion; improving the conditions for the passage of product particles through openings, achieved by providing the sieve surface with volume oscillations; reduction of energy consumption and improvement of operating conditions for support nodes during the operation of the designed vibrating screen, achieved due to the installation of additional elastic elements between the separator body and bearing assemblies of the vertical drive shaft in vibration exciter. Providing the working bodies of the designed vibrating screen with volume oscillating motion allows increasing the performance and quality of the separation process of solid bulk materials. To determine the rational parameters for vibration screening process, the equations of motion of working bodies as a conical sieve surface were obtained using the method of the Lagrange equations of the second order. When applying solutions of the Cauchy problem for linear nonhomogeneous differential equations, the solution of the latter was obtained. The obtained dependences of oscillation amplitudes, vibration velocity and vibration acceleration, and the intensity of oscillating motion allowed us to perform a mathematical analysis for power and energy parameters of vibration drive in the developed separator. The inclined placement of the conical sieve surface allows for spatial gyration or circular translational motion, which makes it possible to realize the advantages of volumetric separation of bulk materials. The results of the conducted analytical study made it possible to substantiate the optimal inclination angle for working sieve surface. Based on our analysis, the design parameters of vibration exciter were substantiated and clarified, and the design of this technical system was demonstrated.

Relativistic Maxwell Theory and Einstein Field Equation derived from Variational Principle

In this article, I'll be reviewing relativistic mechanisms using the calculus of variation in the classical limit. The variational principle is considered to be one of the most important mechanisms to build a theory. Newton's second law of motion is a consequence of Euler-Lagrange equations which gives the least (or stationary) trajectory of a particle between any two arbitrary points. I'll the use action principle by deriving the relativistic Maxwell's field equation, geodesic equation, and Einstein's field equation.

Lagrangian mechanics for fields

An introduction to Lagrangian methods for classical fields in flat spacetime and then in curved spacetime. The Euler-Lagrange equations for Lagrangian densities are obtained, and applied to the wave, Klein-Gordan, Weyl, Dirac, Maxwell and Proca equations. The canonical energy tensor is obtained. Conservation laws and Noether’s theorem are described. An example of the treatment of Interactions is given by presenting the the QED Lagrangian. Finally, covariant Lagrangian methods are described, and the Einstein field eqution is derived from the Einstein-Hilbert action.

Aplicación del formalismo de Lagrangianos Controlados en la regulación de velocidad del motor de inducción trifásico

In this work the Controlled Lagrangian Formalism applied to electrical machines is explored for the first time. It begins with an analysis of the purely mechanical systems, once understood, the study is carried out on a two-phase induction motor, this implying a greater degree of complexity because there is no reference that has done it before. Finally, this study is expanded to the three-phase motor, this being the main research object of the project. The main guide used was the Bloch article cite bloch2000controlled on the analysis of mechanical systems. Regarding the procedure, the first thing that is done is the selection of the generalized coordinates, the Lagrangian is proposed and the model is obtained from it through the Euler-Lagrange equations, followed by that the symmetries are identified (which in the case of MI is especially interesting because these symmetries are obvious from the choice of coordinates) and the configuration space is divided into vertical and horizontal directions, the horizontal directions are redefined and the Controlled Lagrangian is proposed. Finally, generalized forces are sought, using Noether's Theorem as support and thus establishing the control law. The development to obtain the Controlled Lagrangian and the control law is done in detail, explaining each step of the procedure and using specific algebraic methods of this formalism that are strongly based on the geometric structure of the variety of configuration. The results obtained are an approach in the direction of Controlled Lagrangians applied electrical machines.