Daulet Nurakhmetov

This paper presents a tutorial on programming the ESP32 microcontroller using MicroPython firmware and the Thonny development environment on the KEIT (Knowledge ESP32 Integration Trainer) training rig. The designed and manufactured rig, its operating principles, and a schematic diagram and printed circuit board (PCB) are provided. The MicroPython programming curriculum includes 12 lab sessions, ranging from basic GPIO control (LEDs, buttons, and buzzer) to integration with cloud services via the MQTT protocol. Sequentially completing the tasks allows students to master the fundamentals of working with digital and analog interfaces, learn to interact with sensors, displays, and actuators, and become familiar with the networking capabilities of the ESP32. Particular attention is paid to practical aspects, such as button debounce, working with interrupts, generating PWM signals, and measuring time intervals. The authors also present the specialized control software «KEIT Master Control», which complements the entire hardware and software system and reinforces the theoretical foundations of microcontroller programming in MicroPython. The final lessons focus on creating a simple web server on the ESP32 and exchanging data via an MQTT broker, providing students with a basic understanding of the principles of the Internet of Things. The course concludes with mini-projects («smart room», «parking assistant», and «Wi-Fi weather station») that integrate the technologies covered and demonstrate the potential of the ESP32 for automation and smart home systems. The curriculum can be used in universities and colleges for students majoring in Information Technology, Automation, Mechatronics and Radioelectronics.

We demonstrate an analytical solution for the dynamic transversal vibrations of non-uniform beams on variable foundations. The exact expressions of eigenvalues and eigenfunctions are derived. The proposed dynamic model of the non-uniform beam with clamped conditions reduces to the dynamic model of the uniform beam with the same boundary conditions. It is shown that this reduction is associated with the isospectral properties of a non-uniform beam with clamped-clamped ends. The analytical solution is used to study the behavior of the beam. The analytical results obtained are illustrated by numerical examples.

This paper presents a comprehensive analytical study of the transverse vibration of a simply supported Euler–Bernoulli beam with two intermediate concentrated masses. Two cases are considered: when the masses are identical and non-identical, and when they are located symmetrically and asymmetrically relative to the middle of the beam. The main objective is to derive closed-form approximate expressions for the first two natural frequencies, which are particularly relevant in engineering applications involving structural dynamics, sensor systems and vibration analysis. The problem is modelled using a characteristic determinant obtained from the exact solution of the fourth-order differential equation of motion, with continuity and jump conditions imposed at the locations of the masses. The obtained closed formulas are used to calculate the natural frequencies asymptotically for small deviations in the values and location of the concentrated masses. A comparative analysis is carried out between the asymptotic and exact values of the natural frequencies.

In this paper, the models of Euler–Bernoulli non-uniform beams with the axial loads on the Winkler foundations are considered. The non-uniform beam in the model is described by three variable parameters/coefficients: bending stiffness, foundation and beam mass per unit length. The key finding of this study is the clear demonstration of how the agreed symmetry of variable parameters affects the spectral properties of a problem. The qualitative results for the symmetric equivalence (factorisation of sets of eigenvalues and eigenfunctions) of eigenvalues of non-uniform beams for two types of fixing at the ends (clamped-clamped and hinged-hinged) have been obtained. In order to demonstrate equivalence, a hybrid algorithm has been devised, based on the qualitative spectral properties of fourth-order ordinary differential equations and axial load calculations. The results have been validated using examples on the Maple computer package and compared with the experimental measurements.

In this paper, we study one Sturm-Liouville problem with a nonlinear boundary condition that depends on a parameter. Depending on the value of the boundary parameter, eigenvalue problems can arise with complete, incomplete, and overflowing systems of eigenfunctions in the functional space L2[0, 1]. An example of a Sturm-Liouville operator with an incomplete system of eigenfunctions is given and the finite defect of incompleteness is calculated. Also it is given, the system of eigenfunctions of which has an excess equal to minus one. The interval of variation of the boundary parameter is found for which the system of eigenfunctions of the Sturm-Liouville operator is complete.

The inverse problem of determining the weight of three intermediate masses on a uniform beam from the known three natural frequencies has been solved. The performed numerical analysis allows restoring the value of only the second mass in a unique way. The inverse problem of determining the weight of three intermediate masses is solved uniquely except in the case when the first and the third masses are located geometrically symmetric relative to the middle of the beam. The hybrid algorithm for the unique solving inverse problem of determining the weight of three intermediate masses has been developed. The first three natural frequencies of the beam are calculated numerically by using the Maple computer package. Analytical relations between the masses are found.

The control problem the first eigenvalues of the Euler-Bernoulli beam vibration with hinged and clamped fixings at both ends is considered. The control is based on Kanguzhin’s algorithm through integral perturbations of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found.