Eihab Abdel-Rahman

Eihab Abdel-Rahman is Professor of Systems Design Engineering. His research interests are in the nonlinear dynamics of electromechanical and biomechanical systems, particularly Micro- and Nano-Electronic Mechanical Systems (MEMS/NEMS) sensors, actuators, and energy harvesters as well as workplace ergonomics.

• Sensors and Actuator
• Micro-electromechanical systems
• Nano-electromechanical systems
• Energy Harvesting / Micro-Power Generators
• Biomechanics
• Ergonomics
• Vibrations and control
• Nonlinear Systems
• Nonlinear Dynamics
• Complex Systems
• Bifurcations and Chaos

• 1997, Doctorate PhD, University of Toledo, United States
• 1991, Master's MS, University of Toledo, United States
• 1988, Bachelor's BS, Kuwait University, Kuwait

• BME 451 - Biomechanics of Human Movement
  • Taught in
• BME 551 - Biomechanics of Human Movement
  • Taught in
• NANO 605 - Design of MEMS and NEMS
  • Taught in
• NANO 702 - Nanotechnology Tools
  • Taught in
• SYDE 182 - Physics 2: Dynamics
  • Taught in
• SYDE 683 - Design of MEMS and NEMS
  • Taught in

* Only courses taught in the past 5 years are displayed.

• Alneamy, Ayman and Khater, Mahmoud and Alghamdi, Majed and Abdel-Aziz, Ahmed and Heppler, Gleen and Abdel-Rahman, Eihab M, Large Oscillation of Electrostatically Actuated Curved Beams, Journal of Micromechanics and Microengineering, , 2020
• Kayaharman, Muhammed and Das, Taylan and Seviora, Gregory and Saritas, Resul and Abdel-Rahman, Eihab and Yavuz, Mustafa, Long-Term Stability of Ferroelectret Energy Harvesters, Materials, 42, 2020
• Ryu, JuHyeong and Alwasel, Abdullatif and Haas, Carl T and Abdel-Rahman, Eihab, Analysis of Relationships between Body Load and Training, Work Methods, and Work Rate: Overcoming the Novice Mason’s Risk Hump, Journal of Construction Engineering and Management, 04020097, 2020
• Alneamy, Ayman M and Khater, Mahmoud E and Abdel-Aziz, Ahmed K and Heppler, Glenn R and Abdel-Rahman, Eihab M, Electrostatic arch micro-tweezers, International Journal of Non-Linear Mechanics, 103298, 2020
• Arabi, Mohamed and Gopanchuk, Mary and Abdel-Rahman, Eihab and Yavuz, Mustafa, Measurement of In-Plane Motions in MEMS, Sensors, 3594, 2020
• Al-Ghamdi, MS and Khater, ME and Abdel-Rahman, EM and Nepomuceno, EG, Quasi-Static pull-in: an instability in electrostatic Actuators, Scientific Reports, 1, 2020
• Novodchuk, I and Kayaharman, M and Ibrahim, K and Al-Tuairqi, S and Irannejad, M and Abdel-Rahman, E and Sanderson, J and Bajcsy, M and Yavuz, M, B/N co-doped graphene oxide gel with extremely-high mobility and ION/IOFF for large-area field effect transistors, Carbon, 624, 2020
• Meesala, Vamsi C and Hajj, Muhammad R and Abdel-Rahman, Eihab, Bifurcation-based MEMS mass sensors, International Journal of Mechanical Sciences, 105705, 2020
• Zhang, Lichen and Diraneyya, Mohsen Mutasem and Ryu, JuHyeong and Haas, Carl T and Abdel-Rahman, Eihab M, Jerk as an indicator of physical exertion and fatigue, Automation in Construction, 120, 2019
• Hammad, Bashar and Abdelmoula, Hichem and Abdel-Rahman, Eihab and Abdelkefi, Abdessattar, Nonlinear analysis and performance of electret-based microcantilever energy harvesters, Energies, 4249, 2019
• Seo, JoonOh and Alwasel, Abdullatif and Lee, SangHyun and Abdel-Rahman, Eihab M and Haas, Carl, A comparative study of in-field motion capture approaches for body kinematics measurement in construction, Robotica, 928, 2019
• Alneamy, A and Al-Ghamdi, M and Park, S and Khater, M and Abdel-Rahman, E and Heppler, G, Dimpled electrostatic MEMS actuators, Journal of Applied Physics, 024304, 2019
• Mahmud, Alam and Khan, Asif Abdullah and Voss, Peter and Das, Taylan and Abdel-Rahman, Eihab and Ban, Dayan, A high performance and consolidated piezoelectric energy harvester based on 1D/2D hybrid zinc oxide nanostructures, Advanced Materials Interfaces, 1801167, 2018
• Singh, Tejinder and Elhady, Alaa and Jia, Huayong and Mojdeh, Ali and Kaplan, Cemalettin and Sharma, Vipul and Basha, Mohamed and Abdel-Rahman, Eihab, Modeling of low-damping laterally actuated electrostatic MEMS, Mechatronics, 1, 2018
• Sassi, S Ben and Khater, ME and Najar, F and Abdel-Rahman, EM, A square wave is the most efficient and reliable waveform for resonant actuation of micro switches, Journal of Micromechanics and Microengineering, 055002, 2018
• Dagdelen, Turker and Abdel-Rahman, Eihab and Yavuz, Mustafa, Reliability Criteria for Thick Bonding Wire, Materials, 618, 2018
• Bakri-Kassem, Maher and Dhaouadi, Rached and Arabi, Mohamed and Estahbanati, Shahabeddin V and Abdel-Rahman, Eihab, Nonlinear dynamic modeling of a V-shaped metal based thermally driven MEMS actuator for RF switches, Journal of Micromechanics and Microengineering, 054004, 2018
• Al-Ghamdi, MS and Khater, ME and Stewart, KME and Alneamy, Ayman and Abdel-Rahman, Eihab M and Penlidis, Alexander, Dynamic bifurcation MEMS gas sensors, Journal of Micromechanics and Microengineering, 015005, 2018
• Ghajar, Mohammad Hossein and Mousavi, M and Burzhuev, Salamat and Irannejad, Mehrdad and Yavuz, Mustafa and Abdel-Rahman, Eihab, A Short Review on Fabrication Methods of Micro-Cantilever for Ionic Electroactive Polymer Sensors/Actuators, International Journal of Nanoscience and Nanotechnology, 101, 2018
• El-Rayes, Karim and Gabran, Salam and Abdel-Rahman, Eihab and Melek, William, Variable-Flux Biaxial Vibration Energy Harvester, IEEE Sensors Journal, 3218, 2018
• Ghajar, Mohammad Hossein and Mashhadi, Mahmoud Mousavi and Irannejad, Mehrdad and Yavuz, Mustafa and Abdel-Rahman, Eihab, Effects of static electricity and fabrication parameters on PVDF film properties, Bulletin of Materials Science, 43, 2018
• Al-Ghamdi, MS and Khater, ME and Abdel-Rahman, EM, Switching intermittency, Applied Physics Letters, 153501, 2018
• Alneamy, AM and Khater, ME and Al-Ghamdi, MS and Park, S and Heppler, GR and Abdel-Rahman, EM, Dual actuation micro-mirrors, Journal of Micromechanics and Microengineering, 075014, 2018
• Ghajar, Mohammad Hossein and Mosavi Mashhadi, Mahmoud and Irannejad, Mehrdad and Jebril, Seid and Yavuz, Mustafa and Abdel-Rahman, Eihab, Degree of Crystallinity and Phase Fraction of Polyvinylidene Fluoride Nanocomposites Containing Ionic Liquid and Graphene/Carbon Nanotube, Polymer Composites, , 2018
• Park, Sangtak and Khater, Mahmoud and Effa, David and Abdel-Rahman, Eihab and Yavuz, Mustafa, Detection of cyclic-fold bifurcation in electrostatic MEMS transducers by motion-induced current, Journal of Micromechanics and Microengineering, 085007, 2017
• Alwasel, Abdullatif and Abdel-Rahman, Eihab M and Haas, Carl T and Lee, SangHyun, Experience, productivity, and musculoskeletal injury among masonry workers, Journal of Construction Engineering and Management, 05017003, 2017
• Alwasel, Abdullatif and Sabet, Ali and Nahangi, Mohammad and Haas, Carl T and Abdel-Rahman, Eihab, Identifying poses of safe and productive masons using machine learning, Automation in Construction, 345, 2017
• Lajimi, SAM and Heppler, GR and Abdel-Rahman, EM, A parametric study of the nonlinear dynamics and sensitivity of a beam-rigid body microgyroscope, Communications in Nonlinear Science and Numerical Simulation, 180, 2017
• Mahmoud, MAE and Abdel-Rahman, Eihab M and Mansour, RR and El-Saadany, EF, Out-of-plane continuous electrostatic micro-power generators, Sensors, 877, 2017
• Alwasel, Abdullatif and Yung, Marcus and Abdel-Rahman, Eihab M and Wells, Richard P and Haas, Carl T, Fatigue Detection Using Phase-Space Warping, Journal of biomechanical engineering, 031001, 2017
• Lajimi, SAM and Heppler, GR and Abdel-Rahman, EM, A mechanical--thermal noise analysis of a nonlinear microgyroscope, Mechanical Systems and Signal Processing, 163, 2017
• Al-Ghamdi, Majed S and Alneamy, Ayman M and Park, Sangtak and Li, Beichen and Khater, Mahmoud E and Abdel-Rahman, Eihab M and Heppler, Glenn R and Yavuz, Mustafa, Nonlinear parameter identification of a resonant electrostatic MEMS actuator, Sensors, 1121, 2017
• Lajimi, SA Mousavi and Heppler, GR and Abdel-Rahman, E, On modeling beam-rigid-body microgyroscopes, Applied Mathematical Modelling, 753, 2017
• Kayaharman, Muhammed and Ternon, Celine and Park, Sangtak and Legallais, Maxime and Salem, Bassem and Irannejad, Mehrdad and Abdel-Rahman, Eihab and Yavuz, Mustafa, Characterization of Silicon Nanonet FETs, , , 2017
• Bendame, Mohamed and Abdel-Rahman, Eihab and Soliman, Mostafa, Wideband, low-frequency springless vibration energy harvesters: part II, Journal of Micromechanics and Microengineering, 115022, 2016
• Lajimi, SAM and Heppler, GR and Abdel-Rahman, EM, A mechanical--thermal noise analysis of a nonlinear microgyroscope, Mechanical Systems and Signal Processing, , 2016
• Bendame, Mohamed and Abdel-Rahman, Eihab and Soliman, Mostafa, Wideband, low-frequency springless vibration energy harvesters: part I, Journal of Micromechanics and Microengineering, 115021, 2016
• Saritas, Resul and Khater, M and Park, Sangtak and Dagdelen, T and Abdel-Rahman, E and Yavuz, Mustafa, Techniques for dynamic analysis of bonding wire, Microelectronics Reliability, 73, 2016
• Saritas, R and Khater, M and Park, S and Dagdelen, T and Abdel-Rahman, E and Yavuz, M, Techniques for dynamic analysis of bonding wire, Microelectronics Reliability, 73, 2016
• Eltaher, MA and Khater, ME and Park, S and Abdel-Rahman, E and Yavuz, M, On the static stability of nonlocal nanobeams using higher-order beam theories, Advances in nano research, 51, 2016
• Liu, Guocheng and Zhao, Songrui and Henderson, Robert DE and Leonenko, Zoya and Abdel-Rahman, Eihab and Mi, Zetian and Ban, Dayan, Nanogenerators based on vertically aligned InN nanowires, Nanoscale, 2097, 2016
• Park, Sangtak and Al-Ghamdi, Majed S and Khater, Mahmoud E and Abdel-Rahman, Eihab, A tunable MEMS magnetic sensor, Journal of Microelectromechanical Systems, 255, 2016
• Liu, Guocheng and Mrad, Nezih and Abdel-Rahman, Eihab and Ban, Dayan, Cascade-type hybrid energy cells for driving wireless sensors, Nano Energy, 641, 2016
• Nayfeh, Ali H and Abdel-Rahman, Eihab M and Ghommem, Mehdi, A novel differential frequency micro-gyroscope, Journal of Vibration and Control, 872, 2015
• Lajimi, SAM and Heppler, GR and Abdel-Rahman, EM, Primary resonance of a beam-rigid body microgyroscope, International Journal of Non-Linear Mechanics, 364, 2015
• Ozdemir, Savas and Akhtar, Sohail and Gunal, Ozgur E and Khater, Mahmoud E and Saritas, Resul and Abdel-Rahman, Eihab M and Yavuz, Mustafa, Measuring the Quality Factor in MEMS devices, Micromachines, 1935, 2015
• Liu, Guocheng and Abdel-Rahman, Eihab and Ban, Dayan, Performance optimization of pn homojunction nanowire-based piezoelectric nanogenerators through control of doping concentration, Journal of Applied Physics, 094307, 2015
• Khater, ME and Akhtar, S and Park, S and Ozdemir, S and Abdel-Rahman, E and Vyasarayani, CP and Yavuz, M, Contact damping in microelectromechanical actuators, Applied Physics Letters, 253501, 2014
• Yilmaz, Mehmet and Tunkar, Bassam A and Park, Sangtak and Elrayes, Karim and Mahmoud, Mohamed AE and Abdel-Rahman, Eihab and Yavuz, Mustafa, High-efficiency passive full wave rectification for electromagnetic harvesters, Journal of Applied Physics, 134902, 2014
• Khater, ME and Al-Ghamdi, M and Park, S and Stewart, KME and Abdel-Rahman, EM and Penlidis, A and Nayfeh, AH and Abdel-Aziz, AKS and Basha, M, Binary MEMS gas sensors, Journal of Micromechanics and Microengineering, 065007, 2014
• Khater, ME and Eltaher, MA and Abdel-Rahman, E and Yavuz, M, Surface and thermal load effects on the buckling of curved nanowires, Engineering Science and Technology, an International Journal, 279, 2014
• Chung, So-Ra and Park, Sangtak and Abdel-Rahman, Eihab M and Yeow, John TW and Khater, Mahmoud, Architecture for MEMS-based analogue demodulation, Journal of Micromechanics and Microengineering, 045013, 2013
• Forouzanfar, Sepehr and Mansour, Raafat and Abdel-Rahman, Eihab, Lorentz-force transduction for RF micromechanical filters, Journal of Micromechanics and Microengineering, 035018, 2012
• Vyasarayani, CP and Abdel-Rahman, Eihab M and McPhee, John, Modeling of contact and stiction in electrostatic microcantilever actuators, Journal of Nanotechnology in Engineering and Medicine, 011003, 2012
• Alwasel, Abdullatif and Elrayes, Karim and Abdel-Rahman, Eihab and Haas, Carl, Reducing shoulder injuries among construction workers, Gerontechnology, 242, 2012
• Seleim, Abdulrahman and Towfighian, Shahrzad and Delande, Emmanuel and Abdel-Rahman, Eihab and Heppler, Glenn, Dynamics of a close-loop controlled MEMS resonator, Nonlinear Dynamics, 615, 2012
• Towfighian, Shahrzad and Heppler, Glenn R and Abdel-Rahaman, Eihab M, Low-voltage closed loop MEMS actuators, Nonlinear Dynamics, 565, 2012
• Stewart, KME and McManus, NT M and Abdel-Rahman, E and Penlidis, A, Doped polyaniline for the detection of formaldehyde, Journal of Macromolecular Science, Part A, 1, 2012
• Vyasarayani, Chandrika P and Abdel-Rahman, Eihab M and McPhee, John and Birkett, Stephen, Modeling MEMS resonators past pull-in, Journal of computational and nonlinear dynamics, , 2011
• Khater, ME and Vummidi, K and Abdel-Rahman, EM and Nayfeh, AH and Raman, S, Dynamic actuation methods for capacitive MEMS shunt switches, Journal of Micromechanics and Microengineering, 035009, 2011
• Hammad, Bashar K and Nayfeh, Ali H and Abdel-Rahman, Eihab M, On the use of the subharmonic resonance as a method for filtration, Journal of computational and nonlinear dynamics, , 2011
• Towfighian, Shahrzad and Seleim, A and Abdel-Rahman, EM and Heppler, GR, A large-stroke electrostatic micro-actuator, Journal of Micromechanics and Microengineering, 075023, 2011
• Towfighian, S and Heppler, GR and Abdel-Rahman, EM, Analysis of a chaotic electrostatic micro-oscillator, Journal of Computational and Nonlinear Dynamics, 011001, 2011
• Ghommem, M and Nayfeh, AH and Choura, S and Najar, F and Abdel-Rahman, EM, Modeling and performance study of a beam microgyroscope, Journal of Sound and Vibration, 4970, 2010
• Nayfeh, AH and Ouakad, HM and Najar, F and Choura, S and Abdel-Rahman, EM, Nonlinear dynamics of a resonant gas sensor, Nonlinear Dynamics, 607, 2010
• Ghafari, SH and Abdel-Rahman, EM and Golnaraghi, F and Ismail, F, Vibrations of balanced fault-free ball bearings, Journal of Sound and Vibration, 1332, 2010
• Mahmoud, MAE and Abdel-Rahman, EM and El-Saadany, EF and Mansour, RR, Electromechanical coupling in electrostatic micro-power generators, Smart Materials and Structures, 025007, 2010
• Najar, F and Nayfeh, AH and Abdel-Rahman, EM and Choura, S and El-Borgi, S, Nonlinear analysis of MEMS electrostatic microactuators: primary and secondary resonances of the first mode, Journal of Vibration and Control, 1321, 2010
• Hammad, Bashar K and Abdel-Rahman, Eihab M and Nayfeh, Ali H, Modeling and analysis of electrostatic MEMS filters, Nonlinear Dynamics, 385, 2010
• Najar, Fehmi and Nayfeh, Ali H and Abdel-Rahman, Eihab M and Choura, Slim and El-Borgi, Sami, Dynamics and global stability of beam-based electrostatic microactuators, Journal of Vibration and Control, 721, 2010
• Soliman, Mostafa SM and Abdel-Rahman, Eihab M and El-Saadany, Ehab F and Mansour, Raafat R, A design procedure for wideband micropower generators, Journal of Microelectromechanical Systems, 1288, 2009
• Daqaq, Mohammed F and Abdel-Rahman, Eihab M and Nayfeh, Ali H, Two-to-one internal resonance in microscanners, Nonlinear Dynamics, 231, 2009
• Arafat, Haider N and Nayfeh, Ali H and Abdel-Rahman, Eihab M, Modal interactions in contact-mode atomic force microscopes, Nonlinear Dynamics, 151, 2008
• Daqaq, MF and Abdel-Rahman, EM and Nayfeh, AH, Towards a stable low-voltage torsional microscanner, Microsystem technologies, 725, 2008
• Soliman, MSM and Abdel-Rahman, EM and El-Saadany, EF and Mansour, RR, A wideband vibration-based energy harvester, journal of micromechanics and microengineering, 115021, 2008
• Nayfeh, Ali H and Younis, Mohammad I and Abdel-Rahman, Eihab M, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear dynamics, 153, 2007
• Najar, Fehmi and Choura, Slim and Abdel-Rahman, Eihab M and El-Borgi, Sami and Nayfeh, A, Dynamic analysis of variable-geometry electrostatic microactuators, Journal of micromechanics and microengineering, 2449, 2006
• Nayfeh, Ali H and Younis, Mohammad I and Abdel-Rahman, Eihab M, Reduced-order models for MEMS applications, Nonlinear dynamics, 211, 2005
• Abdel-Rahman, Eihab M and Nayfeh, Ali H, Contact force identification using the subharmonic resonance of a contact-mode atomic force microscopy, Nanotechnology, 199, 2005
• Najar, F and Choura, S and El-Borgi, S and Abdel-Rahman, EM and Nayfeh, AH, Modeling and design of variable-geometry electrostatic microactuators, Journal of micromechanics and microengineering, 419, 2004
• Abdel-Rahman, Eihab M and Younis, Mohammad I and Nayfeh, Ali H, Finite-amplitude motions of beam resonators and their stability, Journal of Computational and Theoretical Nanoscience, 385, 2004
• Zhao, Xiaopeng and Abdel-Rahman, Eihab M and Nayfeh, Ali H, A reduced-order model for electrically actuated microplates, Journal of Micromechanics and Microengineering, 900, 2004
• Abdel-Rahman, Eihab M and Nayfeh, Ali H, Secondary resonances of electrically actuated resonant microsensors, Journal of Micromechanics and Microengineering, 491, 2003
• Abdel-Rahman, Eihab M and Nayfeh, Ali H and Masoud, Ziyad N, Dynamics and control of cranes: A review, Journal of Vibration and Control, 863, 2003
• Abdel-Rahman, Eihab M and Faris, Waleed F and Nayfeh, Ali H, Axisymmetric natural frequencies of statically loaded annular plates, Shock and Vibration, 301, 2003
• Abdel-Rahman, Eihab and Nayfeh, Ali H, Two-dimensional control for ship-mounted cranes: a feasibility study, Journal of Vibration and Control, 1327, 2003
• Younis, Mohammad I and Abdel-Rahman, Eihab M and Nayfeh, Ali, A reduced-order model for electrically actuated microbeam-based MEMS, Journal of Microelectromechanical systems, 672, 2003
• Abdel-Rahman, Eihab M and Younis, Mohammad I and Nayfeh, Ali H, Characterization of the mechanical behavior of an electrically actuated microbeam, Journal of Micromechanics and Microengineering, 759, 2002
• Abdel-Rahman, EM and Nayfeh, AH, Pendulation reduction in boom cranes using cable length manipulation, Nonlinear Dynamics, 255, 2002
• Chin, C and Nayfeh, AH and Abdel-Rahman, E, Nonlinear dynamics of a boom crane, Journal of Vibration and Control, 199, 2001
• Abdel-Rahman, Eihab Muhammed and Hefzy, Mohamed Samir, Three-dimensional dynamic behaviour of the human knee joint under impact loading, Medical engineering \& physics, 276, 1998
• Hefzy, Mohamed Samir and Abdel-Rahman, Eihab, Dynamic modeling of the human knee joint: formulation and solution techniques. a review paper, Biomedical Engineering - Applications, Basis and Communications, 5, 1995
• Dagdelen, Turker and El-Rayes, Karim and Park, Sangtak and Khater, Mahmoud and Saritas, Resul and Abdel-Rahman, Eihab and Yavuz, Mustafa, Fatigue Test for Thick Wire Bonds, ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, , 2014
• Xie, Michael and Park, Sangtak and Abdel-Rahman, Eihab and Yavuz, Mustafa, Actuation of a Frequency Modulated MEMS Gyroscope, ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, , 2014
• Effa, David and Abdel-Rahman, Eihab and Yavuz, Mustafa, Cantilever beam microgyroscope based on Frequency modulation, 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 844, 2013
• Park, Sangtak and Khater, Mahmoud and Abdel-Rahman, Eihab, Low Voltage Electrostatic Actuation for MEMS Actuator Using frequency Modulation, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, , 2013
• Park, Sangtak and Abdel-Rahman, Eihab, Low voltage electrostatic actuation and displacement measurement through resonant drive circuit, ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 119, 2012
• Park, Sangtak and Abdel-Rahman, Eihab, Stabilization of Electrostatic Actuators Through Variable Gain Amplifier, ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 127, 2012
• Park, Sangtak and Pallapa, Manu and Yeow, John TW and Abdel-Rahman, Eihab, Low voltage electrostatic actuation and angular displacement measurement of micromirror coupled with resonant drive circuit, IECON 2012-38th Annual Conference on IEEE Industrial Electronics Society, 3976, 2012
• Mahmoud, Mohamed AE and Abdel-Rahman, Eihab M and Mansour, Raafat R and El-Saadany, Ehab F, Springless vibration energy harvesters, ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 703, 2010
• Vummidi, Krishna and Abdel-Rahman, Eihab M and Hammad, Bashar K and Raman, Sanjay and Nayfeh, Ali H, Micromechanical Resonators With Near-Linear Response, ASME 2008 International Mechanical Engineering Congress and Exposition, 357, 2008
• Elhady, Alaa and Basha, Mohamed and Abdel-Rahman, Eihab M, Tunable Bleustein--Gulyaev Permittivity Sensors, New Trends in Nonlinear Dynamics, 3, 2020