please do only part 3 using data project data provided. and please use matlab to plot.thanks
VIBRATON ISOLATION This project requires the analysis of vibration isolation of a machine mounted on a beam using various assumptions and under various scenarios. Basic Problem A machine of mass is to be placed on the floor of an industrial plant. The floor is modeled as a beam of length , cross sectional moment of inertia , cross sectional area and made from a material of mass density and elastic modulus . The beam is fixed at one end and pinned at its other end. The mass is attached to the beam a distance from the beam's left-hand support. During operation the machine develops a force . Also on the floor of the industrial plant is a machine of mass located a distance from the left support. The beam is made of a material of yield strength. It has fatigue properties of and . Recall that Basquin’s criterion predicts that the fatigue strength for cycles is . Let be the force for a single frequency harmonic excitation A vibration isolation system is to be designed for the machine. Assume a worst case scenario and use an upper limit on the damping ratio of 0.1. The machine operates at within a range of frequencies . Please follow REQUIREMENTS according to this. A. The group assignments are for purposes of using the data given on Brightspace only, B. Each student is responsible for completing and preparing a power point presentation on one part of this project (part I, part II, part III or part IV. C. All graphs and plots must be appropriately annotated with axis labels including units and legends if appropriate. The graphics must be computer generated, preferably using MATALB. D. Each student is responsible for calculating the basic isolator design. E. All information about the beams is available in the AMC textbook. Project Data APPENDIX A Group 7 General: Mass of machine: Length of beam: Distance from machine to left support: Type of beam: WT178x89 Mass of second machine Distance of second machine form left support Beam material: Structural steel Density: Elastic modulus: Yield strength: Fatigue properties: , Basic isolator design , , , When number of cycles is specified use N=1.5x108 cycles Damping ratio of isolator designed to protect machine of mass is The maximum acceleration amplitude is to be Fourier series specifics: , , , I. Vibration isolation for a single frequency harmonic excitation A. Determine the minimum static deflection of isolators and the maximum stiffness of isolators that lead to a transmitted force over the entire operating range. Call this isolator design the basic design. Suggest a commercially available isolation system that can be used. B. Calculate and plot the transmitted force versus frequency when the basic isolator design is used. C. Determine the number of cycles to failure when the basic isolator design is used. Use the Soderberg failure criterion to account for the mean stress that arises from the weight of the machines and the weight of the beam. Assume the beam’s weight is uniformly distributed along the span of the beam. Assume the failure point is at the fixed support at the location where the beam has maximum tension. Plot the number of cycles to failure versus the frequencies within the operating range. C. Now assume that you are still designing the isolator. You feel that it would be helpful if you could have plots of the number of cycles to failure versus the stiffness of the isolator for various frequencies within the operating range. Develop plots for safety factors of 1, 1.25, 1.5, 1.75 and 2. D. Plot the number cycles to failure versus the steady-state amplitude of the machine. Develop plots for safety factors of 1, 1.25, 1.5, 1.75 and 2. E. Determine and plot the minimum static deflection of an isolator of damping ratio such that the beam will not fail in N cycles of operation for various frequencies within the operating range. That is assume a frequency and plot the minimum static deflection versus the number of cycles of failure. Do this for several frequencies within the operating range. II. Added mass to the isolation system The isolation system consists of three parameters:. Assume that the damping ratio is fixed at 0.1. One strategy to effect isolation is to add mass to the system. Take the mass of the machine and the mounting to be . A. Determine and plot the force transmitted to the foundation versus when the basic isolator design is used. B. Determine and plot the steady-state amplitude of the machine versus when the basic isolator design is used. C. Determine and plot the maximum stiffness of an isolator such that the maximum force transmitted to the floor from the machine is . versus frequency for an operating range of . Show plots for values of . That is plot on the vertical axis versus on the horizontal axis. D. Determine and plot the maximum stiffness of an isolator versus the frequency of excitation such that the maximum force transmitted to the floor is . Show plots for values of . E. If the mean stress is 100+50* MPa plot the number of cycles to failure vs. , III. Vibration isolation taking into account the stiffness of the beam(only need to do this part using project data) A machine subject to a single frequency harmonic excitation of the form is to be analyzed over a range of frequencies . The machine is mounted on a beam at a location where the of equivalent stiffness is . The model of a machine mounted on a damped isolator then attached to a beam of negligible mass is A. Calculate the equivalent stiffness of the beam at the location where the mass is attached assuming the mass of the beam is negligible. B. Plot the maximum stiffness of an undamped isolator versus the maximum transmitted force to the beam for various frequencies within the operating range. Use the model in Figure 1. C. Consider the model of the vibrations of the machine on a damped isolator with the stiffness of the beam considered. This model is shown in Figure 1. Derive expressions for the force transmitted to the beam through the isolator, the steady-state amplitude of the machine and the maximum deflection of the isolator. You may use concepts from SDR such as the sinusoidal transfer function. D. Does the basic isolator design still work when the stiffness of the beam is taken into account? Explain using both mathematical (calculating the transmitted force) and physical reasoning. E. Determine the absolute amplitude of vibration of the machine and the amplitude of deflection of the isolator when the basic isolator design is used. 1 520 kg m = 1 2.3 m a = 1 m 0.06, z = 2 14.2 m/s all A = , and mk z m T F k T F 1 m 1 a