A. Pépin, T. Tkaczyk, N. O’Dowd, K. Nikbin, S. V. Chettiar
{"title":"Application of Limit Load Solutions for Engineering Critical Assessment of Embedded Flaws in Evenmatch Pipeline Girth Welds","authors":"A. Pépin, T. Tkaczyk, N. O’Dowd, K. Nikbin, S. V. Chettiar","doi":"10.1115/pvp2020-21261","DOIUrl":"https://doi.org/10.1115/pvp2020-21261","url":null,"abstract":"\u0000 Engineering Critical Assessment (ECA) is commonly undertaken to derive the acceptance criteria for girth weld flaws in rigid pipelines deployed subsea by low-strain installation methods, such as S-Lay or J-Lay, or high-strain installation methods, such as Reel-Lay. The ECA generally considers the whole load history seen by the pipeline from fabrication to the end of service, and involves fracture and fatigue assessments. Fracture, which is the main focus of this paper, is deemed to have initiated when either (i) the crack driving force, expressed in terms of the J-integral or the Crack Tip Opening Displacement (CTOD), δ, is greater than the materials resistance, or (ii) the applied load exceeds the bearing capacity of the ligament of a cracked structure, also referred to as the plastic collapse or limit load. The robustness of the ECA procedure relies on the accuracy of the assessment solutions.\u0000 Most flaws in pipeline girth welds are embedded. Unlike surface breaking flaws, embedded flaws are typically not directly assessed in a high-strain fracture ECA because the available assessment solutions are too conservative. A work-around approach is often followed, where the maximum acceptable surface breaking flaw sizes are also considered acceptable below the surface if the embedment depth is equal to or greater than half of the flaw height. Otherwise, an embedded flaw must be reclassified as a surface breaking flaw with a height equal to the sum of the embedded flaw height and embedment depth.\u0000 To enable the direct fracture assessment of embedded flaws, the authors undertook in a previous work a parametric finite-element (FE) study on the effect of the embedment depth, the crack height and the crack length on the plastic collapse load of the shorter ligament of embedded flaws. Subsequently, a new limit load solution was proposed for the fracture assessment of embedded flaws in evenmatch pipeline girth welds subjected to tension and/or bending. This closed-form solution was shown to be significantly more accurate for estimating the crack driving force and the ligament plastic collapse load than other solutions available in the literature. For some geometries, however, the predicted limit load still needs to be significantly adjusted (increased) to correctly evaluate the J-integral, in a combined tearing and collapse assessment. This suggests that further enhancement of the solution is possible.\u0000 This paper describes small-scale fracture tests which were undertaken to determine the load required to collapse a smaller ligament of embedded flaws in a modified middle crack tension (MMCT) specimen. A closed-form solution, which can also be used as a flaw reclassification criterion, is fitted to the test results and then compared to the FE-based solution. Finally, recommendations are made for the direct fracture assessment of embedded flaws in evenmatch pipeline girth welds subjected to load or displacement-controlled conditions.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122252990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Preload Assurance in Bolted Flanges With a Model and Test Based Optimized Assembly Procedure","authors":"M. Du, F. Song, Haoming Li, Ke Li","doi":"10.1115/pvp2020-21688","DOIUrl":"https://doi.org/10.1115/pvp2020-21688","url":null,"abstract":"\u0000 Bolted flanges are widely used to connect pipelines in many industries. To assure sealability of a flange, generation of proper preloads in the bolts during the assembly process is critical. However, in the existing standard practice, identical torques are typically applied to all bolts to assemble the flange. Due to elastic interactions between the bolts, tightening one bolt can alter the tensile loads in the other bolts. Hence, the resultant preloads can vary significantly. Even with an improved makeup sequence, the variation in the bolt preloads can be still substantial, as high as 60%. This could pose a risk of leakage. When the bolted flange works under non-benign conditions, such as vibration, pressure and temperature variation, the risk could become even higher.\u0000 This paper introduces a new methodology to greatly enhance the preload assurance in bolted flanges with an optimized assembly procedure, which is enabled with advanced numerical modeling. A significantly improved uniform distribution of bolt preloads is achieved by optimizing the makeup torques, which is implemented by using physical test data as input and uniformly distributed preloads as the target function. The complexity of the elastic interactions between the flange, the sealing gasket, and the bolts presents uncertainties for the numerical model for quantitative prediction of the torque distribution that is required to yield uniform resultant bolt preloads. This paper resolves this modeling limitation through iterations between modeling and testing. These iterations calibrate and finally validate the model to generate the optimized makeup torque distribution which then leads to improved bolt preload uniformity. Based on the tests conducted on two different sizes of API flanges, 3-API-15K and 5-API-10K, the final preload distribution variation has been reduced to around 30% by utilizing the optimized makeup torque distributions.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129489772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ryuta Hashidate, S. Kato, T. Onizawa, T. Wakai, N. Kasahara
{"title":"Proposal of Simulation Materials Test Technique and Their Constitutive Equations for Structural Tests and Analyses Simulating Severe Accident Conditions","authors":"Ryuta Hashidate, S. Kato, T. Onizawa, T. Wakai, N. Kasahara","doi":"10.1115/pvp2020-21397","DOIUrl":"https://doi.org/10.1115/pvp2020-21397","url":null,"abstract":"\u0000 Nuclear structure’s integrity must be confirmed under severe accident conditions. However, performing structure tests using actual steels is very difficult and expensive. Therefore, the authors conducted structure tests using the lead alloy to evaluate the structure integrity under severe accident conditions. Because the strength of the lead alloy is considerably less than that of actual steels, structure tests can be conducted under low-pressure, low-temperature conditions. To quantitatively correlate the structural response of the lead alloy to that of actual steels, finite-element analyses (FEAs) must be performed. Because the inelastic constitutive equations, namely, inelastic stress–strain relationship equation, creep rupture equation, and creep strain equation, are required to perform the inelastic FEA, the authors introduced material tests using the lead alloy and, subsequently, proposed the inelastic constitutive equations based on the material test results in a previously conducted PVP conference. However, the proposed inelastic constitutive equations could not successfully express the material characteristic of the lead alloy because of large variations observed in the material tests of the lead alloy. Furthermore, the authors observed that the material characteristic of the lead alloy could be stabilized by aging. In this study, we propose the improved inelastic constitutive equations of the lead alloy on the basis of test results newly obtained from a series of material test performed using aged alloy.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130019220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Ashrafizadeh, R. Schultz, Bo-Han Xu, P. Mertiny
{"title":"Development of a Novel Technique Using Finite Element Method to Simulate Creep in Thermoplastic Fiber Reinforced Polymer Composite Pipe Structures","authors":"H. Ashrafizadeh, R. Schultz, Bo-Han Xu, P. Mertiny","doi":"10.1115/pvp2020-21529","DOIUrl":"https://doi.org/10.1115/pvp2020-21529","url":null,"abstract":"\u0000 High strength-to-weight ratio, excellent corrosion resistance, flexibility, superior fatigue performance, and cost competitiveness have made thermoplastic fiber reinforced polymer composites (TP-FRPCs) a material of choice for the manufacture of pipe products for use in the oil and gas industry. The TP matrix not only protects the composite structure from brittle cracking caused by dynamic loads, it also provides improved flexibility for bending of pipes to enable easier field installation and reduces the requirement for pre-fabricated bent connections. Despite the attractive mechanical performance, the design, development and qualification evaluation of TP-FRPC components for a large portion relies on experimental testing. The time and expense of manufacturing new composite prototypes and performing full-scale testing emphasizes the value of a predictive modeling. But, modeling TP-FRPC structures is not a trivial task due to their anisotropic and time-dependent properties. In this study, a new technique based on the finite element method is proposed to model anisotropic time-dependent behavior of TP-FRPCs. In the proposed technique the composite mechanical properties are captured by superimposing the properties of two fictitious materials. To that end, two overlapping three-dimensional elements with similar nodes were assigned different material properties. One of the elements is assigned to have time-dependent properties to capture the viscoelastic behavior of the matrix while the other element is given linear anisotropic properties to account for the anisotropy induced by the fiber reinforcement. The model was calibrated using data from uniaxial tensile creep tests on coupons made from pure matrix resin and uniaxial tension tests on TP-FRPC tape parallel to the fiber direction. Combined time hardening creep formulation, ANSYS 19.2 implicit analysis, and ANSYS Composite PrepPost were employed to formulate the three-dimensional finite element model. The model was validated by comparison of model predictions with experimental creep strain obtained from TP FRPC tubes with ±45° fiber layups subjected to uniaxial intermediate and high stress for 8 hours. The results obtained showed that for the tubes subjected to intermediate stress, the model predicted the creep rate in the secondary region with less than 5% error. However, for tubes subjected to high stress, the model overestimated the creep rate with over 30% error. This behavior was due to large deformation at this high level of stress and inability of the model to capture fiber realignment towards the pipe longitudinal direction and, therefore, capture an increase in stiffness. Overall, comparison of the simulation results with experimental data indicated that the technique proposed can be used as a reliable model to account for deformations caused by secondary creep in the design of TP-FRPC structures as far as deformations are relatively small and limited to a certain strain threshold. Acce","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131574287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xinfang Zhang, Allan Okodi, Leichuan Tan, J. Leung, S. Adeeb
{"title":"Failure Pressure Prediction of Crack in Corrosion Defects in 2D by Using XFEM","authors":"Xinfang Zhang, Allan Okodi, Leichuan Tan, J. Leung, S. Adeeb","doi":"10.1115/pvp2020-21046","DOIUrl":"https://doi.org/10.1115/pvp2020-21046","url":null,"abstract":"\u0000 Aging pipelines may experience several different types of degradation, such as crack and corrosion, which pose serious concerns for the pipeline integrity. Hybrid flaws such as crack-in-corrosion (CIC), can be challenging to model and understand. For instance, predicting the failure pressure using the finite element method (FEM) is relatively difficult; therefore, the extended finite element method (XFEM) is introduced here. Compared to the conventional FEM, which requires extremely fine meshes and is impractical for modelling dynamic crack propagation, XFEM is computationally efficient as there is no need to update the mesh elements for tracking the crack path. This paper aims to study the applicability of XFEM in predicting the failure pressure of CIC defects in 2D. In particular, mesh size sensitivity and the effects of different CIC parameters on the final failure pressure were examined. ABAQUS v 6.14 was used for this simulation study. For simplicity, only half of the pipe was modelled assuming symmetry around the horizontal plane. A CIC defect was placed at the exterior of the pipe. The corroded area was assumed to be semi-elliptical, and the crack was simulated as a longitudinal crack. In this paper, failure criterion was satisfied when the crack has propagated to the last element. Several models were built in which the length and width of the elements at the crack tip were changed. An optimum mesh size was determined and was applied subsequently in several other models to study the impacts of crack depths, corroded area widths, and corrosion profiles. The results showed that when the total defect depth was fixed at 50% of the wall thickness, the failure pressure decreased with increasing the crack depth, while both corroded area width and corrosion profile only have a secondary effect on the failure pressure. In addition, the failure pressure of a CIC defect was bound between that of a crack-only defect and a corrosion-only defect. When the depth of the crack is higher than 50% of the total defect area, the CIC defect can be treated as a crack only defect with a crack depth equal to the total defect depth.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132995724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Heramb P. Mahajan, M. Elbakhshwan, B. Beihoff, T. Hassan
{"title":"Mechanical and Microstructural Characterization of Diffusion Bonded 800H","authors":"Heramb P. Mahajan, M. Elbakhshwan, B. Beihoff, T. Hassan","doi":"10.1115/pvp2020-21502","DOIUrl":"https://doi.org/10.1115/pvp2020-21502","url":null,"abstract":"\u0000 Compact heat exchangers have high compactness and efficiency, which is achieved by joining a stack of chemically etched channeled plates through diffusion bonding. In the diffusion bonding process, compressive stress is applied on plates at elevated temperatures for a specified period. These conditions lead to atomic diffusion, which results in the joining of all plates into a monolithic block. The diffusion bonding temperatures are above recrystallization temperatures, which changes the mechanical and microstructural properties of the bonded metal. Hence, diffusion bonded material needs mechanical and microstructural property evaluation. In this study, Alloy 800H is selected to study the influence of the diffusion bonding process on mechanical and microstructure properties of base metal. A series of tensile, fatigue, creep, and creep-fatigue experiments are conducted on base metal 800H (BM 800H) and diffusion bonded 800H (DB 800H) to explore the mechanical properties. Microstructure evolution during diffusion bonding is studied and presented in the paper. The mechanical and microstructural observations indicated ductile fracture at room temperature and brittle failure with bond delamination at elevated temperatures. The microstructure evolution during diffusion bonding is studied through tensile, fatigue, creep and creep-fatigue tests, and the implied root causes for the mechanical property changes are investigated. Efforts are made to correlate the microstructure change with mechanical property change in DB 800H.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129618775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Comparison of the Criteria for Ratcheting in ASME VIII-2 and Methods Given by C-TDF","authors":"Liping Wan, Wangping Dong","doi":"10.1115/pvp2020-21156","DOIUrl":"https://doi.org/10.1115/pvp2020-21156","url":null,"abstract":"\u0000 Ratcheting assessment by elastic-plastic stress analysis is presented in ASME VIII-2, paragraph 5.5.7. There are three criteria. The first one is strict in engineering design. It’s hard for most of structures to satisfy it. If the plastic strain in the structure is zero, it means that the material is not fully utilized and maybe the structure is unreasonable. Therefore, the second and third criteria are used much more. The first one and the third one can be observed directly and judged accurately by the finite element analysis results. The second one demands an elastic core in the primary-load-bearing boundary. It could be easily observed when the structure is axisymmetric, but hard to judge in the 3D structure.\u0000 Okamoto in Committee on Three Dimensional Finite Element Stress Evaluation (C-TDF) has studied two thermal stress ratchet criteria: evaluating variations in the plastic strain increments and evaluating variations in the elastic core region, which can accurately assess ratcheting. Recent years, based on the criteria above, more researches have been performed by engineers not only from C-TDF but from all over the world.\u0000 In this work, several two-dimensional structures and three-dimensional structures under particular load and displacement boundaries are performed by using finite element software ANSYS, aiming to compare the similarities and differences between the criteria in ASME VIII-2, 5.5.7.2 and those given by C-TDF. The assessment of these structures presented in this work will help engineers understand the realization of the criteria and methods in engineering design, especially how to utilize the results from ANSYS.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133003939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effect of Piping System Vibration (FIV, AIV, PIV) on Pipe Support Loads","authors":"E. Appiah, P. Wiseman","doi":"10.1115/pvp2020-21301","DOIUrl":"https://doi.org/10.1115/pvp2020-21301","url":null,"abstract":"\u0000 Integrity of a piping system is a prerequisite for personnel safety and operational reliability in industries where pipelines are critical means of transferring products from one process point to the other, such as power plants, refinery plants, and chemical industries. An essential aspect of designing a reliable piping system is to design supports of suitable load carrying capacity. This also depends on accurate determination of expected support loads including loads due to vibration of the system. Piping design codes such as ASME B31.3 and B31.1 provide a general framework but do not address vibration and its impact from a detailed perspective. In many situations, the potential impact of vibration is overlooked during support load determination. In recent piping system construction, the effect of vibration has increased due to increase in fluid flow rates and use of high strength thin wall materials. Common factors that contribute to vibration include: turbulent flow (flow induced vibration, FIV), relief valve operation (acoustic induced vibration, AIV), rotating and reciprocating equipment (pulsation induced vibrations, PIV). The effect of vibration depends on the strength of excitation and the flexibility of the piping system. As vibration of the piping system increases, loads transfer to the pipe supports also increase. Catastrophic failure of a piping system can occur if its natural frequency lock-in with the frequency of the excitation source. For holistic system integrity, the loads induced due to vibrations need to be accounted for in the support design. In this paper, we investigate the contributions of the various vibration loads in a piping system, the effect of neglecting the various vibration loads on the system integrity, and an empirical method to readily determine the vibration loads to reduce cost and time require in support design processes.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129230044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Novel Assessment Method for Wrinkle Defects in Composites","authors":"Chuanchuan Shen, Li Ma, Jinyang Zheng","doi":"10.1115/pvp2020-21177","DOIUrl":"https://doi.org/10.1115/pvp2020-21177","url":null,"abstract":"\u0000 Fiber reinforced composite structures have been increasingly used in the field of pressure vessels and piping. Various process-induced defects of composite structures are accumulated during their manufacture processes for the variations of environment temperature and humidity, pre-stress of fiber and curing temperature. Wrinkle defect is one of the most frequently encountered defects in fiber reinforced composite structures. In this paper, a new method for detecting wrinkle defects based on the relation of the displacement fields between flawed and flawless areas is proposed. The orthotropic finite element analysis codes combined with wrinkle model were developed based on Matlab platform to predict structural responses of laminates under three different loading types, including transverse compression, axial tension and bending. The effective elastic moduli disturbed by wrinkles were determined based on a mesomechanics model and a two-step homogenization procedure. Two different wrinkle models including definite and heterogeneous distributed models were considered. It is found that the out-of-plane displacement obviously increases at the wrinkle region under the axial load. The fluctuant displacement fields under axial tensile load can be clearly observed when the heterogeneity wrinkle model is considered. However, the transverse compression cannot produce any displacement distortion. All the results bring us a new idea of non-destructive evaluation for composites, wherein the defects that mainly weakening the stiffness can be detected by measuring the displacement distribution under some specified loads.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126562665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. M. Nasrekani, Shymal Shivneel Kumar, Sumesh Narayan
{"title":"Structural Dynamic Modification of Cylindrical Shells With Variable Thickness","authors":"F. M. Nasrekani, Shymal Shivneel Kumar, Sumesh Narayan","doi":"10.1115/pvp2020-21118","DOIUrl":"https://doi.org/10.1115/pvp2020-21118","url":null,"abstract":"\u0000 In this paper, the effects of some geometrical parameters on dynamic behavior of cylindrical shells with constant and variable thickness are studied. The equation of motion for the shell with constant thickness is extracted based on classical shell theory using Hamilton’s principle. These equations which are a system of coupled partial differential equations are solved analytically and the natural frequency is determined for cylindrical shells with constant thickness. The natural frequency for cylindrical shells with variable thickness is determined using finite element method by employing ANSYS. The results are compared and the effect of different geometric parameters such as length, thickness, and radius on natural frequency is discussed. The specific ranges for geometric parameters have been determined in which there is no significant difference between shells with constant or variable thickness. Cylindrical shells with variable thickness have better stress and strain distribution and optimum weight, in compare with the shells with constant thickness and it is important to know in which ranges of dimensions and geometrical parameters, there are some significant differences between their mechanical properties such as natural frequency. The results are compared with some other references.","PeriodicalId":150804,"journal":{"name":"Volume 3: Design and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126765257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}