mproving of cutting process is one of the most important requirements that are expected from the machining methods in the recent years. In some machining processes, the positive effect of ultrasonic waves to improve the cutting process is used. The cutting process efficiency depends on the structure of excitation system which generates ultrasonic waves. One of the most important elements of this system is the ultrasonic waveguide. The role of waveguide is the transfer of ultrasonic vibration energy from ultrasonic transducer to the tool cutting edge interacting with the workpiece (ultrasonic assisted machining-UAM). The UAM system performance depends on well-designed ultrasonic waveguide. The most important aspects of waveguide design are a resonant frequency, amplification factor and the determination of waveguide resonant wavelength - usually integer multiple of half wavelength. The effect of geometrical parameters of stepped waveguide on dynamical properties is presented in this paper.

The beams can be considered as fundamental structural elements applied in many technical structures and equipment. In the operating regimes, these beam structures are very often loaded by the time-dependent forces which cause their undesirable dynamical behavior and the whole system is getting into critical resonant state. It is clear that the reduction of the level of unwanted vibrations or prevention of their occurrence should be one of the important objectives in the design of machine equipment and structures. To achieve these aims, the knowledge of modal properties of beam structures in relation to their internal structure is necessary. The insertion of reinforcing core into a beam body is one of the possible techniques to achieve the required changes in modal properties (mode shapes, natural frequencies) of the beam structure. The dependency of the modal properties of structurally modified beam structure on the geometric parameters and material properties of the inserted reinforcing core is studied in this paper.

Improving of machining process is one of the most important requirements that are expected from the machining methods. In many machining processes, the positive effects of ultrasound are applied. The performance of these machining systems and quality of machining process depends on the correct design of the individual system elements, mainly waveguide. For the correct functioning of the system, the waveguide must have the required dynamic properties - natural frequencies and amplification factors. The waveguide modal properties (natural frequencies, mode shapes) are determined by the numerical simulations using finite element method (FEM) design procedures. The effect of different waveguide shapes (conical, exponential, catenoidal) and their dimensions on modal properties and amplification factors are presented in this paper.

Rotary ultrasonic machining (RUM) is a hybrid process that combines diamond grinding with ultrasonic machining. It is most suitable to machine hard brittle materials such as ceramics and composites. Due to its excellent machining performance, RUM is very often applied for drilling of hard machinable materials. In the final phase of drilling, the edge deterioration of the drilled hole can occur, which results in a phenomenon called edge chipping. During hole drilling, a change in the thickness of the bottom of the drilled hole occurs. Consequently, the bottom of the hole as a plate structure is exposed to the transfer through the resonance state. This resonance state can be considered as one of the important aspects leading to edge chipping. Effects of changes in the bottom thickness and as well as the fillet radius between the wall and bottom of the borehole on the stress-strain states during RUM are analyzed.