This paper proposes the dissipation of the energy analysis approach for vehicle plane motion stability analysis. The vehicle uses a three-degree-of-freedom vehicle model, and a unified ...tire-sideslip-angle model suitable for large tire-sideslip-angle and wheel reverse rotation conditions. Two calculation methods of total dissipation of energy are proposed: the integral calculation method and the energy difference calculation method. This paper analyses the system stability of the vehicle model, using the total dissipation of the energy indicator and compares the results with the Lyapunov exponent indicator. It shows that the dissipation of the energy analysis approach has a fast calculation speed, strong interpretability and high calculation accuracy, which can intuitively and quantitatively reveal the global stability characteristics of vehicle plane motion.
•The strength, deformation, failure and energy evolution of parallel double fractured sandstone are studied.•The crack propagation process of parallel double fractured sandstone is studied ...quantitatively.•From the perspective of experiment to engineering, we propose a new method of rock burst prevention.
To obtain the mechanical characteristics and energy evolution law of sandstone with double cracks under dynamic load, the test is carried out by using the SHPB test system, and the failure process of the sample is recorded by the high-speed camera system. The stress-strain curves under dynamic load and the failure characteristics of the sample are obtained, and the effects of crack angle and impact pressure on the mechanical characteristics of sandstone with double cracks are analyzed. The results show that the compressive strength of the specimen decreases initially and increases afterwards with the increase of the crack angle under dynamic load, and the compressive strength of the specimen increases gradually with the increase of the impact pressure. At the pressure of 0.03 MPa, the peak strain increases initially, followed by decreases with the increase of crack angle, and shows the opposite law with the increase of impact pressure. Under dynamic loading, the crack tip first starts to crack outwards along the axial direction, and the penetration of the rock bridge lags. The macroscopic cracks of 0° and 90° sandstone are mostly tensile cracks, while those of 30°, 45°, and 60° are mostly shear cracks. With the increase of crack angle, the failure mode changes from tensile failure to shear failure and then to tensile failure. The fractal dimension increases with the increase of impact pressure, and increases and then decreases with the increase of crack angle, and the fractal dimension increases with the increase of energy dissipation per unit volume. In addition, in the process of rock burst prevention and control, the size of the dynamic load and crack angle should be evaluated in advance. When the dynamic load in this area is large, the surrounding rock pressure relief should be carried out in advance to increase the dissipation energy. When there are 60° and 45° crack angles in the rock mass, the stress propagation path should be changed by structural regulation based on grouting filling micro-fracture modification.
Capturing fine magnetic particles in axial magnetic filter from non-Newtonian suspension was examined theoretically. A trajectory model was formed for the movement of the particle in bounded flow ...field magnetic filter that has advantages for various theoretical modeling and practical applications as presented in the literature 1–8. The effects of the non-Newtonian properties of the suspension on the particle capture distance were evaluated. Since the magnetized ferromagnetic wire was outside the cylindrical tube in which the suspensions flow, the velocity profile within the tube was determined according to the power law rheological model. The conditions to use the approximation expression for the flow profile in the tube were determined by considering the energy dissipation. Analytical solutions for the particle trajectory equation were obtained under above-mentioned conditions. Based on these results, the effects of the non-Newtonian properties of the carrier suspension on the movement trajectory of the particle and the capture cross-section were scrutinized.
Trajectories in Newtonian (n=1) and non-Newtonian (n=0.9) flow. Display omitted
•A trajectory model, analytical solutions and analysis for the particle capture in the non-Newtonian flow were obtained.•The conditions to use the approximation expression for the flow profile in the tube were determined.•Analytical solutions for the particle trajectory equation were obtained.•The effects of non-Newtonian properties of the carrier suspension were analyzed.
Coastal protection structures reduce risks and economic losses by eliminating coastal erosion, wave damage, and flooding. Fixed breakwaters are used along the coast but are often inappropriate due to ...their negative environmental impact. Permeable breakwaters resemble a row of breakwaters with continuous walls and are proposed as a more environmentally friendly alternative. The wave-structure interaction and flow behavior of this type of breakwater are more complex but must be analyzed before designing it. This study develops a mathematical model of wave interaction with a permeable three-row vertical breakwater based on the least squares method. Comparison with experimental measurements of the reflection, transmission, and dissipation coefficients shows that the mathematical model adequately reproduces most of the important features of the results. This study provides a deeper understanding of the hydrodynamic performance of a permeable three-row vertical continuous wall breakwater.
•Energy dissipated by plate bending and interface shear is never dominant.•Strong subduction zones weakly affect the classical Nusselt/Rayleigh scaling law.•The minimum radius of curvature strongly ...overestimates plate bending dissipation.
Several authors have suggested that mantle convection is primarily resisted by strong subduction zones, which if true implies small or even negative values of the exponent β in the Nusselt number/Rayleigh number relation Nu∼Raβ. To evaluate this hypothesis, we use the boundary element method (BEM) to study the energetics of subduction in a two-dimensional system comprising two purely viscous plates, a subducting plate (SP) and an overriding plate (OP), immersed in an infinitely deep ambient fluid beneath a free-slip surface. The negative buoyancy of the slab is the only driving force. The principal quantity of interest is the fraction R of the total viscous dissipation that occurs in the upper convective boundary layer comprising the SP, the OP and the subduction interface (SI) between them. Scaling analysis and BEM solutions of the instantaneous flow driven by an isolated SP yield R∼St/St+F(θ), where St is the flexural stiffness of the SP and F(θ) is a function of the dip θ of the plate's leading edge. More realistic time-dependent solutions for the SP+OP case show that R(t)≤0.4 for reasonable viscosity contrasts ηSP/ηambient∈250,2500, indicating that the dissipation is dominated by the ambient mantle contribution. Finally, we formulate a parameterized model of mantle convection to evaluate the influence of subduction-zone dissipation on the effective value of β, motivated by the possibility that the use of the classical value β=1/3 in global parameterized convection models may be the cause of their failure to predict reasonable thermal histories. Using the correct length scale to describe bending (the ‘bending length’; Ribe (2010)), we find β∈0.25,0.34, which is not much different than the classical result. We conclude that subduction zone dissipation is not large enough to change substantially the classical Nusselt number/Rayleigh number scaling law. It is therefore probably necessary to look elsewhere to reconcile geodynamical and geochemical arguments regarding the thermal history of the Earth.
This contribution discusses the effect of steel tie-rods installed in a church façade subjected to 60 recorded earthquakes. The church façade is firstly analysed as a two-sided and a one-sided ...rocking SDOF system. For the one-sided rocking, sidewalls are modelled through either elastic or rigid contact to compare the two modelling techniques. Secondly, two configurations of tie-rods are investigated: (i) traditional tie-rods with a specific elasto-plastic constitutive law and (ii) innovative tie-rods with a dissipative component. The chosen case study is the San Francesco Church located in Mirandola, hit by the 2012 Emilia Romagna earthquake. The results of nonlinear dynamic analyses are presented in terms of median and standard deviation of maximum normalised displacements for each of the 60 seismic inputs. The results show the great benefit introduced by both traditional and dissipative tie-rods, with remarkable reductions of maximum rotations up to an order of magnitude with respect to the unrestrained façade. Moreover, the increment of damping coefficient is associated to a reduction of the standard deviation of the amplitude peaks, which is a positive aspect for the reliability of the response of the damped wall. Finally, the two models, rigid and elastic contact, of sidewalls provide results in excellent agreement in terms of median and standard deviation of the maximum normalised rotations.
This work investigates the effect of international ground-motion sequences on the out-of-plane response of an ordinary-building façade. The following assumptions are made on the wall boundary ...conditions: the wall is resting on a foundation, it is adjacent to transverse walls and restrained by elasto-plastic tie rods with finite elongation capacity. Four walls are considered of different aspect ratio and size; two types of masonry are assumed, and the tie is designed following a force-based procedure according to the Commentary to the Italian Building Code. The walls are modelled as rigid blocks of finite thickness and free to rotate on one side only. The rocking response of the walls, excited in the out-of-plane direction under 56 sequences of records, is evaluated. The effect of sequences is estimated by the comparison of the response experienced during the sequence and under a single record, strongest in terms of either peak ground acceleration or velocity. Finally, in order to reduce the vulnerability originated by a seismic sequence, a proposal of a reduced behaviour factor to be adopted in the design of tie rods is formulated.
In 13 it was conjectured by Zhang and Zheng that dissipative solutions of the Hunter–Saxton equation, which are known to be unique in the class of weak solutions, dissipate the energy at the highest ...possible rate. The conjecture of Zhang and Zheng was proven in 4 by Dafermos for monotone increasing initial data with bounded energy. In this note we prove the conjecture in 13 in full generality. To this end we examine the evolution of the energy of any weak solution of the Hunter–Saxton equation. Our proof shows in fact that for every time t>0 the energy of the dissipative solution is not greater than the energy of any weak solution with the same initial data.
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