[2] P. Langevin, French Patents Nr. 575435 (1924).
[3] Ando E, Kagawa Y (1992) Finite-element simulation of transient heat response in ultrasonic transducers. IEEE Trans Ultrason Ferroelectr Freq Control 39.
[4] Karnaukhov VG, Senchenkov IK, Mikhailenko VV, Dyachenko SM (1996) Numerical modeling of vibrational heating and thermal stresses in a Lagrangian piezoelectric rod transducer. Int Appl Mech 32.
[5] Sherrit S, Dolgin BP, Bar-Cohen Y, Pal D, Kroh J, Peterson T (1999) Modeling of horns for sonic/ultrasonic applications. IEEE Int Ultrason Symp 647-651.
[6]Joo H, Lee C, Rho J, Jung H (2006) Analysis of temperature rise for piezoelectrictransformer using finite-element method. IEEE Trans Ultrason Ferroelectr Freq Control 53.
[7] Abdullah A, Shahini A, Pak A (2008) An approach to design a high power piezoelectric ultrasonic transducer. Electroceram 22: 369-382.
[8] Pak A, Abdullah A (2008) Correct prediction of the vibration behavior of a high power ultrasonictransducer by FEM simulation. Adv Manuf Technol 39: 21-28.
[9] Gallego-Juárez JA, Rodriguez G, Acosta V, Riera E (2010) Power ultrasonic transducers with extensive radiators for industrial processing. Ultrason Sonochem 17: 953-964.
[10] Ganesan R, Muthupandian A (2010) Simulation of heat generation from vibration in COMSOL multiphysics. Excerpt from the Proceedings of the COMSOL Conference India.
[11] Peshkovsky AS, Peshkovsky SL (2010) Acoustic cavitation theory and equipment design principles for industrial applications of high-intensity ultrasound. Nova Science Publishers.
[12] Hosseni R, Ebrahimi Mamaghani A, Asa A (2013) An investigation into the effects of friction and anisotropy coefficients andwork hardening exponent on deep drawing with FEM. Adv Mater Process 1(2): 39-50.
[13] Abdullah A, Malaki M (2013) On the damping of ultrasonic transducers’ components. Aerosp Sci Technol 28: 31-39.
[14] Rani MR, Prakasan K, Rudramoorthy R (2015) Studies on thermo-elastic heating of horns used in ultrasonic plastic welding. Ultrasonics 55: 123-132.
[15] Lu X, Hu J, Peng H, Wang Y (2017) A new topological structure for the Langevin-type ultrasonic transducer. Ultrasonics. 75: 1-8.
[16] Karafi MR, Khorasani F (2019) Evaluation of mechanical and electric power losses in a typical piezoelectric ultrasonic transducer. Sensor Actuat A-Phys 288: 156-164.
[2] P. Langevin, French Patents Nr. 575435 (1924).
[3] Ando E, Kagawa Y (1992) Finite-element simulation of transient heat response in ultrasonic transducers. IEEE Trans Ultrason Ferroelectr Freq Control 39.
[4] Karnaukhov VG, Senchenkov IK, Mikhailenko VV, Dyachenko SM (1996) Numerical modeling of vibrational heating and thermal stresses in a Lagrangian piezoelectric rod transducer. Int Appl Mech 32.
[5] Sherrit S, Dolgin BP, Bar-Cohen Y, Pal D, Kroh J, Peterson T (1999) Modeling of horns for sonic/ultrasonic applications. IEEE Int Ultrason Symp 647-651.
[6]Joo H, Lee C, Rho J, Jung H (2006) Analysis of temperature rise for piezoelectrictransformer using finite-element method. IEEE Trans Ultrason Ferroelectr Freq Control 53.
[7] Abdullah A, Shahini A, Pak A (2008) An approach to design a high power piezoelectric ultrasonic transducer. Electroceram 22: 369-382.
[8] Pak A, Abdullah A (2008) Correct prediction of the vibration behavior of a high power ultrasonictransducer by FEM simulation. Adv Manuf Technol 39: 21-28.
[9] Gallego-Juárez JA, Rodriguez G, Acosta V, Riera E (2010) Power ultrasonic transducers with extensive radiators for industrial processing. Ultrason Sonochem 17: 953-964.
[10] Ganesan R, Muthupandian A (2010) Simulation of heat generation from vibration in COMSOL multiphysics. Excerpt from the Proceedings of the COMSOL Conference India.
[11] Peshkovsky AS, Peshkovsky SL (2010) Acoustic cavitation theory and equipment design principles for industrial applications of high-intensity ultrasound. Nova Science Publishers.
[12] Hosseni R, Ebrahimi Mamaghani A, Asa A (2013) An investigation into the effects of friction and anisotropy coefficients andwork hardening exponent on deep drawing with FEM. Adv Mater Process 1(2): 39-50.
[13] Abdullah A, Malaki M (2013) On the damping of ultrasonic transducers’ components. Aerosp Sci Technol 28: 31-39.
[14] Rani MR, Prakasan K, Rudramoorthy R (2015) Studies on thermo-elastic heating of horns used in ultrasonic plastic welding. Ultrasonics 55: 123-132.
[15] Lu X, Hu J, Peng H, Wang Y (2017) A new topological structure for the Langevin-type ultrasonic transducer. Ultrasonics. 75: 1-8.
[16] Karafi MR, Khorasani F (2019) Evaluation of mechanical and electric power losses in a typical piezoelectric ultrasonic transducer. Sensor Actuat A-Phys 288: 156-164.