On the interrelation of equilibrium positions and work of friction forces on brake squeal

Brake noise, in particular brake squeal, is a permanent topic both in industry and academia since decades. Nonlinearities play a decisive role for this phenomenon. One nonlinear effect widely ignored so far is that the brake can engage multiple equilibrium positions with severe consequences on the noise behavior. In fact in an automotive disk brake, the essential elements carrier, caliper and pad are elastically coupled with each other and their behavior is nonlinear that multiple equilibrium positions are possible. The engaged equilibrium position depends, for example, on the initial conditions, external disturbances, and the transient application of the brake pressure, and in consequence configurations with or without self-exciting characteristics of the friction forces result. Obviously, a self-exciting characteristic of the friction force is a necessary precondition for the occurrence of squeal. The authors recently published some corresponding results (Koch et al. FU Mech Eng, 2021. https://doi.org/10.22190/FUME210106020K) demonstrating that for same operating parameters with respect to brake pressure (i.e., brake torque), rotational speed and temperature the engaged equilibrium position has decisive influence whether squeal occurs or not. While in Koch et al. (2021) it has just been detected whether there is squeal or not, the excitation characteristic of the friction forces becomes, beside the engaged equilibrium position, the additional focus in the present paper. Therefore, a work criterion already successfully applied in earlier publications for squeal tendency is considered. For the experimental application of the work criterion, accelerometers have to be mounted. The accelerometers’ location to be applied can be determined in the chosen setup by the camera system anyway necessary for the measurement of the engaged equilibrium position. With this refined setup, it is possible to specify the states squeal, close to squeal and far from squeal. The test series again demonstrate the decisive influence of the engaged equilibrium position (for constant operation parameters) on the occurrence of the respective state. These findings can have consequences for simulations (consideration of multiple equilibrium positions in models and respective linearization with consequences on system’s eigenvalues), but also for the design (avoidance of equilibrium positions suspicious for squeal) and experimental setups (determination of special positions) of brakes.

Structures With Multiple Rigid Configurations Due to Prestress and Unilateral Contacts

This paper presents structures with multiple equilibrium configurations arising from the combination of a state of prestress and unilateral contacts. A design problem is posed where preloaded elastic springs and unilateral constraints are embedded throughout a mechanism. The spring parameters are designed such that multiple target configurations are immobilized due to contact. In each of these configurations, the spring forces maintain compressive reaction forces, immobilizing the structure. Each immobilized configuration can rigidly resist perturbation forces up to some finite magnitude where contact is lost. Hence, this case of multiple configurations in equilibrium due to the combination of prestress and contact is referred to as multi-configuration rigidity. Two examples of structures exhibiting multi-configuration rigidity are presented. First, a four bar linkage with a single kinematic degree of freedom is used to introduce the concept. In the context of the linkage, multi-configuration rigidity is compared to multi-stability, exhibiting the key differences between the two concepts. Then, a 24-degree-of-freedom kirigami surface is presented that can morph between flat and spherical configurations, motivated by RF antenna applications. By embedding torsional springs and fold angle stops throughout the structure, flat and spherical configurations are made rigid. Actuation between the configurations can easily be achieved by snapping the structure between the rigid configurations.

On occurrence of sudden increase of spiking amplitude via fold limit cycle bifurcation in a modified Van der Pol-Duffing system with slow-varying periodic excitation

The main purpose of the paper is to reveal the mechanism of certain special phenomena in bursting oscillations such as the sudden increase of the spiking amplitude. When multiple equilibrium points coexist in a dynamical system, several types of stable attractors via different bifurcations from these points may be observed with the variation of parameters, which may interact with each other to form other types of bifurcations. Here we take the modified van der Pol-Duffing system as an example, in which periodic parametric excitation is introduced. When the exciting frequency is far less than the natural frequency, bursting oscillations may appear. By regarding the exciting term as a slow-varying parameter, the number of the equilibrium branches in the fast generalized autonomous subsystem varies from one to five with the variation of the slow-varying parameter, on which different types of bifurcations, such as Hopf and pitch fork bifurcations, can be observed. The limit cycles, including the cycles via Hopf bifurcations and the cycles near the homo-clinic orbit may interact with each other to form the fold limit cycle bifurcations. With the increase of the exciting amplitude, different stable attractors and bifurcations of the generalized autonomous fast subsystem involve the full system, leading to different types of bursting oscillations. Fold limit cycle bifurcations may cause the sudden change of the spiking amplitude, since at the bifurcation points, the trajectory may oscillate according to different stable limit cycles with obviously different amplitudes. At the pitch fork bifurcation point, two possible jumping ways may result in two coexisted asymmetric bursting attractors, which may expand in the phase space to interact with each other to form an enlarged symmetric bursting attractor with doubled period. The inertia of the movement along the stable equilibrium may cause the trajectory to pass across the related bifurcations, leading to the delay effect of the bifurcations. Not only the large exciting amplitude, but also the large value of the exciting frequency may increase inertia of the movement, since in both the two cases, the change rate of the slow-varying parameter may increase. Therefore, a relative small exciting frequency may be taken in order to show the possible influence of all the equilibrium branches and their bifurcations on the dynamics of the full system.

YOUTH ATTITUDES TOWARDS GENDER ROLES WITHIN FAMILY

Young people are leaders of change in any society; therefore, studying their attitude towards gender roles in the family is of particular interest in predicting changes in their behaviour and identifying the policy measures needed to achieve sustainable progress in gender equality. The study aimed to research the attitude of youth towards gender roles in the family to determine the influence of the levels of education, gender and other characteristics on gender preferences in relations – traditional or egalitarian. It is based on data from a sociological survey of youth in Chisinau, conducted in 2019 on a representative sample (N = 506). The theoretical basis of the study was the multiple equilibrium theory (Esping-Andersen et al., 2013). The study results showed that the perception of young people regarding the essential qualities of men and women is still under the pressure of stereotypes and corresponds to the intermediate balance model characteristic of the transition from traditional roles based on the division of labour to modern egalitarian ones. This circumstance implies an equal division of responsibilities and family roles between women and men. On the one hand, youth tend to an egalitarian type of marriage and family relationships, and on the other, they adhere to traditional views of family roles. Although there are some differences in attitudes towards gender roles within the family between natives of Chisinau and young people from other localities, they are still not so pronounced. Youth with higher education are more likely to prefer an egalitarian distribution of gender roles than youth with a lower level of education. Girls more often than boys strive for gender equality in the family. However, in some aspects, such as the responsibility of men for the family’s financial support, the importance of the material situation of a partner, they more often express traditional views.

The Atlantic's freshwater budget under climate change in the Community Earth System Model with strongly eddying oceans

We investigate the freshwater budget of the Atlantic and Arctic oceans in coupled climate change simulations with the Community Earth System Model and compare a strongly eddying setup with 0.1∘ ocean grid spacing to a non-eddying 1∘ configuration typical of Coupled Model Intercomparison Project phase 6 (CMIP6) models. Details of this budget are important to understand the evolution of the Atlantic Meridional Overturning Circulation (AMOC) under climate change. We find that the slowdown of the AMOC in the year 2100 under the increasing CO2 concentrations of the Representative Concentration Pathway 8.5 (RCP8.5) scenario is almost identical between both simulations. Also, the surface freshwater fluxes are similar in their mean and trend under climate change in both simulations. While the basin-scale total freshwater transport is similar between the simulations, significant local differences exist. The high-ocean-resolution simulation exhibits significantly reduced ocean state biases, notably in the salt distribution, due to an improved circulation. Mesoscale eddies contribute considerably to the freshwater and salt transport, in particular at the boundaries of the subtropical and subpolar gyres. Both simulations start in the single equilibrium AMOC regime according to a commonly used AMOC stability indicator and evolve towards the multiple equilibrium regime under climate change, but only the high-resolution simulation enters it due to the reduced biases in the freshwater budget.

Priority Pricing for Efficient Resource Usage of Mobile Internet Access

Radio-frequency spectrum resources are finite and scarce, but their demand is increasing exponentially every year. Therefore, wireless network resources are too expensive to be wasted. To avoid waste, pricing techniques can efficiently control resource usage and manage user needs in networks. This study focuses on QoS-aware pricing for usage-based mobile Internet access charging. Specifically, I propose a heuristic algorithm for priority pricing with multiple service levels. The proposed algorithm is built on top of the existing equilibrium analysis methods. While being extensively studied for optimal price selection, the equilibrium methods make a few unrealistic assumptions, and so my methods adjust the solutions of the equilibrium methods to account for distortions that the real world creates. The evaluation results indicate that multiple equilibrium prices may exist, and the proposed scheme produces a pricing plan that is substantially more effective than existing equilibrium methods.

Cordon of Conformity: Why DSGE models Are Not the Future of Macroeconomics

The Rebuilding Macroeconomic Theory Project, led by David Vines and Samuel Wills (2020), is an important, albeit long overdue, initiative to rethink a failing mainstream macroeconomics. Professors Vines and Wills, who must be congratulated for stepping up to the challenge of trying to make mainstream macroeconomics relevant again, call for a new multiple-equilibrium and diverse (MEADE) paradigm for macroeconomics. Their idea is to start with simple models, ideally two-dimensional sketches, that explain mechanisms that can cause multiple equilibria. These mechanisms should then be incorporated into larger DSGE models in a new, multiple-equilibrium synthesis – to see how the fundamental pieces of the economy fit together, subject to it being ‘properly micro-founded’. This paper argues that the MEADE paradigm is bound to fail, because it maintains the DSGE model as the unifying framework at the center of macroeconomic analysis. The paper reviews 10 fundamental weaknesses inherent in DSGE models which make these models irreparably useless for macroeconomic policy analysis. Mainstream macroeconomics must put DSGE models, once and for all, in the Museum of Implausible Economic Models – and learn important lessons from non-DSGE macroeconomic approaches.

Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>

Stabilizing multiple equilibria and cycles with noisy prediction-based control

<p style='text-indent:20px;'>Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global stabilization are obtained. Introduction of noise can relax restrictions on the control intensity. We estimate how the control can be decreased with noise and verify it numerically.</p>