Transient Structural Analysis Research Articles

Numerical Evaluation and High-Speed Rotating Test on Circular Arc Spring Dampers for Centrifugal Compressors

Abstract A circular arc spring damper (CASD) is a recently proposed fluid-film damper that has two or more arc-shaped centering springs and dual radial clearances formed by wire electric discharge machining (WEDM). CASD requires less space and weight than a conventional cage-centered squeeze-film damper (SFD). It provides linear stiffness and stable damping force in rotor-bearing systems to attenuate vibration due to imbalance or to improve rotordynamic stability. The authors have been investigated the dynamic characteristics of CASD in component-level experiments. However, their performance and applicability to real machines have not been confirmed in system-level experiments. Additionally, a theoretical means of evaluation for CASD should be established to predict its dynamic coefficients and to understand the mechanism of dynamic force generation. In the first part of this study, a numerical evaluation method using two-way fluid–structure interaction (FSI) analysis and its theoretical background is presented. Transient structural analysis and fluid-film flow analysis with a simple homogeneous cavitation model are coupled in the commercial multiphysics platform ansys. The accuracy of the method was validated by comparing the damping and added-mass coefficients with results from previous experiments. Furthermore, several aspects of the force generation mechanism and the difference from conventional SFD were studied numerically. The second part of the study addresses the application of CASD in a multistage centrifugal compressor. A combined 4-in. diameter, five-pad tilting pad journal bearing (TPJB) with four-arc type CASD was newly designed and manufactured. To prove the applicability of the developed damper bearing, a series of rotating tests were conducted at a high-speed balancing facility with a full-scale dummy rotor with a critical speed ratio (CSR) of approximately 3.1. The measured unbalance response showed a much lower amplification factor (AF) than that of the conventional TPJB without the damper, which infers a significant improvement in the stability. The measured responses agreed with the rotordynamic analysis, which uses the dynamic coefficients of CASD derived from the proposed numerical evaluation method.

Dimensionality reduction-based extremum surrogate modeling strategy for transient reliability analysis of complex structures

To improve the transient reliability analysis of complex structures, dimensionality reduction (DR)-based extremum surrogate modeling strategy (DRESMS) is developed by absorbing the strengths of DR strategy and extremum response surface method (ERSM). In the proposed method, the DR is applied to find the embedding mapping the input data to high-dimensional space which has the potential to improve the transient reliability model, and the ERSM is used to build the regression relationship between input parameters and output response to establish a reliable surrogate model based on capturing dynamic extreme moments. The transient reliability analysis of turbine blisk is performed to verify the approximate accuracy and simulation performance of the proposed DRESMS with the assist of the comparison of methods. As seen in this study, (i) the reliability degree of turbine blisk fatigue life is 0.9939 when the allowable value of fatigue life is 1.7738×103 cycles (subject to 3 sigma levels), and (ii) the developed DRESMS holds advantages of high-modeling efficiency and low-fitting error, and (iii) the DRESMS holds excellent simulation efficiency and simulation precision. The efforts of this study provide the promising DRESMS to solve the transient probabilistic analysis of complex structures with multi-dimensional input parameters, which is significant in monitoring and maintaining complex structures and mechanical systems with the consideration of large-scale parameters.

Optimization Parameters of Disc Brake

Abstract: In recent time due to high performance of electronic component the heat generation is increasing drastically. Due to this scenario heat dissipation becomes a major issue in efficiency promation and stable operation. Silicon based microchannel heat sink fabricated using semiconductor production technique plays important role in cooling devices. The effect of the thermophysical properties of working fluids on the performance of microchannel is tested or we can say investigated. For this purpose the different working fluids are selected. water, hepthane, ammonia, methanol, and ethanol. The disc brake is a device for slowing or stopping the rotation of a wheel. Repetitive braking of the vehicle leads to heat generation during each braking event. Transient Thermal and Structural Analysis of the Rotor Disc of Disk Brake is aimed at evaluating the performance of disc brake rotor of a car under severe braking conditions and there by assist in disc rotor design and analysis. Disc brake model and analysis is done using ANSYS workbench 14.5. The main purpose of this study is to analysis the thermo mechanical behavior of the dry contact of the brake disc during the braking phase. The coupled thermal-structural analysis is used to determine the deformation and the Von Mises stress established in the disc for the both solid and ventilated disc with two different materials to enhance performance of the rotor disc. A comparison between analytical and results obtained from FEM is done and all the values obtained from the analysis are less than their allowable values. Hence best suitable design, material and rotor disc is suggested based on the performance, strength and rigidity criteria. Keywords- disc break, thermal analysis, structure analysis.

MODELING OF STEEL ELBOW MANUFACTURING PROCESSES VIA FINITE ELEMENT METHOD AND OPTIMIZATION OF PRODUCTION PARAMETERS

With the advancement of today's technologies, parts of pipe and elbow elements, natural gas pipelines, petrochemicals, machinery manufacturing industry, water distribution and flow systems, sewage systems, foundation piles, shipbuilding industry, nurse containers, aviation, space and defense industry, pipe networks, refineries , steel structures, tube and pipe engineering, etc. widely used in areas. In this study, extrusion method, which is one of the cold forming methods of elbow pipes, has been investigated. When the literature is examined, the production conditions of steel pipes and the problems that occur in production have been examined by different people and suggestions have been made. In this study, the production process of AISI 316L (EN 1.4404) quality stainless steel elbow pipes has been investigated. The mold design model created with the Solidworks program was transferred to the non-linear finite element analysis software ANSYS program for simulations. The process was modeled and simulated in the transient structural analysis section of the ANSYS program. In the process of transforming the pipe into an elbow product, we have learned about the stress distributions and obtaining the total deformation changes on the elbow. The parameters of the production process have been optimized by comparing the work done in the simulation and experimental data. In this way, cost-effective production is aimed by minimizing production costs. The data was extracted by simulating the production environment and conditions.

Structural Response of a Single-Stage Centrifugal Compressor to Fluid-Induced Excitations at Low-Flow Operating Condition: Experimental and Numerical Study

The article describes an assessment of possible changes in constant fatigue life of a medium flow-coefficient centrifugal compressor impeller subject to operation at close-to-surge point. Some aspects of duct acoustics are additionally analyzed. The experimental measurements at partial load are presented and are primarily used for validation of unidirectionally coupled fluid-structural numerical model. The model is based on unsteady finite-volume fluid-flow simulations and on finite-element transient structural analysis. The validation is followed by the model implementation to replicate the industry-scale loads with reasonably higher rotational speed and suction pressure. The approach demonstrates satisfactory accuracy in prediction of stage performance and unsteady flow field in vaneless diffuser. The latter is deduced from signal analysis relying on continuous wavelet transformations. On the other hand, it is found that the aerodynamic incidence losses at close-to-surge point are underpredicted. The structural simulation generates considerable amounts of numerical noise, which has to be separated prior to evaluation of fluid-induced dynamic strain. The main source of disturbance is defined as a stationary region of static pressure drop caused by flow contraction at volute tongue and leading to first engine-order excitation in rotating frame of reference. Eventually, it is concluded that the amplitude of excitation is too low to lead to any additional fatigue.

Turbine mode start-up simulation of a variable speed Francis pump-turbine prototype – Part II: 3-D unsteady CFD and FEM

The Z’Mutt pumping station, part of the Grande Dixence hydroelectric scheme, is one of the demonstrators of the XFLEX HYDRO project. A 5 MW reversible pump-turbine prototype equipped with a full-size frequency converter (FSFC) is used to investigate dynamic variable speed operation in pumping and generating mode. Since the FSFC converter is always connected to the electrical grid, the full rotational speed range of the motor-generator can theoretically be exploited. Furthermore, this technology enables fast operating point transitions and therefore increased grid regulation capacities. The advantages of the FSFC technology in generating mode are compared to a conventional fixed speed start-up with a variable speed start-up. The operating point trajectories are extracted from 1-D hydraulic transient simulations. Detailed hydrodynamic and structural aspects of the pump-turbine during the two start-up scenarios are further studied. Simplified unsteady 3-D CFD simulations and transient structural FEM analyses of the pump-turbine prototype are carried out to assess the harshness of the flow and to anticipate runner fatigue. The present work aims to point out potential mitigation of partial runner damages during start-up in generating mode using FSFC technology.

Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation

We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation of finite elasticity coupled with Fickian diffusion has a two-field minimization structure, wherein the deformation map and the fluid-volume flux are obtained as minimizers of a time-discrete potential involving internal and external energetic contributions. To analyze the structural stability of a certain equilibrium state of the gel satisfying the minimization principle, we apply the local stability criterion on the incremental potential, which is based on the idea that a stable equilibrium state has the lowest potential energy among all possible states within an infinitesimal neighborhood. Using this criterion in a finite-element context, it is understood that bifurcation-type structural instabilities are activated when the coupled global finite-element stiffness matrix loses its positive definiteness. This concept is then applied to determine the onset and nature of wrinkling instabilities occurring in a pair of representative film-substrate hydrogel systems. In particular, we analyze the dependencies of the critical buckling load and mode shape on the system geometry and material parameters.

Deformation of an airfoil-shaped brain surrogate under shock wave loading

Improvised explosive devices (IEDs), during military operations, has increased the incidence of blast-induced traumatic brain injuries (bTBI). The shock wave is created following detonation of the IED. This shock wave propagates through the atmosphere and may cause bTBI. As a result, bTBI research has gained increased attention since this injury's mechanism is not thoroughly understood. To develop better protection and treatment against bTBI, further studies of soft material (e.g. brain and brain surrogate) deformation due to shock wave exposure are essential. However, the dynamic mechanical behavior of soft materials, subjected to high strain rates from shock wave exposure, remains unknown. Thus, an experimental approach was applied to study the interaction between the shock wave and an unconfined brain surrogate fabricated from a biomaterial (i.e. polydimethylsiloxane (PDMS)). The 1:70 ratio of curing agent-to-base determined the stiffness of the PDMS (Sylgard 184, Dow Corning Corporation). A stretched NACA 2414 (upper airfoil surface) geometry was utilized to resemble the shape of a porcine brain. Digital image correlation (DIC) technique was applied to measure the deformation on the brain surrogate's surface following shock wave exposure. A shock tube was utilized to create the shock wave and pressure transducers measured the pressure in the vicinity of the brain surrogate. A transient structural analysis using ANSYS Workbench was performed to predict the elastic modulus of 1:70 airfoil-shaped PDMS, at a strain rate on the order of 6 × 103 s−1. Both compression and protrusion of the PDMS surface were found due to the shock wave exposure. Negative pressure was found in a semi-ring area, which was the cause of protrusion. Oscillation of the brain surrogate, due to the shock wave loading, was found. The frequency of oscillation does not depend on the geometry. This work will add to the limited data describing the dynamic behavior of soft materials due to shock wave loading.

Transient thermo-mechanical analysis of FGM hollow cylindrical structures involving micro-scale effect

Thermo-mechanical properties of the functionally graded materials (FGMs) are the pivotal role to improve their service lives exposed to some extraordinary thermal circumstances. An analytical procedure to explore the thermo-mechanical interaction involving the micro-scale effect is proposed for the first time in this work. The governing equations are firstly constructed in a cylindrical coordinate in the context of the generalized Chandrasekharaiah–Tzou theory (C–T theory). An asymptotic approach, based on the Laplace transform technique and its limit theorem, is then employed to solve these equations analytically, in which a common linearization technique is prior to introduce to disperse the non-linear terms involving variable material properties with different gradient patterns. The layer-formed solutions of a typical FGM hollow cylindrical structure with its inner boundary subjected to a sudden temperature rise is finally obtained and validated. A detailed parametric study has been conducted to explore the effect of the micro-structure interaction, physical properties distribution patterns, and the structure size on the thermo-mechanical response. The results state that the effect of micro-structure interaction mainly focuses on the thermal wave propagation and is more significant for the ceramic-rich case. The delay effect on the heat transport induced by thermal inertia is also wakened significantly by the micro-structure interaction, which leads to a larger range of thermo-elastic response and smaller peak stress.

Transient Structural Analysis of a Skid Mounted on a Hydrogen Tube Trailer under Shock and Vibration Induced by Road Irregularities

Due to environmental pollution and depletion of fossil fuels, hydrogen is becoming an increasingly practical, clean and environmentally friendly option for transportation and energy storage among all green alternative energy sources introduced. Hydrogen storage and delivery is expensive because of the lower energy density per unit volume as compared with conventional fossil fuels. Hence, hydrogen is usually stored in a gaseous state and delivered via tube trailers or pipelines. In this study, a transient structural analysis of a skid structure mounted on a hydrogen tube trailer was performed under shock load induced by road irregularities. The dynamics of the driving trailer according to the unevenness of the road surface were obtained through multibody dynamic simulations considering the full car model equipped with 64 hydrogen tubes. The transient structural analysis of the tube skid was performed by considering the resulting acceleration values as constraints. Through the sequential simulations, we evaluated the structural safety of the designed tube skid mounted on a trailer during hydrogen transport.

A novel modeling approach for multi-passes butt-welded plates

Numerical simulation of welding process in the industrial field requires flexibility, speed, and accuracy at the same time. The use of conventional 3D models in detailed simulations of multi-pass welds is time-consuming, and it often slows down the design phase of large welded structures. Shell elements are usually employed in the finite element (FE) simulation of large structures like vessels and pipes. Nevertheless, employing a simple shell model to simulate multi-pass welds would most likely produce inaccurate outcomes. This article introduces a new equivalent parametric modeling methodology for the simulation of longitudinal multi-pass welds on plane structures, such as plates and rectangular hollow sections. The proposed Weld Equivalent Model (WEM) is made with single and multi-layer shell, link and beam elements. It helps detect residual stress and local distortion that are typical of multi-pass welds. This method employs thermal transient and steady-state structural analyses. The WEM model is generated by an automatic subroutine acting on a pre-existing FE shell model. In addition to this, a case study is reported of multi-pass welding of two plates featuring a V-shaped groove. This innovative weld modeling technique shows remarkable results and helps shorten computational time up to ten times compared to classical 3D numerical models.

Electromagnetic analysis of ITER equatorial Wide Angle Viewing System (WAVS) in-vessel components

In the framework of ITER diagnostics, the visible and infrared equatorial Wide Angle Viewing System (WAVS, referenced as 55.G1.C0 in ITER Plant Breakdown Structure) plays a key role. Indeed, this system is devoted to monitor the surface temperature of the plasma facing components by infrared thermography and to image the edge plasma emission in the visible range. As a consequence, it is mandatory to verify that WAVS components are able to withstand all the foreseen loads and load combinations. This paper is dedicated to present the methods and results of electromagnetic (EM) and Transient Structural (TS) analyses for determining the loads due to Eddy Currents and the associated stresses and displacements in the in-vessel components of WAVS at its Preliminary Design Review (PDR) stage.Specifically, the analysed WAVS in-vessel components comprise First Mirror Units, shutters and Hot Dog Legs of the EPP#12 (Equatorial Port Plug). The selected EM loads derive from the IO-assumed worst EM scenario for EPP#12 (specifically a plasma exponential major disruption).Given the variation maps of the global magnetic field in the regions of interest during the transient, the EM loads have been estimated using a local 3D EM model of the WAVS components by means of the ANSYS Electromagnetics Suite v.19.2, employing the tool ANSYS Maxwell. Successively, the obtained results have been used as inputs to the corresponding TS analyses (carried out using ANSYS Workbench v.19.2). Therefore, the related outcomes can be combined with the set of all other structural studies (i.e. thermal and seismic analyses) to assess the overall mechanical behaviour of the components under study for the WAVS PDR level. Moreover, the results obtained have shown how EM loads are often design driving loads for the WAVS components.

Sliding speed effect in press-fit connection using Finite Element Analysis

Solderless press-fit contacts in power module packages are now gaining more attention in the automotive industry especially in hybrid electric vehicles because of the Restriction of Hazardous Substances (RoHS) directive to eliminate lead-based connections. The production of press-fit assembly is also faster, more convenient, safer, and cheaper than soldered connections. In this paper, the effect of insertion speed of pin to the press-in force as well as the pull-out speed to the retention force was investigated using finite element analysis. An eye-of-the-needle (EON) shape compliant pin with general dimensions was adapted and a transient structural analysis in ANSYS mechanical was used to add and vary the speed of the press-fit pin geometry. Four simulations were conducted with different speeds. The results obtained by FEA show that the speed when kept at constant has no significant effect both on the press-in and retention force. However, when the speed changes due to acceleration, the press-in and pull-out force are both affected.

Numerical investigation of wing–wing interaction and its effect on the aerodynamic force of a hovering dragonfly

The present research focuses on the timing of wing–wing interaction that benefits the aerodynamic force of a dragonfly in hovering flight at Reynolds number 1350. A 3-D numerical simulation method, called the system coupling, was utilised by implementing a two-way coupling between the transient structural and flow analysis. We further explore the aerodynamic forces produced at different phase angles on the forewing and hindwing during the hovering flight condition of a dragonfly. A pair of dragonfly wings is simulated to obtain the force generated during flapping at a 60° inclination stroke plane angle with respect to the horizontal. The hovering flight is simulated by varying the phase angle and the inter-distance between the two wings. We observe a significant enhancement in the lift (16%) of the hindwing when it flaps in-phase with the forewing and closer to the forewing, maintaining an inter-wing distance of 1.2 cm (where cm is the mean chord length). However, for the same condition, the lift of the hindwing reduces by 9% when the wings are out of phase/counterstroke flapping. These benefits and drawbacks are dependent on the timing of the interactions between the forewing and hindwing. The time of interaction of wake capture, wing–wing interaction, dipole structure and development of root vortex are examined by 2-D vorticity of the flow field and isosurface of the 3-D model dragonfly. From the isosurface, we found that the root vortex elicited at the root of the hindwing in counter-flapping creates an obstacle for the shedding of wake vortices, which results in reduction of vertical lift during the upstroke of flapping. Hence, at the supination stage, a dragonfly uses a high rotation angle for the hovering flight mode. It is observed that the system coupling method was found to be more efficient and exhibited better performance. The present numerical methodology shows a very close match to the previously reported results.

Thermo-Structural Analysis of Steam Turbine Startup With and Without Integrated Prewarming System Using Hot Air

Abstract Motivated by the urgent need for flexibility and startup capability improvements of conventional power plants in addition to extending their life cycle, General Electric provides its customers with a product to prewarm steam turbines using hot air. In this paper, the transient thermal and structural analyses of a 19-stage intermediate pressure (IP) steam turbine in various startup operating modes are discussed in detail. The presented research is based on previous investigations and utilizes a hybrid finite element method (HFEM—numerical FEM and analytical) approach to efficiently determine the time-dependent temperature distribution in the components of the steam turbine. The simulation strategy of the HFEM model applies various analytical correlations to describe heat transfer in the turbine channel. These are developed by means of extensive unsteady multistage conjugate heat transfer (CHT) simulations for both startup turbine operation with steam and prewarming operation with hot air. Moreover, the complex numerical setup of the HFEM model also considers the thermal contact resistance (TCR) on the surfaces between vane and casing as well as blades and rotor. Prior to the analysis of other turbine startup operating modes, the typical startup turbine process is calculated and validated against an experimental data as a benchmark for subsequent analysis. In addition to heat transfer correlations, the simulation of a turbine startup from cold state uses an innovative analytic pressure model to allow for a consideration of condensation effects during first phase of startup procedure. Finally, the presented thermal investigation focuses on the comparison of transient temperature fields in the turbine for different startup scenarios after prewarming with hot air and provides the subsequent structural investigation with required boundary conditions. As a result, the values of the highest stress are numerically determined and compared to the values obtained by means of cold startup simulation. The final evaluation clearly displays the technical potential and the benefits of the prewarming concept.

Pressure wave behavior and its effects on structure under In-box LOCA in a helium-cooled lead lithium blanket of hydrogen fusion reactors

The helium-cooled lead lithium (PbLi) blanket is considered as one of the candidate blanket concepts selected for the hydrogen fusion DEMO reactors and beyond, which has the advantages of simple structure, strong heat removal capacity and high tritium breeding ratio. However, due to the harsh environment such as high-energy neutron irradiation, high thermal load and great pressure gradient, there is a high possibility that one or some of the thousands of coolant channels will break in the breeding zone, which is so-called In-box Loss of Coolant Accident (In-box LOCA). When the accident occurs, the high pressure helium will rapidly inject into the lead lithium flow channel, generating a complex two-phase flow and great pressure shock effect, which may cause the peak pressure to exceed the design limit and threaten the integrity of the blanket structure. Therefore, it is of great significance to perform the transient analysis of in-box LOCA to improve the safety of the blanket and avoid the leakage of radioactive materials. In this paper, a two-way coupling model for fluid-solid interaction was established based on the ANSYS Workbench, and the model were validated through the experimental data obtained by injecting the high pressure helium gas into liquid lithium lead. Then the validated model was applied to the transient pressure wave propagation analysis and structural stress analysis of the Dual-Functional Lithium Lead (DFLL) blanket in order to explore the integrity of blanket structure under In-box LOCA. In addition, the effects of break location on pressure and structural stress was also investigated through six cases. The study found that the transient pressure in the DFLL blanket gone through three stages in any case: step rise, oscillate, and flatten out. Pressure peaks occurred during oscillations and their values were strongly dependent on the break location. The closer to the inlet/outlet, the higher the peak pressure was. The maximum pressure reached more than twice of the inlet pressure (up to ~16 MPa). As a result, the structural stress in some local areas has exceeded the allowable limits, and the corresponding suggestions for improvement have also been put forward. This study can provide guidance for safety design, operation and accident mitigation measures of helium-cooled lead lithium blankets.

Numerical investigation of thermo-mechanical properties for disc brake using light commercial vehicle

A brake is a device using which frictional resistance is applied for stopping a moving vehicle. In disc brakes, the component on which the pads are squeezed when the brake pedal is applied. Disc brakes are subjected to both mechanical and thermal stresses. The cyclic thermal stress is more significant than mechanical stress. In this study, three-disc brakes with different profiles are selected to investigate the thermo-mechanical behavior analytically and numerically. This analysis develops a three-dimensional (3D) thermo-structural coupling model, implements transient thermal Analysis and transient structural Analysis of disc brake profiles with a frictional heat. The thermo-structural problem is solved by the finite element method to get the transient temperature and thermal stress fields of the disc brake under emergency braking. Comparison between the three profiles has been made using different parameters, including the maximum temperature on the surface, equivalent thermal stress (Von-Mises), and thermal deformation. The result has shown that the having grooved profile on its surface exhibited 34Mpa of equivalent stress, whereas the solid type and the drilled type have shown 80Mpa and 57Mpa. It also shows that the grooved type brake is efficient by far more magnitude than the other two profiles. In general, the thermal stress developed and thermal deformation on the would significantly decrease when it has a profile that allows for better heat dissipation to the surrounding.

Comparison between an uncoupled one-way and two-way fluid structure interaction simulation on a super-tall slender structure

This paper presents a comprehensive analysis on a super-tall structure where a numerical approach is used to measure its structural response when subjected to turbulent wind. The aim of this study is to provide a feasible alternate approach, to the experimental multi-degree of freedom (MDOF) aeroelastic wind tunnel tests, which are commonly used in industry to estimate structural responses of super-tall structures. An innovative and time-efficient uncoupled one-way Fluid-Structure Interaction (FSI) simulation technique was used to measure the structural response. This novel method was evaluated against a commercially available two-way FSI analysis technique and validated with an experimental MDOF aeroelastic model. It is shown that the uncoupled one-way FSI analysis is capable of estimating structural responses and provides similar numerical accuracy to that of the experimental response. This performance was achieved in a total of 74clock hours which accounts for the CFD simulation and transient structural analysis calculated for eighteen different structural configurations. In comparison, the two-way FSI analysis, which uses a commercial code, took 4800clock hours to calculate for six configurations. The uncoupled one-way FSI technique also provided good correlations with experimentally observed trends such as vortex-induced resonance. In comparison the two-way FSI simulation was not as accurate due to the practical limitations (such as mesh size) that needed to be introduced in order to obtain results within a feasible time frame. Finally through validation, it is demonstrated that the proposed uncoupled one-way FSI analysis technique can provide accurate results at a feasible cost.

A New Approach to Transient Vibration Analysis of Two-Dimensional Beam Structures at Medium and High Frequencies

Abstract Transient analysis of medium-frequency (mid-frequency) and high-frequency vibrations plays an important role in the research and development of complex structures in aerospace, automobile, civil, mechanical, and ship engineering. Low-frequency analysis tools, like the finite element methods, do not work well for mid- and high-frequency problems because they require a huge number of degrees-of-freedom and consequently costly computation, and are sensitive to material properties and boundary conditions. High-frequency analysis tools, such as the statistical energy analysis (SEA) and its variations, are unsuitable for midfrequency problems because they describe the vibrational behaviors of multibody structures in a global manner and cannot provide detailed local information about displacements and internal forces. In this paper, a new method, which is called the augmented distributed transfer function method (DTFM), is proposed for transient vibration analysis of two-dimensional beam structures at medium and high frequencies. Without the need for discretization and numerical integration, the augmented DTFM consistently delivers analytical transient solutions from low to high-frequency regions. A unique feature of the proposed method is that it can provide local information about system response, such as the displacements and internal forces of a structure, at any point and in any frequency region. Additionally, the proposed method provides a platform for model reduction, by which, a balance of efficiency and accuracy in mid- and high-frequency analyses can be achieved. The proposed method is demonstrated in numerical examples.

Thermo-mechanical analysis and estimation of turbine blade tip clearance of a small gas turbine engine under transient operating conditions

Turbine blade tip clearance is one of the significant factors that influence turbine efficiency, Specific Fuel Consumption (SFC), Exhaust Gas Temperature (EGT), and emissions. Controlling these parameters in a small gas turbine engine (SGT) is a challenging task due to small blade height and viscous working environment. SGT are subjected to high-temperature gradients at the combustor outlet, which affects the turbine blade tip clearance. This paper presents the thermo-mechanical analysis of a typical SGT engine to study the blade tip clearance influenced by the deformation of turbine stage components (turbine rotor, nozzle guide vane (NGV) with integral blade shroud) during transient phases. ANSYS Workbench is used to perform transient thermal and structural analyses. The structural analysis is performed taking the material properties to be temperature-dependent. The SGT engine under consideration operates at a design speed of 45,000 rpm. Initially, steady-state thermal analysis and static structural analysis were carried out to understand the structural behaviour of the system under a thermal and centrifugal loading environment. Since different components of the engine assembly operate at different temperatures, the effects of convection and conduction at the interfaces influence the radial clearances between the static and rotating parts of the engine. A one-way coupled transient thermal-structural analysis was performed on a three-dimensional model to capture the actual behaviour of the tip clearance during transient operating conditions. Significant growth of blade and rotor was observed relative to the casing resulting in minimal clearances during these transient operations. Hence, it is important to estimate desired cold clearance, considering transient phenomena, to avoid mechanical blade rub with the shroud. It is observed that high-temperature gradients contribute primarily to the stresses and radial displacement of the rotor compared to centrifugal effects. The turbine rotor takes more time (t = 600 s) to reach steady-state temperatures compared to NGV (t = 120 s) due to the solid mass of the disc. The location and magnitude of maximum and minimum equivalent stress changes with time in NGV and rotor, and they experience maximum stress at the initial time steps compared to steady-state.