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Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness

Yıl 2025, Cilt: 25 Sayı: 1, 206 - 214

Sinan Maraş , Çağın Bolat

Öz

Additive manufacturing, commonly referred to as 3D printing, stands out for its ability to rapidly produce complex objects, contrasting with conventional manufacturing techniques such as machining, forging, welding, and powder sintering. Today, additive manufacturing is often used to create functional and lightweight final products. Therefore, free vibration analysis is crucial in the design process of structures composed of such materials. The objective of this study is to investigate the effects of variations in parameters such as opening angle, curvature radius, and thickness of 3D-printed curved beams made of PET-G, PLA, and ABS materials, which have clamped-clamped boundary conditions, on the in-plane vibration characteristics of the structure. The vibration parameters of the curved beam structure, modeled using the ANSYS finite element program, have been determined. Numerical results have been compared with findings from the literature to validate the accuracy and applicability of the proposed model. Consequently, it has been found that changes in the material and geometric properties of 3D-printed curved beams significantly influence the natural frequencies of the structure.

Anahtar Kelimeler

Free vibration Curved beams Additive Manufacturing Finite element method

Kaynakça

  • Bolat, Ç., Ergene, B. and Ispartalı, H., 2023. A comparative analysis of the effect of post production treatments and layer thickness on tensile and impact properties of additively manufactured polymers. International Polymer Processing, 38, 244-256. https://doi.org/10.1515/ipp-2022-4267
  • Bolat, Ç., and Ergene, B., 2023. An Experimental Effort on Impact Properties of Polylactic Acid Samples Manufactured by Additive Manufacturing. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 11, 998-1013. https://doi.org/10.29130/dubited.1075259
  • Boron, P., Chelmecki, J., Dulinska, J.M., Jurkowska, N., Ratajewicz, B., Stecz, P. and Tatara, T. 2023. On the Possibility of Using 3D Printed Polymer Models for Modal Tests on Shaking Tables: Linking Material Properties Investigations, Field Experiments, Shaking Table Tests, and FEM Modeling. Materials, 16, 1471. https://doi.org/10.3390/ma16041471
  • Cao, H., Bao, W., Bai, C., Yan, Q., Wang, B., Yang, Y. and Fan, H., 2023. Manufacturing and mechanical testing of curved sandwich beams with zero‐Poisson's ratio honeycomb cores. Polymer Composites, 44, 8849-8856. https://doi.org/10.1002/pc.27742
  • Cuan-Urquizo, E., Martínez-Magallanes, M., Crespo-Sánchez, S.E., Gómez-Espinosa, A., Olvera-Silva, O. and Roman-Flores, A., 2019. Additive manufacturing and mechanical properties of lattice-curved structures. Rapid Prototyping Journal, 25, 895-903. https://doi.org/10.1108/RPJ-11-2018-0286
  • De Agostinis, M., Olmi, G. and Arcidiacono, G., 2021. Mechanical characterization of parts fabricated by additive manufacturing. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235, 1701-1702. https://doi.org/10.1177/0954406220948759
  • Depboylu, F.N., Poyraz, Ö., Yasa, E. and Korkusuz, F., 2023. Lazer-Toz Yatağında Füzyon ile Üretilen Ti6Al4V Gyroid Yapıların Basma Dayanımlarının Nümerik Modellenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23, 270-283. https://doi.org/10.35414/akufemubid.1171673
  • Erdoğan, H., Sayrugaç, A., and Yalçın, B., 2023. Tarımsal İlaçlamada X tipi Katlanabilen ve Geleneksel Kanatlarda Oluşan Gerilme-Gerinimin Tahmini ve Taguchi Analizi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23, 797-810. https://doi.org/10.35414/akufemubid.1264988
  • Ergene, B., Atlıhan, G. and Pinar, A.M., 2023. Experimental and finite element analyses on the vibration behavior of 3D-printed PET-G tapered beams with fused filament fabrication. Multidiscipline Modeling in Materials and Structures, 19, 634-651. https://doi.org/10.1108/MMMS-11-2022-0265
  • Ergene, B., and Bolat, Ç., 2023. Simulation of fused deposition modeling of glass fiber reinforced ABS impact samples: The Effect of fiber ratio, infill rate, and infill pattern on warpage and residual stresses. Hittite Journal of Science and Engineering, 10, 21-3. https://doi.org/10.17350/HJSE19030000287
  • Gebhard, L., Mata-Falcón, J., Anton, A., Dillenburger, B. and Kaufmann, W., 2021. Structural behaviour of 3D printed concrete beams with various reinforcement strategies. Engineering Structures, 240, 112380. https://doi.org/10.1016/j.engstruct.2021.112380
  • Grammatikopoulos, A., Banks, J. and Temarel, P., 2020. Prediction of the vibratory properties of ship models with realistic structural configurations produced using additive manufacturing. Marine Structures, 73, 102801. https://doi.org/10.1016/j.marstruc.2020.102801
  • Guerra Silva, R., Torres, M.J., Zahr Viñuela, J. and Zamora, Z.G., 2021. Manufacturing and characterization of 3D miniature polymer lattice structures using fused filament fabrication. Polymers, 13, 635. https://doi.org/10.3390/polym13040635
  • Günyar, A., Öztürk, H. and Sabuncu, M., 2012. Tabakalı Eğri Çubukların Dinamik Kararlılık Analizi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 14, 43-55.
  • Hajianmaleki, M. and Qatu, M.S., 2012. Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions. Composites Part B: Engineering, 43, 1767-1775. https://doi.org/10.1016/j.compositesb.2012.01.019
  • Hsueh, M.H., Lai, C.J., Wang, S.H., Zeng, Y.S., Hsieh, C.H., Pan, C.Y. and Huang, W.C. 2021. Effect of printing parameters on the thermal and mechanical properties of 3d-printed pla and petg, using fused deposition modeling. Polymers, 13, 1758. https://doi.org/10.3390/polym13111758
  • Kannan, S., Manapaya, A. and Selvaraj, R., 2023. Frequency and deflection responses of 3D‐printed carbon fiber reinforced polylactic acid composites: Theoretical and experimental verification. Polymer Composites, 44, 4095-4108. https://doi.org/10.1002/pc.27382
  • Layani, M., X. Wang, and Magdassi, S., 2018. Novel materials for 3D printing by photopolymerization. Advanced Materials, 30, 1706344. https://doi.org/10.1002/adma.201706344
  • Ma, Q., Rejab, M., Kumar, A.K., Fu, H., Kumar, N.M. and J. Tang, J., 2021. Effect of infill pattern, density and material type of 3D printed cubic structure under quasi-static loading. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235, 4254-4272. https://doi.org/10.1177/0954406220971667
  • Ma, Q., Cheng, H., Jang, K.I., Luan, H., Hwang, K.C., Rogers, J.A., Huang, Y. and Zhang, Y., 2016. A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures. Journal of the Mechanics and Physics of Solids, 90, 179-202. https://doi.org/10.1016/j.jmps.2016.02.012
  • Maidin, S., Ting, K. and Sim, Y., 2022. Investigation of mechanical properties of recycled ABS printed with open source FDM printer integrated with ultrasound vibration. International Journal of Integrated Engineering, 14, 57-63
  • Malekzadeh, P. and Setoodeh, A., 2009. DQM in-plane free vibration of laminated moderately thick circular deep arches. Advances in Engineering Software, 40, 798-803. https://doi.org/10.1016/j.advengsoft.2009.01.011
  • Mao, H., G. Yu, W. Liu, and Xu, T., 2020. Out‐of‐Plane free vibration and forced harmonic response of a curved beam. Shock and Vibration, 2020, 8891585. https://doi.org/10.1155/2020/8891585
  • Merkt, S., Hinke, C., Bültmann, J., Brandt, M. and Xie, Y., 2015. Mechanical response of TiAl6V4 lattice structures manufactured by selective laser melting in quasistatic and dynamic compression tests. Journal of Laser Applications, 27. https://doi.org/10.2351/1.4898835
  • Mishra, D. and Das, A.K., 2021. Linear model analysis of fused deposition modeling process parameters for obtaining the maximum tensile strength in acrylonitrile butadiene styrene (ABS) and carbon fiber polylactic acid (PLA) materials. Multidiscipline Modeling in Materials and Structures, 17, 915-930. https://doi.org/10.1108/MMMS-09-2020-0239
  • Najafi, M., Ahmadi, H. and Liaghat, G., 2022. Investigation on the flexural properties of sandwich beams with auxetic core. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44, 61. https://doi.org/10.1007/s40430-022-03368-3
  • Özyiğit, H.A., M. Yetmez, and Uzun, U. 2017. Out‐of‐plane vibration of curved uniform and tapered beams with additional mass. Mathematical Problems in Engineering, 2017, 8178703. https://doi.org/10.1155/2017/8178703
  • Parpala, R.C., Popescu, D. and Pupaza, C., 2021. Infill parameters influence over the natural frequencies of ABS specimens obtained by extrusion-based 3D printing. Rapid Prototyping Journal, 27, 1273-1285. https://doi.org/10.1108/RPJ-05-2020-0110
  • Ramian, J., Ramian, J. and Dziob, D., 2021. Thermal deformations of thermoplast during 3D printing: warping in the case of ABS. Materials, 14, 7070. https://doi.org/10.3390/ma14227070
  • Russo, A., Sellitto, A., Saputo, S., Acanfora, V. and Riccio, A., 2019. A numerical–analytical approach for the preliminary design of thin-walled cylindrical shell structures with elliptical cut-outs. Aerospace, 6, 52. https://doi.org/10.3390/aerospace6050052
  • Stano, G. and Percoco, G., 2021. Additive manufacturing aimed to soft robots fabrication: A review. Extreme Mechanics Letters, 42, 101079. https://doi.org/10.1016/j.eml.2020.101079
  • Süsler, S. and Kazancı, Z., 2023. Delamination Strength Comparison of Additively Manufactured Composite Curved Beams Using Continuous Fibers. Polymers, 15, 3928. https://doi.org/10.3390/polym15193928
  • Taşkin, M. and Demir, Ö., 2023. Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core. Engineering Computations. 40, 538-563. https://doi.org/10.1108/EC-04-2022-0269
  • Wang, Y., 2023. Finite element mesh refinement for in-plane and out-of-plane vibration of variable geometrical Timoshenko beams based on superconvergent vibration modes. Engineering Computations, 2023. 40, 22-40. https://doi.org/10.1108/EC-01-2022-0015
  • Yang, C., Tian, X., Liu, T., Cao, Y. and Li, D., 2017. 3D printing for continuous fiber reinforced thermoplastic composites: mechanism and performance. Rapid Prototyping Journal, 23, 209-215. https://doi.org/10.1108/RPJ-08-2015-0098
  • Yao, T., Deng, Z., Zhang, K., and Li, S., 2019. A method to predict the ultimate tensile strength of 3D printing polylactic acid (PLA) materials with different printing orientations. Composites Part B: Engineering, 163, 393-402. https://doi.org/10.1016/j.compositesb.2019.01.025
  • Yılmaz, C., Ali, H.Q., and Yıldız, M., 2022. Application of Classical Lamination Theory to Fused Deposition Method 3-D Printed Plastics and Full Field Surface Strain Mapping. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi,22, 342-352. https://doi.org/10.35414/akufemubid.1018774
  • Zhang, X., P. Sun, Y. Zhang, F. Wang, Y. Tu, Y. Ma, and Zhang, C., 2024. Design and Optimization of 3D-Printed Variable Cross-Section I-Beams Reinforced with Continuous and Short Fibers. Polymers, 16, 684. https://doi.org/10.3390/polym16050684

3B Baskı ile Üretilen ABS, PET-G ve PLA Eğrisel Kirişlerin Serbest Titreşim Analizi: Açılma Açısı, Eğrilik Yarıçapı ve Parça Kalınlığının Etkileri

Yıl 2025, Cilt: 25 Sayı: 1, 206 - 214

Sinan Maraş , Çağın Bolat

Öz

Yaygın olarak kullanılan üç boyutlu (3B) baskı şeklinde adlandırılan eklemeli üretim, işleme, dövme, kaynak ve toz sinterleme gibi geleneksel üretim tekniklerinin aksine, karmaşık nesneleri hızla üretme kabiliyeti ile öne çıkmaktadır. Günümüzde eklemeli üretim, işlevsel ve hafif son ürünler oluşturmak için sıklıkla kullanılmaktadır. Bu nedenle, bu tür malzemelerden oluşan yapıların tasarım sürecinde serbest titreşim analizi büyük önem taşımaktadır. Bu çalışmanın amacı, kelepçeli-kenetlenmiş sınır koşullarına sahip PET-G, PLA ve ABS malzemelerinden yapılmış 3D yazdırılmış eğrisel kirişlerin açılma açısı, eğrilik yarıçapı ve kalınlık gibi parametrelerdeki değişikliklerin yapının düzlem içi titreşim karakteristikleri üzerindeki etkilerini araştırmaktır. ANSYS sonlu elemanlar programı kullanılarak modellenen eğrisel kiriş yapısının titreşim parametreleri belirlenmiştir. Önerilen modelin doğruluğunu ve uygulanabilirliğini doğrulamak için sayısal sonuçlar literatürdeki bulgularla karşılaştırılmıştır. Sonuç olarak, 3D yazdırılmış eğrisel kirişlerin malzeme ve geometrik özelliklerindeki değişikliklerin yapının doğal frekanslarını önemli ölçüde etkilediği bulunmuştur.

Anahtar Kelimeler

Serbest titreşim Eğri kirişler Eklemeli imalat Sonlu elemanlar yöntemi

Kaynakça

  • Bolat, Ç., Ergene, B. and Ispartalı, H., 2023. A comparative analysis of the effect of post production treatments and layer thickness on tensile and impact properties of additively manufactured polymers. International Polymer Processing, 38, 244-256. https://doi.org/10.1515/ipp-2022-4267
  • Bolat, Ç., and Ergene, B., 2023. An Experimental Effort on Impact Properties of Polylactic Acid Samples Manufactured by Additive Manufacturing. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 11, 998-1013. https://doi.org/10.29130/dubited.1075259
  • Boron, P., Chelmecki, J., Dulinska, J.M., Jurkowska, N., Ratajewicz, B., Stecz, P. and Tatara, T. 2023. On the Possibility of Using 3D Printed Polymer Models for Modal Tests on Shaking Tables: Linking Material Properties Investigations, Field Experiments, Shaking Table Tests, and FEM Modeling. Materials, 16, 1471. https://doi.org/10.3390/ma16041471
  • Cao, H., Bao, W., Bai, C., Yan, Q., Wang, B., Yang, Y. and Fan, H., 2023. Manufacturing and mechanical testing of curved sandwich beams with zero‐Poisson's ratio honeycomb cores. Polymer Composites, 44, 8849-8856. https://doi.org/10.1002/pc.27742
  • Cuan-Urquizo, E., Martínez-Magallanes, M., Crespo-Sánchez, S.E., Gómez-Espinosa, A., Olvera-Silva, O. and Roman-Flores, A., 2019. Additive manufacturing and mechanical properties of lattice-curved structures. Rapid Prototyping Journal, 25, 895-903. https://doi.org/10.1108/RPJ-11-2018-0286
  • De Agostinis, M., Olmi, G. and Arcidiacono, G., 2021. Mechanical characterization of parts fabricated by additive manufacturing. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235, 1701-1702. https://doi.org/10.1177/0954406220948759
  • Depboylu, F.N., Poyraz, Ö., Yasa, E. and Korkusuz, F., 2023. Lazer-Toz Yatağında Füzyon ile Üretilen Ti6Al4V Gyroid Yapıların Basma Dayanımlarının Nümerik Modellenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23, 270-283. https://doi.org/10.35414/akufemubid.1171673
  • Erdoğan, H., Sayrugaç, A., and Yalçın, B., 2023. Tarımsal İlaçlamada X tipi Katlanabilen ve Geleneksel Kanatlarda Oluşan Gerilme-Gerinimin Tahmini ve Taguchi Analizi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23, 797-810. https://doi.org/10.35414/akufemubid.1264988
  • Ergene, B., Atlıhan, G. and Pinar, A.M., 2023. Experimental and finite element analyses on the vibration behavior of 3D-printed PET-G tapered beams with fused filament fabrication. Multidiscipline Modeling in Materials and Structures, 19, 634-651. https://doi.org/10.1108/MMMS-11-2022-0265
  • Ergene, B., and Bolat, Ç., 2023. Simulation of fused deposition modeling of glass fiber reinforced ABS impact samples: The Effect of fiber ratio, infill rate, and infill pattern on warpage and residual stresses. Hittite Journal of Science and Engineering, 10, 21-3. https://doi.org/10.17350/HJSE19030000287
  • Gebhard, L., Mata-Falcón, J., Anton, A., Dillenburger, B. and Kaufmann, W., 2021. Structural behaviour of 3D printed concrete beams with various reinforcement strategies. Engineering Structures, 240, 112380. https://doi.org/10.1016/j.engstruct.2021.112380
  • Grammatikopoulos, A., Banks, J. and Temarel, P., 2020. Prediction of the vibratory properties of ship models with realistic structural configurations produced using additive manufacturing. Marine Structures, 73, 102801. https://doi.org/10.1016/j.marstruc.2020.102801
  • Guerra Silva, R., Torres, M.J., Zahr Viñuela, J. and Zamora, Z.G., 2021. Manufacturing and characterization of 3D miniature polymer lattice structures using fused filament fabrication. Polymers, 13, 635. https://doi.org/10.3390/polym13040635
  • Günyar, A., Öztürk, H. and Sabuncu, M., 2012. Tabakalı Eğri Çubukların Dinamik Kararlılık Analizi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 14, 43-55.
  • Hajianmaleki, M. and Qatu, M.S., 2012. Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions. Composites Part B: Engineering, 43, 1767-1775. https://doi.org/10.1016/j.compositesb.2012.01.019
  • Hsueh, M.H., Lai, C.J., Wang, S.H., Zeng, Y.S., Hsieh, C.H., Pan, C.Y. and Huang, W.C. 2021. Effect of printing parameters on the thermal and mechanical properties of 3d-printed pla and petg, using fused deposition modeling. Polymers, 13, 1758. https://doi.org/10.3390/polym13111758
  • Kannan, S., Manapaya, A. and Selvaraj, R., 2023. Frequency and deflection responses of 3D‐printed carbon fiber reinforced polylactic acid composites: Theoretical and experimental verification. Polymer Composites, 44, 4095-4108. https://doi.org/10.1002/pc.27382
  • Layani, M., X. Wang, and Magdassi, S., 2018. Novel materials for 3D printing by photopolymerization. Advanced Materials, 30, 1706344. https://doi.org/10.1002/adma.201706344
  • Ma, Q., Rejab, M., Kumar, A.K., Fu, H., Kumar, N.M. and J. Tang, J., 2021. Effect of infill pattern, density and material type of 3D printed cubic structure under quasi-static loading. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235, 4254-4272. https://doi.org/10.1177/0954406220971667
  • Ma, Q., Cheng, H., Jang, K.I., Luan, H., Hwang, K.C., Rogers, J.A., Huang, Y. and Zhang, Y., 2016. A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures. Journal of the Mechanics and Physics of Solids, 90, 179-202. https://doi.org/10.1016/j.jmps.2016.02.012
  • Maidin, S., Ting, K. and Sim, Y., 2022. Investigation of mechanical properties of recycled ABS printed with open source FDM printer integrated with ultrasound vibration. International Journal of Integrated Engineering, 14, 57-63
  • Malekzadeh, P. and Setoodeh, A., 2009. DQM in-plane free vibration of laminated moderately thick circular deep arches. Advances in Engineering Software, 40, 798-803. https://doi.org/10.1016/j.advengsoft.2009.01.011
  • Mao, H., G. Yu, W. Liu, and Xu, T., 2020. Out‐of‐Plane free vibration and forced harmonic response of a curved beam. Shock and Vibration, 2020, 8891585. https://doi.org/10.1155/2020/8891585
  • Merkt, S., Hinke, C., Bültmann, J., Brandt, M. and Xie, Y., 2015. Mechanical response of TiAl6V4 lattice structures manufactured by selective laser melting in quasistatic and dynamic compression tests. Journal of Laser Applications, 27. https://doi.org/10.2351/1.4898835
  • Mishra, D. and Das, A.K., 2021. Linear model analysis of fused deposition modeling process parameters for obtaining the maximum tensile strength in acrylonitrile butadiene styrene (ABS) and carbon fiber polylactic acid (PLA) materials. Multidiscipline Modeling in Materials and Structures, 17, 915-930. https://doi.org/10.1108/MMMS-09-2020-0239
  • Najafi, M., Ahmadi, H. and Liaghat, G., 2022. Investigation on the flexural properties of sandwich beams with auxetic core. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44, 61. https://doi.org/10.1007/s40430-022-03368-3
  • Özyiğit, H.A., M. Yetmez, and Uzun, U. 2017. Out‐of‐plane vibration of curved uniform and tapered beams with additional mass. Mathematical Problems in Engineering, 2017, 8178703. https://doi.org/10.1155/2017/8178703
  • Parpala, R.C., Popescu, D. and Pupaza, C., 2021. Infill parameters influence over the natural frequencies of ABS specimens obtained by extrusion-based 3D printing. Rapid Prototyping Journal, 27, 1273-1285. https://doi.org/10.1108/RPJ-05-2020-0110
  • Ramian, J., Ramian, J. and Dziob, D., 2021. Thermal deformations of thermoplast during 3D printing: warping in the case of ABS. Materials, 14, 7070. https://doi.org/10.3390/ma14227070
  • Russo, A., Sellitto, A., Saputo, S., Acanfora, V. and Riccio, A., 2019. A numerical–analytical approach for the preliminary design of thin-walled cylindrical shell structures with elliptical cut-outs. Aerospace, 6, 52. https://doi.org/10.3390/aerospace6050052
  • Stano, G. and Percoco, G., 2021. Additive manufacturing aimed to soft robots fabrication: A review. Extreme Mechanics Letters, 42, 101079. https://doi.org/10.1016/j.eml.2020.101079
  • Süsler, S. and Kazancı, Z., 2023. Delamination Strength Comparison of Additively Manufactured Composite Curved Beams Using Continuous Fibers. Polymers, 15, 3928. https://doi.org/10.3390/polym15193928
  • Taşkin, M. and Demir, Ö., 2023. Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core. Engineering Computations. 40, 538-563. https://doi.org/10.1108/EC-04-2022-0269
  • Wang, Y., 2023. Finite element mesh refinement for in-plane and out-of-plane vibration of variable geometrical Timoshenko beams based on superconvergent vibration modes. Engineering Computations, 2023. 40, 22-40. https://doi.org/10.1108/EC-01-2022-0015
  • Yang, C., Tian, X., Liu, T., Cao, Y. and Li, D., 2017. 3D printing for continuous fiber reinforced thermoplastic composites: mechanism and performance. Rapid Prototyping Journal, 23, 209-215. https://doi.org/10.1108/RPJ-08-2015-0098
  • Yao, T., Deng, Z., Zhang, K., and Li, S., 2019. A method to predict the ultimate tensile strength of 3D printing polylactic acid (PLA) materials with different printing orientations. Composites Part B: Engineering, 163, 393-402. https://doi.org/10.1016/j.compositesb.2019.01.025
  • Yılmaz, C., Ali, H.Q., and Yıldız, M., 2022. Application of Classical Lamination Theory to Fused Deposition Method 3-D Printed Plastics and Full Field Surface Strain Mapping. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi,22, 342-352. https://doi.org/10.35414/akufemubid.1018774
  • Zhang, X., P. Sun, Y. Zhang, F. Wang, Y. Tu, Y. Ma, and Zhang, C., 2024. Design and Optimization of 3D-Printed Variable Cross-Section I-Beams Reinforced with Continuous and Short Fibers. Polymers, 16, 684. https://doi.org/10.3390/polym16050684
Toplam 38 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliği (Diğer)
Bölüm Makaleler
Yazarlar

Sinan Maraş 0000-0002-2651-374X

Çağın Bolat 0000-0002-4356-4696

Erken Görünüm Tarihi 28 Ocak 2025
Yayımlanma Tarihi
Gönderilme Tarihi 19 Temmuz 2024
Kabul Tarihi 14 Eylül 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 25 Sayı: 1

Kaynak Göster

APA Maraş, S., & Bolat, Ç. (2025). Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 25(1), 206-214.
AMA Maraş S, Bolat Ç. Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. Ocak 2025;25(1):206-214.
Chicago Maraş, Sinan, ve Çağın Bolat. “Free Vibration Analysis of 3D-Printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 25, sy. 1 (Ocak 2025): 206-14.
EndNote Maraş S, Bolat Ç (01 Ocak 2025) Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 25 1 206–214.
IEEE S. Maraş ve Ç. Bolat, “Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 25, sy. 1, ss. 206–214, 2025.
ISNAD Maraş, Sinan - Bolat, Çağın. “Free Vibration Analysis of 3D-Printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 25/1 (Ocak 2025), 206-214.
JAMA Maraş S, Bolat Ç. Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2025;25:206–214.
MLA Maraş, Sinan ve Çağın Bolat. “Free Vibration Analysis of 3D-Printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 25, sy. 1, 2025, ss. 206-14.
Vancouver Maraş S, Bolat Ç. Free Vibration Analysis of 3D-printed ABS, PET-G and PLA Curved Beam: Effects of Opening Angle, Curvature Radius, and Part Thickness. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2025;25(1):206-14.
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