Definition Of Boundary Conditions Research Articles

High-precision spectral inversions: Determining what is important for the accurate definition of incident radiation boundary conditions

Spectral inversions are used to analyse spectroscopic observations with the aim of deriving the physical properties of the observed plasma, such as the kinetic temperature, density, pressure, degree of ionisation, or macroscopic velocities. One of the key factors ensuring the high precision of the derived plasma properties is having accurately defined input parameters of the models on which spectral inversions rely. The illumination, which chromospheric and coronal structures receive from the solar surface (and corona), is one of the most crucial input parameters of these models. We do not perform spectral inversions in this work. Our aim is to study two important factors that contribute to the accurate definition of the incident radiation boundary conditions: the altitude above the solar surface and the dynamics of the illuminated plasma. This investigation takes into account a diverse range of solar structures from the high-rising eruptive prominences to low-lying spicules. To study the influence of the altitude and dynamics of the observed plasma on the incident radiation boundary conditions, we used geometrical principles valid for any spectral line. However, to demonstrate the strong impact of dynamics, we considered the specific case of narrow spectral lines of which are highly sensitive to the presence of velocities. We argue that the altitude of the illuminated plasma strongly influences the way we need to define the incident radiation boundary conditions to achieve the most accurate results. For low-lying structures, generally below 50,000 km, the incident radiation may need to be specified directly from the composition of the portion of the solar disc that illuminates them. For high-altitude structures, generally above 300,000 km, the fraction of the solar disc illuminating the analysed plasma is large enough to be realistically approximated by the composition of the entire disc. We also show that for the narrow spectral lines, such as the lines, the impact of dynamics on the incident radiation intensity and profile shapes starts from radial velocities of 30 km $. Such velocities are even exhibited by the fine structures of quiescent prominences and are easily exceeded in spicules or eruptive prominences. The two aspects of the incident radiation definition studied here are relevant for spectral inversions based on any kind of modelling approach. However, their impact on the precision of the results of spectral inversions is likely less significant than the impact of the choice of the complexity of the model geometry, for example.

Investigation of the Tunnel Water Inflow Prediction Method Based on the MODFLOW-DRAIN Module

The precise prediction of water inflow in tunnels is a key aspect of civil engineering. It is directly related to the progress of construction, the stability of caverns and the safety of construction personnel. Currently widely used calculation methods include the empirical formula method, the analytical method and the numerical simulation method. In situations where the geological conditions are complex and the boundary conditions are irregular, numerical simulation methods have clear advantages. However, there are still discussions about the rationality, accuracy and applicability of the definition of tunnel boundary conditions in numerical simulation methods. Based on the Groundwater Model System (GMS10.7) software, we investigate the feasibility of using the DRAIN module to describe tunnel boundaries and calculate water inflow. By comparing it with traditional empirical formulas, the feasibility of the method is verified, and the error is about 8%. In addition, this method is applied to predict the water inflow in the construction of an underground pumping station under complex geological conditions and the prediction is compared with the measured water inflow, and the error is about 20%. This article explains the physical meaning and the value method of the relevant parameters of the DRAIN module, providing basic support for the prediction of water inflow in tunnels.

A precise method for the spectral adjustment of LED and multi‐light source solar simulators

AbstractSolar simulators based on light‐emitting diodes (LEDs) usually consist of many spectrally different LEDs, which in sum produce a sun‐like spectrum. On the one hand, this results in the advantage of a high spectral tunability of these systems and on the other hand, however, also in the challenge of a high number of parameters which have to be set for the adjustment of a suitable simulator spectrum. Multijunction solar cells consisting of series‐connected subcells are very sensitive to spectral irradiance conditions, which are affecting the current and the fill factor of the device. A precise adjustment of the simulator spectrum based on the spectral responsivity of the subcells is therefore essential for accurate multijunction measurements. Therefore, the number of spectrally different light sources used should be at least as high as the number of subcells in the device under test. However, for the measurement of multijunction devices, the much higher number of spectrally different light sources in common LED solar simulators results in a plethora of different simulator spectra, potentially suitable for the measurement. Furthermore, the nonlinear intensity characteristics of the utilized LEDs as well as the distance‐dependent illumination uniformity of such solar simulators add complexity when aiming for a precise spectral adjustment. To tackle these challenges, a new spectral adjustment procedure which is based on a least square's solution algorithm and the definition of appropriate boundary conditions for the calculation of suitable simulator settings is introduced in this publication. Focusing on measurements carried out under constant illumination makes the presented method especially applicable for perovskite‐on‐silicon multijunction devices. Therefore, an adapted method for the determination of the solar simulator's spectral properties, considering thermal influences which are particularly relevant when carrying out continuous illumination measurements, is introduced in this work. The presented method is verified applying it on a Wavelabs SINUS 220 LED solar simulator by performing a measurement comparison on a multijunction solar cell with Fraunhofer ISE CalLab's well‐established multilight source solar simulator.

Review: Toward sustainable management of groundwater in the deserts of Egypt

To achieve its ambitious plans to reclaim its deserts through mega projects, Egypt is heavily relying on fossil or little-recharged groundwater. This article revisits the results and methodologies of the studies conducted over the last two decades on groundwater management and uses in the Western Desert. Most previous studies aimed at simulating different groundwater abstraction scenarios by modeling local areas in aquifer systems, but with poor definitions of boundary conditions and limited historical data. Studies were constrained by the unavailability of data, access difficulties, and high collection costs in desert lands. Thus, to propose reliable sustainable groundwater resources development plans and recommendations for future protection strategies, an open-access monitoring network representing regional aquifers is needed. More investigations based on extensive field visits are essential to monitor environmental, economic, and social conditions, identify constraints, and learn lessons for reclaiming desert lands. Moreover, this review highlighted the need to frame a rational strategy for the long-term sustainable exploitation of non-renewable groundwater in the aquifer systems of Egypt and develop an appropriate exit strategy for desert communities in case of serious water resource depletion.

Integrating electric double layer time-varying and dual interface slip for predicting migration behavior of moisture and ions

Migration of moisture and chloride ions in calcium-silicate-hydrates (C-S-H) nanopores is important factor for controlling the durability of concrete and affecting the physical and chemical properties of cement-based binder. Quantitative analysis of experimental results indicates that the pore in C-S-H is mainly distributed on the nanometer scale. Due to the prominent interfacial effects at the nanoscale, moisture and ions in different regions within nanochannels exhibit distinct molecular structures and dynamic properties. Therefore, the wetting behavior of the synthesized C-S-H surface and its influence on microfluid dynamics analysis and boundary condition definition were systematically analyzed based on the contact angle experiment. Statistical thermodynamics were introduced to describe the time-varying characteristics of the electric double layer (EDL). With the interaction as the theoretical framework and interaction energy as an important parameter, the equilibrium behavior of interacting particles was studied to describe the stability of EDL system. The flow control equation and boundary conditions were modified considering the action of EDL. The transport model of moisture and chloride ions under the combined influence of electric double layer and dual interface slip was proposed. The results show that the existence of EDL impedes the movement of the fluid, while the dual slippage of water film and time-varying of EDL reduce the resistance. Quantitative analysis indicates the contribution ratios of water film slip and EDL time-varying can reach 85% and 29%, respectively. In addition, water film slip has a greater influence on water migration and EDL time-varying has a greater influence on ions. This research can provide new insights into the transport mechanism of water and chloride ions at micro-nanoscale.

A Review of the Computational Studies on the Separated Subsonic Flow in Asymmetric Diffusers Focused on Turbulence Modeling Assessment

Separated turbulent diffuser flows have long been an object of experimental and computational investigations due to their wide use in engineering applications and fundamental importance for understanding turbulent effects. The accuracy of simulating such flows depends mainly on turbulence modeling subtleties, numerical method, and the correspondence between the boundary conditions and the experimental set-up. The current review of selected articles focuses on revealing some of the computational challenges that may occur while modeling asymmetric subsonic diffuser flows. These challenges include the influence of sidewalls on the separation, issues with grid convergence, and the definition of boundary conditions. Several known experimental test cases and attempts at simulating them are studied. The novelty of this paper is in the fact that it is focused on a specific type of diffusers (asymmetric and subsonic) and based on relatively recent data. It is concluded that for all the test cases considered, Reynolds stress models and hybrid eddy-resolving methods are the most appropriate tools for obtaining reasonable results.

Working with Different Building Energy Performance Tools: From Input Data to Energy and Indoor Temperature Predictions

Energy consumption calculations and thermal comfort conditions assessment are crucial issues in building simulations when using Building Energy Performance Simulation (BEPS) tools. The available software has been separately validated under different boundaries and operating conditions. Consequently, the predicted output of the same building simulated with two separate software can disagree. This issue is relevant not only for research purposes but also for professionals who need to compare the energy performance of the same building with different simulation engines. This work aims at contributing to the field in two ways. Above all, it clarifies the preparation of the building model and the correct definition of input data and boundary conditions when different software are used (IDA ICE and Design Builder/Energy Plus). In addition, it compares the output (energy and indoor temperatures) of two BEPS for the same building (in different configurations) exposed to the same weather conditions. The study shows that the two most significant differences are represented by the temperature values, while the energy predictions agree.

On the modeling of boundary conditions for determining the critical speeds of rotation of rotors

The article is devoted to the definition of boundary conditions that allow achieving adequate results when calculating the critical speeds of rotation of rotors based on finite element models. Experimental determination of the frequencies of free vibrations of a laboratory rotor on ball bearings was carried out using a vibration measuring complex developed by the authors. Numerical studies of the free vibrations of a laboratory rotor and a cylindrical pipe with a wall thickness to length ratio of 1/10 were performed on the basis of a three-dimensional finite element model under various boundary conditions. Movable and fixed cylindrical hinges corresponding to floating bearings are used as supports in the calculation scheme of the laboratory rotor. Due to the fact that the dimensions of the bearings along the length of the shaft are small compared to the total length, it is assumed in the calculation model that the shaft is hinged along the edges at separate points of one circle on each bearing. Shaft mounting options at two, four and eight points are considered. The options for fastening a cylindrical pipe in the extreme sections at two points, a quarter of a circle and a full circle are considered. Comparison of experimental and numerical results, solutions obtained analytically and on the basis of the finite element method is carried out. An analysis of the modes of natural vibrations showed that with various options for fixing a cylindrical pipe, vibration modes arise associated with the deformation of the pipe as a shell. For example, when fixing a pipe along a quarter of a circle, among the forms №1-№10, only the second corresponds to the deformation of the pipe as a beam. The results of the study of free vibrations of a laboratory rotor show that the best option for boundary conditions, which makes it possible to approach the results of the experiment, is fastening on each bearing at two points located on the neutral line of the cross section when the rotor is bent. Numerical studies of the eigen frequencies of a cylindrical pipe show that it is with this type of boundary conditions that one can obtain results that are closest to the analytical solution.

NUMERICAL AND EXPERIMENTAL ANALYSIS OF A CENTRIFUGAL PUMP WITH DIFFERENT ROTOR GEOMETRIES

The paper presents a comparative analysis of the operation of two variants of centrifugal pump rotors, a description of the main parameters, and the influence of the blade geometry on the performance characteristics obtained. Rotors have been designed using the arc and point method. Based on the developed 3D CAD models, the rotors were printed using the rapid prototyping method on a 3D printer in FFF (Fused Filament Fabrication) technology, in order to experimentally verify the performance, by placing them on the Armfield FM50 test stand. The analysis part of the CFD includes a fluid flow in Ansys Fluent. The process of creating a flow domain and generating a structural mesh was described, along with the definition of boundary conditions, the definition of physical conditions and the turbulence model. The distribution of pressures and velocities in the meridional sections is shown graphically. The chapter with the experimental analysis contains a description of the measuring stand and the methodology used. The results obtained made it possible to generate the characteristics, making it possible to compare the results received. The results allowed to note the influence of geometry on the behavior of the rotors during operation in the system and to indicate that the arc rotor gets a 7% higher head and 2% higher efficiency than the point method rotor, which gives the basis for its commercial use in industry.

Epistemic uncertainty in URANS based CFD analysis of buoyancy driven flows—Comparison of URANS and LES

The containment is the last barrier to prevent the release of radioactive materials into the environment in case of a severe reactor accident. Thus, it is important to understand the flow and transport processes of combustible gases and to develop strategies to maintain the integrity of the containment. A holistic OpenFOAM-based CFD software package, containmentFOAM, is developed for containment analysis. During the validation of the code with regard to free convection flows and mixing processes, it became apparent that the simulation results are fairly sensitive to the definition of initial and boundary conditions, which are often not precisely known from the experiment. Therefore, establishing the validity of the models is impossible without a quantification of uncertainties.Generally, the uncertainty is categorized in two types, namely aleatoric and epistemic uncertainties. The first exhibits stochastic variations around the exact value. The latter has two possible effects on the uncertainty quantification: first a different sensitivity of the model to the input variation and second a bias to the exact value. Both effects can affect the significance of an aleatoric uncertainty quantification. The epistemic uncertainty originating from URANS turbulence modelling is investigated in this study by means of a direct comparison with the results obtained by LES, assuming that LES turbulence closures have smaller epistemic uncertainty. For a buoyancy driven natural circulation flow as well as a superimposed mixing process, both epistemic effects of the URANS approach are identified in terms of different sensitivities with respect to a variation of uncertain input parameters and the deviations of the URANS output variation ranges to those of LES. Nevertheless, the analysis of uncertainty bands derived on the basis of the most relevant parameter revealed that these epistemic effects ultimately result in a negligible effect on the aleatoric uncertainty quantification conducted with URANS.

Biomechanical Modelling for Tooth Survival Studies: Mechanical Properties, Loads and Boundary Conditions-A Narrative Review.

Recent biomechanical studies have focused on studying the response of teeth before and after different treatments under functional and parafunctional loads. These studies often involve experimental and/or finite element analysis (FEA). Current loading and boundary conditions may not entirely represent the real condition of the tooth in clinical situations. The importance of homogenizing both sample characterization and boundary conditions definition for future dental biomechanical studies is highlighted. The mechanical properties of dental structural tissues are presented, along with the effect of functional and parafunctional loads and other environmental and biological parameters that may influence tooth survival. A range of values for Young's modulus, Poisson ratio, compressive strength, threshold stress intensity factor and fracture toughness are provided for enamel and dentin; as well as Young's modulus and Poisson ratio for the PDL, trabecular and cortical bone. Angles, loading magnitude and frequency are provided for functional and parafunctional loads. The environmental and physiological conditions (age, gender, tooth, humidity, etc.), that may influence tooth survival are also discussed. Oversimplifications of biomechanical models could end up in results that divert from the natural behavior of teeth. Experimental validation models with close-to-reality boundary conditions should be developed to compare the validity of simplified models.

Method for indirect determination of soil parameters for numerical simulation of dikes and earth dams

One of the most important steps in the numerical simulation of a hydrogeological system is the precise definition of initial and boundary conditions. The better these are characterized, the more efficient the calculation and the more accurate are the simulation result. In case of simulating processes in the unsaturated soil zone, the water retention curve, the relationship between volumetric water content and matric potential, is of great importance. However, the retention parameters determined locally by different standard methods often do not represent the whole soil system under consideration due to heterogeneities in the soil body caused by variability or different compaction of the soil. Resulting over- or underestimation of the parameters is leading to a worse performance of simulations of the water balance including to a higher calibration effort. Therefore, it is more favorable to identify these soil parameters by a method representing the whole soil system to avoid uncertainties. For this reason, a dike experiment was performed to investigate how soil parameters determined locally and globally can represent the properties of the whole soil system. When comparing the simulation results of the numerical models, a better agreement of measured and simulated water contents as well as a lower effort for calibration is observed by using the soil parameters determined globally.

Reduced T-shaped soil domain for nonlinear dynamic soil-bridge interaction analysis

The one-directional three-component wave propagation in a T-shaped soil domain (1DT-3C) is a numerical modeling technique, in a finite element scheme, to investigate dynamic soil-structure interaction (SSI) coupled with seismic site effects, under the assumption of vertical propagation of three-component seismic motion along a horizontal multilayered soil. A three-dimensional elasto-plastic model is adopted for soils, characterized using their shear modulus reduction curve.In this research, the 1DT-3C wave propagation modeling technique is proposed as an efficient tool for bridge design to take into account directly the spatial variability of seismic loading. This approach, in the preliminary phase of bridge study and design, allows the reduction of the soil domain and the easier definition of boundary conditions, using geotechnical parameters obtained with only one borehole investigation for each pier. This leads to a gain in modeling and computational time.

Boundary conditions for non-residential buildings from the user’s perspective: Literature review

Background and objectiveThis paper aims to review the boundary conditions (B/C) in specific categories (energy, building use, and lighting) within non-residential buildings to pave the way to a better understanding of users’ requirements and needs of the built environment. For this paper, B/C are understood as unique preconditions, specific characteristics for use, determining specific features of buildings, enabling an accurate understanding of non-residential spaces concerning energy use, user behaviour, and lighting. MethodsThis paper describes the results of an overall quantitative (1st method) review and a systematic review (2nd method) of boundary conditions and their factors within different types of non-residential buildings from the users’ perception. Followed by a qualitative experts’ literature review (3rd method) on B/C within offices, schools, and hospitals chosen by a team of international experts working together on Subtask A: User perspective and requirements, Task 61 IEA (International Energy Agency): Solutions for daylighting and electric lighting. ResultsThe first review method led to the selection of 21 papers. The second method resulted in the selection of 7 papers out of 93,143 found in Scopus; during the 3rd review, experts collectively chose 74 additional papers focussing on the users' factors contributing to specific B/C. The scope of this paper is limited only to offices, schools, and hospitals. Based on the findings, the authors recognise a broad definition of boundary conditions from specific values, and conditions to interconnected factors, user profiles, functions of the building types, and operating hours. ConclusionsThis paper is an overview of B/C factors found in the literature that can help explain the occupants’ behaviour and the use of spaces. B/C are often type of building/user/location/situation/simulation input-values and method-specific. Therefore, they cannot be widely applicable but offer patterns and help to understand the correlations between various factors shaping the built environment. A better comprehension of the reasons for identifying B/C and their factors can help in developing a deeper knowledge of how we use buildings to find optimal ways to design them.

Model-Based Analysis of Myocardial Contraction Patterns in Ischemic Heart Disease

ObjectivesThe objective of the current study is to assess the feasibility of using a left ventricle (LV) model in order to reproduce myocardial strains in the case of ischemic heart disease (IHD). Materials and MethodsThe proposed integrated LV model couples a finite element method (FEM) sub-model of the cardiac electrical activity, representing the propagation of the transmembrane potential through the LV, a FEM sub-model of the cardiac mechanical activity, and a lumped-parameter model of the circulatory system that improves the physiological definition of appropriate boundary conditions. Simulations were compared to myocardial strain data obtained from echocardiography, performed on two healthy subjects and two patients diagnosed with chronic IHD. ResultsResults show the model ability to simulate jointly the hemodynamic variables (Systolic and diastolic pressures respectively equal to 110 and 60 mmHg) and myocardial strain curves during each phase of the cardiac cycle. A close match is observed between minimum strains obtained from simulations and clinical data from healthy subjects and IHD patient, with a root mean square error around 2,81% and 2,63% respectively. The modifications of regional LV systolic strains observed from IHD patients with respect to healthy cases were partially explained by a decrease of regional cardiac stress. ConclusionThis paper provides a description of a new coupling algorithm between FEM and lumped-parameter models. Results are promising for the analysis of cardiac strains in the context of IHD.

The Cauê Aquifer on the eastern limb of the Moeda Syncline: characterization, impacts, and flow in the western Iron Quadrangle (Quadrilátero Ferrífero), MG, Brazil

The Cauê Aquifer is an important water supplier to the third largest urban agglomeration in Brazil. The Metropolitan Region of Belo Horizonte is in the Iron Quadrangle, site of intense iron ore mining, requiring large volumes of water and mine dewatering. In this context, we evaluate the regional impact on groundwater level between 2000 and 2019 based on a conceptual hydrogeological flow model on the eastern limb of the Moeda Syncline. This study includes the definition of boundary conditions and aquifer units, the calculation of hydrodynamic parameters, water balance, renewable reserve, and flow analysis. The Cauê, Gandarela, and Moeda aquifers are considered aquifer units, among which the Cauê Aquifer showed the highest hydraulic conductivity (9.45×10-7 m/s on average) as well as the highest recharge rate, with 38.67% rainfall. The average volume pumped was estimated at 41 million m³/year, equivalent to about 150% of the renewable reserve of the Cauê Aquifer, calculated at 27 million m³/year. Underground flow in the area tends southward, and the Cauê Aquifer acts as a water divide, which is less evident in the center of the area, where the greatest impact on groundwater level lowering occurs.

Two-Dimensional-One-Dimensional Alternating Direction Schemes for Coastal Systems Convection-Diffusion Problems

The initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems and extended shallow water bodies is considered. Convective and diffusive transport operators in horizontal and vertical directions for this type of problem have significantly different physical and spectral properties. In connection with the above, a two-dimensional–one-dimensional splitting scheme has been built—a three-dimensional analog of the Peaceman–Rachford alternating direction scheme, which is suitable for the operational suspension spread prediction in coastal systems. The paper has proved the theorem of stability solution with respect to the initial data and functions of the right side, in the case of time-independent operators in special energy norms determined by one of the splitting scheme operators. The accuracy has been investigated, which, as in the case of the Peaceman–Rachford scheme, with the special definition of boundary conditions on a fractional time step, is the value of the second order in dependency of time and spatial steps. The use of this approach makes it possible to obtain parallel algorithms for solving grid convection-diffusion equations which are economical in the sense of total time of problem solution on multiprocessor systems, which includes time for arithmetic operations realization and the one required to carry of information exchange between processors.

Pressure Drop Measurements in Microfluidic Devices: A Review on the Accurate Quantification of Interfacial Slip

AbstractThe correct theoretical definition of boundary conditions of flow underpins all fluid dynamics studies, and is particularly important in situations in which the flow is confined on the nano‐ and micro‐scale. Microfluidic devices are an excellent platform to measure boundary flow conditions, and the pressure drop versus flow rate method is particularly useful in detecting evidence of microscale interfacial slip and drag reduction. This review focuses on the pressure drop method, identifying the main experimental parameters affecting the accuracy and reproducibility of microfluidic experiments of slip, quantifying the magnitude and source of common errors, and providing practical solutions and guidelines. A summary of literature results of interfacial slip obtained with pressure drop measurements in microfluidic devices is also provided, and the slip results are directly compared to expected slip models. This review serves as an introduction for new researchers moving into the field of interfacial slip, and as reminder for established researchers of the need to create highly controlled experimental procedures in order to obtain reproducible and reliable measurements of boundary flow conditions. A direct comparison of accurate experiments with theoretical models is bound to bring about clarity about the mechanisms of slip on smooth and structured surfaces.

River Corridor Model Constrained by Time‐Lapse Seismic Acquisition

AbstractA new hydrogeophysical approach was developed to reveal the spatial and temporal dynamic flow pathways inside a river corridor as well as the pattern of transient surface water and the groundwater (SW‐GW) exchanges. Obtaining such information from traditional hydrological data remains a challenge, both in terms of accuracy and validation. As there is no direct measurement of these fluxes, estimating dynamic pathways and SW‐GW exchanges is frequently tackled with the help of numerical models. Yet, the definition of initial and boundary conditions is generally based on poorly constrained assumptions and restrained to the location of piezometers, due to the lack of knowledge of the water table (WT) geometry. We provide a methodology to build stronger constraints to the numerical simulation and the hydrodynamic parameters calibration, both in space and time, by using a multi‐method approach. On the Orgeval Critical Zone observatory (France), we show how a thorough interpretation of high‐resolution geophysical images, combined with geotechnical data, helps to resolve subsurface structural heterogeneity. This coupling provides a detailed distribution of hydrofacies, valuable prior information about the associated hydrodynamic properties distribution. The temporal dynamic of the WT table can be locally captured with high‐resolution time‐lapse seismic acquisitions. Time‐lapse variations are interpreted as temporal changes in the saturated‐unsaturated zone continuum. Each seismic snapshot is then thoroughly inverted to image spatial WT variations. This posterior geophysical information is then used to calibrate the hydrogeological modeling domain. The use of the WT improves the estimation of transient stream‐aquifer exchanges, especially during the rain event.

Development of calculation procedure for research and refinement of suspended design natural frequencies by example of vehicle exhaust system

The article presents a finite element model exhaust system developed in the ANSA software package. Experimental research of the dynamic characteristics mounts exhaust system. and developed calculation procedure for improvement of the suspended design natural frequencies based on the experimental definition of boundary conditions by the example of the vehicle exhaust system. Requirements for natural frequencies of the exhaust system are developed; finite element models of the exhaust system are developed; physical and mechanical characteristics of mounts are defined; natural frequencies and oscillation modes of the exhaust system taking into account physical and mechanical characteristics of mounts are calculated.