response equation
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In this paper, we study the bifurcations of non-linear dynamical systems. We continue to develop the analytical approach, permitting the prediction of the bifurcation of dynamics. Our approach is based on implicit (approximate) amplitude-frequency response equations of the form FΩ,A;c̲=0, where c̲ denotes the parameters. We demonstrate that tools of differential geometry make possible the discovery of the change of differential properties of solutions of the equation FΩ,A;c̲=0. Such qualitative changes of the solutions of the amplitude-frequency response equation, referred to as metamorphoses, lead to qualitative changes of dynamics (bifurcations). We show that the analytical prediction of metamorphoses is of great help in numerical simulation.

The main scope of the paper is to apply the Design of Experiment (DoE) method and to develop a predictive model of energy losses for non-oriented electrical steels. This approach permits us to determine a mathematical model, which is the predicted response (energy losses) as a function of input data (strip width and peak magnetic polarization) and experimental results. The presented DoE model is based on a classical central composite design of type 2n + 2n + 1 with two-levels (n = 2) and as a consequence only nine experimental points are necessary. The equation system that is associated with the model, generates a surface response equation, which permits the energy loss computation for different values of width strip and peak magnetic polarization. The DoE model was implemented, using different software packages as MathCad, Excel and OriginPro 2018, in the case of two types of electrical steels namely NO20 and M300-35A alloys that are used in small size electrical machines. In this case, the strain hardening phenomena at the cut edge becomes important, due to its negative impact on energy losses. The computed results were compared with the experimental data and errors lower than 5 % were determined.

The accurate quantitative calculation of the volume fraction of mineral components is very important and basic work in formation evaluation. Using well log data to estimate the mineralogy, porosity, and total organic carbon (TOC) content is a mainstream method with core measurements often used. However, in shale reservoirs, there are many mineral components, such as organic matter and pyrite. Additionally, the pore structure is complex, and gas exists in the pores as free state, adsorbed state and dissolved state. These factors make the logging response characteristics of shale gas reservoirs more complex and thus the estimation of the mineral components more difficult. To address this problem, this paper proposes a mineral inversion method based on error analysis and response equation error. Based on the error analysis of the mineral inversion method, we first establish a technique to obtain interpretation parameters and the function of the response equation error combined with the core data. Then, based on the weighted total least square method (WTLS), we construct the objective function, and utilize the improved krill herd algorithm (OCKH) to solve the problem. Finally, we estimate the mineral component volume. The calculated results show that the method can accurately determine the clay, quartz + feldspar, carbonate contents, and porosity by using conventional logging data. Compared with the traditional mineral inversion method, the average relative error of the new method is reduced by 11.1%. In summary, the proposed method has high applicability to shale reservoirs and can supply the basic parameters for formation evaluation.

Abstract In this paper, the ordered single-open-chain (SOC) method in combination with the principle of virtual work is adopted to model and solve the forward dynamics of a single degree-of-freedom (DOF) parallel mechanism (PM), featuring one translation and two rotations (1T2R), which is applied in spatial vibrating screen (i.e., parallel vibrating screen mechanism, PVSM). Afterwards, the dynamic performances of the PVSM is optimized using differential evolution algorithm. Based on the kinematics of the PM, the forward dynamic model is derived and the dynamic response equation is built, of which the coefficient matrix is determined by means of the generalized velocity equation. Moreover, the Euler method was adopted to solve the numerical solution of the differential equation of motion to characterize the motion law and dynamics of the screen surface of the PVSM, which is verified with ADAMS simulation. With the parametric model, the dynamic optimization of PVSM is carried out to maximize the energy transfer efficiency, subject to the constraints on the link mass. The comparison of the dynamic performances of the PVSM with and without optimization reveals the improvement of the PM.

Sloshing may induce adverse loads to cause structural instability and damage. A vertical elastic baffle mounted at the inside bottom of a rectangular container is used as an anti-slosh device to attenuate the liquid oscillation. A semi-analytical model is presented to analyze the hydroelastic problem. The liquid is partitioned into four simple sub-domains with three hypothetical interfaces. The velocity potential of each sub-domain is analytically deduced by the separation of variables. The baffle deflection is expanded into the Fourier series by its dry modals. The eigenvalue equation is formulated by plugging the velocity potentials into the sloshing conditions, interface continuity conditions, as well as the dominant equation and compatibility conditions of the baffle. Then, the velocity potential is expressed by a complete basis of the coupled mode shapes for the system considered under lateral excitation. The system response equation is constituted by inserting the velocity potential into wave equations and baffle equation. The proposed method is verified by comparing the present results with the available data. In addition, numerical analyses are performed to examine the effects of baffle parameters on the natural frequencies, mode shapes and dynamic responses of the container. The sloshing frequency may be altered to a higher value due to the installation of the elastic baffle.

The main purpose of this manuscript is to analyze the stability of the shock response of the electric vehicle (EV) powertrain when considering the electro-mechanical coupling effect. The nonlinear drive-shaft model of the powertrain is built using the Lagrange method, based on which the shock response equation is also deduced. Meanwhile, the number and properties of the equilibrium points are studied. Two kinds of equilibrium points, saddle node and central point, which can induce different dynamic behaviors are found. The simulation results show that the trajectory of the shock response may be unstable if the parameters are chosen in the region that has a saddle node. If the parameters of the powertrain fall into the region that has only one central point, the trajectory of the shock response will be attracted by the stable limit cycle. Therefore, to ensure that the shock response is more stable, the parameters should be chosen in the region where only one central point is present.

The Indonesian Government has issued various policies to fight Coronavirus Disease (COVID-19). However, cases have continued to fluctuate over a year into the pandemic. There is a need to assess the country's healthcare system's capacity to absorb and accommodate the varying healthcare demands. We reviewed the current capacity of Indonesia's healthcare system to respond to COVID-19 based on the four essential elements of surge capacity: staff, stuff, structure, and system. Currently available medical staffs are insufficient to deal with potentially increasing demands as the pandemic highlighted the human resources challenges the healthcare system has been struggling with. The pandemic has exposed the fragility of medical supply chains. Surges in the number of patients requiring hospitalization have led to depleted medical supplies. The existing healthcare infrastructure is still inadequate to deal with the rise of COVID-19 cases, which has also exposed the limited capacity of the healthcare infrastructure to manage medical waste. The COVID-19 pandemic has further exposed the weakness of the patient referral system and the limited capacity of the healthcare system to deliver essential health services under prolonged emergencies. The Indonesian Government needs to ramp up the country's healthcare capacity. A wide range of strategies has been proposed to address those mounting challenges. Notwithstanding, the challenges of increasing healthcare capacity highlight that such efforts could represent only one part of the pandemic response equation. Effective pandemic response ultimately requires governments' commitment to increase healthcare capacity and flatten the curve concurrently.

Abstract Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

A vibration control signal sensing method is proposed utilizing the grid electrode displacement sensitive effect of field-effect transistors. The signal sensing method is applied to nonlinear resonance delay control of a nanobeam that is used as the core component of nano–microdevices. The nonlinear vibration dynamical model of the nanobeam based on the field-effect tube sensing is established and the differential equation of motion with time delay control is presented. The amplitude frequency response equation and phase frequency response equation of the nanobeam are obtained by analyzing the first-order approximate solution of the primary and superharmonic vibration of the nonlinear equation with multi-scale method. The vibration feedback gain and time delay can affect the vibration amplitude and nonlinear behavior of the nanobeam. The nonlinear vibration of the nanobeam can be adjusted and effectively controlled by selecting appropriate feedback gains and time delays.

Abstract The Yinggehai basin is located in the western part of the South China Sea, the burial depth of the Huangliu and Meishan formations in the target layer is close to 4000 meters, the formation temperature is close to 200 degrees Celsius, and the formation pressure is up to 100 MPa. The reservoir is characterized by low porosity-ultra-low permeability, heavy carbonate cement, complex CO2 content, this leads to complex neutron and density logging effects. The solubility of CO2 Above CH4, the solubility change with temperature and pressure is different from CH4, which makes it difficult to identify the CO2 gas layer. In this paper, based on the difference in the physical characteristics of CO2 and CH4, the Boltzmann equation combined with MCNP software was used to simulate the neutron and density logging responses under different CO2 saturations. Environmental factors such as temperature and pressure, carbonate cement, mud content and pores were studied To measure the effect of logging response, the LM inversion method is used to jointly invert CO2 saturation of density and neutron logs. The purpose of the inversion is to reduce the non-uniqueness of the evaluation of porosity and CO2 saturation. By introducing the Levenberg-Marquardt (LM) method, the neutron logging response equation of the porosity, argillaceous content, CO2, CH4 in the rock and the corresponding temperature and pressure is solved, and also the response equation of above parameters to density logging, where porosity and CO2 content are the key parameters, and the calculation results prove the effectiveness of the method by comparing the sampling data. The results show that the accuracy of the estimated CO2 saturation is increased by 10% compared with the conventional interpretation method, and the new simulation method improves the calculation speed several times compared to the MCNP software. The joint inversion method has been successfully applied to field data, which has greatly improved the saturation evaluation results of traditional logging interpretation methods, can be extended to other fields of nuclear logging simulation and inversion.