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The design of machine elements is a process that takes into consideration the different functional groups of a machine, their interactions and how they function within the overall system. In this technique, it is important to take into consideration the natural frequencies associated with each element. This will lead to a design that functions smoothly and has less impact on other parts of the system. In this document, we will study an example, the design of an active valve arrangement in a gas turbine engine disk milling unit. The active valve as shown in Figure 1 consists of a rotor and a stator with gas valves. In this example, we will analyze the design for a single rotor and a single-stage disk milling machine. The material used for modeling will be massless particle models. In order to accomplish the task, we will first determine the natural frequencies of the rotor and stator. The rotor and stator can be modeled as massless particles with an inertia matrix rendered as linear spring elements. Each element is represented as a spring-mass system having total mass , where represents the th element's position on the rotor or stator axis. The mass of each element is defined as where represents the natural frequency of the th element. For rotor, the natural frequencies are given as and for stator. The rotor and stator can also be modeled as linear massless beam elements with a mass where represents the th element's position on the rotor or stator axis formula_1 is a unit vector along which formula_2 is vertical displacement from zero center of mass at the th element position . The state variables for turbine rotor and disk milling machine are respectively as follows: was solved with MATLAB for this problem by using Numerical Functional Analysis (NFA). From the results, the natural frequencies for turbines are as follows: For disk milling machine, the natural frequencies are as follows: It can be observed from the results that the rotor has higher natural frequency than stator. Since there is no flow in rotor, air blast is limited to stator. Therefore, it can be said that stator plays a vital role in disk milling machine. Fig.2 shows the comparison between rotor and stator for this problem where rotating speed of turbine is . It can be observed that rotor has higher natural frequency which leads to high vibration of turbine compared to other elements. Fig.3 presents an image of experimental setup used for this problem 1. Martynov V. N. Introduction to Numerical Analysis 2. Parikh A. G. "Introduction to Numerical Mathematics", Prentice-Hall, Englewood Cliffs, New Jersey, Prentice Hall Press, 1983 3. Tsoi Chuen Fong (2001), Computer-aided design of massless particle models in computational mechanics, Master Thesis, Department of Mechanical Engineering and Technology , National University of Singapore , Singapore1. Martynov V. N., Introduction to Numerical Analysis; 2nd Edition; McGraw Hill; 1997.. 2. Lomax J.. "Introduction to the Theory and Methodology of Numerical Analysis". SpringerVerlag; 1989.. cfa1e77820