This survey is devoted to the significant role of various dry friction laws in engineering sciences. Both advantages and disadvantages of a frictional process are illustrated and discussed, but excluding the nature of friction. It is shown how the classical friction laws and modern friction theories exist in today’s pure and applied sciences. Static and dynamic friction models are described. An important role of purely theoretical and experimental investigations in developing the appropriate friction models is outlined, placing an emphasis on new approaches (models proposed by Bay-Wanheim, Dahl, Bliman-Sorine, Lund-Grenoble, as well as atomic scale and fractal models, among others). Friction treated as a complex process being in interaction with wear, heat emission, and deformation is also discussed. Then the impact of dry friction models on current dynamical systems theory is reviewed. Finally, an application of friction to model a brake mechanism as a mechanical system with two degrees-of-freedom, including experimental and numerical analyses, is given. This review paper contains 254 references.

The paper focuses on continuous models derived from a discrete microstructure. Various continualization procedures that take into account the nonlocal interaction between variables of the discrete media are analysed.

In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina $$\left( {{\text{Al}}_{{2}} {\text{O}}_{{3}} } \right)$$Al 2 O 3 and Copper $$\left( {{\text{Cu}}} \right)$$Cu nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids.

The complex dynamics of a simple memristive tabu learning neuron (MTLN) are considered in this article. The analysis of the stability of its equilibria revealed that it displays self-excited dynamics. The investigation of the dynamics of the considered model highlighted that it is extremely sensitive to the initial conditions. That sensitivity to the initial conditions is supported by the coexistence of an infinite number of stable states for the same set of system parameters but using different initial states. Among the infinity of coexisting stable states, there are periodic, quasiperiodic, and chaotic ones. The coexistence of an infinite number of chaotic attractors found in this work and not yet reported in such a model represents the first important contribution of this work. The circuit of the coupled neuron is also realized in the PSPICE simulation environment to further support the obtained result in extreme multistability. Therefore, the revealed chaotic dynamics of the MTLN is applied to compress and encrypt digital medical images. The compressed sensing (CS) approach is combined with deoxyribonucleic acid (DNA) coding/decoding to achieve high compression/encryption performances, including very low computational cost (encryption time t = 0.162 ms, encryption throughput ET = 1618.1 MB/s, number of CPU cycles NC = 1.8) useful for real-time compression. The compression/encryption method developed in this work represents the second main contribution based on the results of the analysis metrics.

Energy harvesting is becoming more and more essential in the mechanical vibration application of many devices. Appropriate devices can convert the vibrations into electrical energy, which can be used as a power supply instead of ordinary ones. This study investigated a dynamical system that correlates with two devices, namely a piezoelectric device and an electromagnetic one, to produce two novel models. These devices are connected to a nonlinear damping spring pendulum with two degrees of freedom. The damping spring pendulum is supported by a point moving in a circular orbit. Lagrange’s equations of the second kind were utilized to obtain the equations of motion. The asymptotic solutions of these equations were acquired up to the third approximation using the approach of multiple scales. The comparison between the approximate and the numerical solutions reveals high consistency between them. The steady-state solutions were investigated, and their stabilities were checked. The influences of excitation amplitudes, damping coefficients, and the different frequencies on energy-harvesting device outputs are examined and discussed. Finally, the nonlinear stability analysis of the modulation equations is discussed through the stability and instability ranges of the frequency response curves. The work is significant due to its real-life applications, such as a power supply of sensors, charging electronic devices, and medical applications.