Nguyen__'Manufacturing_of_Ultrasonic_Horn_For_Bonding_Non-Woven_Materials'.pdf Eq(1.8) gives tuned L of slotted bar horn. However, doesn't account for effect of nodal R. Unknown derivation. Cardoni__'Enhanced_vibration_performance_of_ultrasonic_block_horns' (https://dokumen.tips/download/link/enhanced-vibration-performance-of-ultrasonic-block-horns) --> Bar horn with additional narrow slots The uniformity requirement for a block horn, measured as the ratio of minimum to maximum response amplitude on the output surface, Umin=Umax, is estimated to be 80% [3].The frequency separation should be at least 1 kHz from the longitudinal mode frequency. [3] = K.O'Shea, Enhanced vibration control of ultrasonic tooling using finite element analysis, Proc. ASME, Vibrat.Anal.-Analyt.Computat.DE-37 (1991) 259-265. Pushing back the nodal radius is equivalent to removing Delta_X from back of horn and adding Delta_X to to face of horn. If tuning from the back was equally effective as tuning from the face, then this would have no effect (i.e., moving the nnode would not cause Delta_f). However, removing material from the back causes Delta_f_back freq increase while adding material to the face causes Delta_f_face freq drop. The net effect is -- Delta_f_node = Delta_f_back + Delta_f_face Therefore, if any 2 of the above are known, then the 3rd can be calc. (1985-10-29)