Dynamics of Machines - Part II - IFS.pdf

4. Vary the number of masses attached to the first coordinate y1 the beam while exciting
the mass-spring system with just an initial velocity at the first coordinate ( ˙y1ini ) (initial
displacements and excitation forces are set zero). (a) Explain what happens with the natural
frequencies of the system; (b) How many natural frequencies change when you change the
mass in just one point of the structure? Explain.
5. Vary the number of masses attached to the second coordinate of the beam, y2, while exciting
the mass-spring system with just an initial velocity at the first coordinate ( ˙y1ini ) (initial
displacements and excitation forces are set zero). (a) Explain what happens with the natural
frequencies of the system; (b) How many natural frequencies change when you change the
mass in just one point of the structure? Explain.
6. Set the damping factor ξ = 0.005, while exciting the mass-spring-damping system with just
an excitation force of f1 = 0.1 · e j·w·t [N] (initial velocities and initial displacements are set
zero). Explain the vibration behavior of the system in terms of amplitudes and frequencies,
when: (a) w = 10%wn1; (b) w = 50%wn1; (c) w = 90%wn1; (d) w = wn1; (e) w = 110%wn1;
(f) w = 90%wn2; (g) w = wn2; (h) w = 110%wn2; (i) w = 200%wn2.
7. Set the damping factor ξ = 0.05, while exciting the mass-spring-damping system with just
an excitation force of f1 = 0.1 · e j·w·t [N] (initial velocities and initial displacements are set
zero). Explain the vibration behavior of the system in terms of amplitudes and frequencies,
when: (a) w = 10%wn1; (b) w = 50%wn1; (c) w = 90%wn1; (d) w = wn1; (e) w = 110%wn1;
(f) w = 90%wn2; (g) w = wn2; (h) w = 110%wn2; (i) w = 200%wn2.
8. Set the damping factor ξ = 0.005, while exciting the mass-spring-damping system with just
an excitation force of f2 = 0.1 · e j·w·t [N] (initial velocities and initial displacements are set
zero). Explain the vibration behavior of the system in terms of amplitudes and frequencies,
when: (a) w = 10%wn1; (b) w = 50%wn1; (c) w = 90%wn1; (d) w = wn1; (e) w = 110%wn1;
(f) w = 90%wn2; (g) w = wn2; (h) w = 110%wn2; (i) w = 200%wn2.
9. Set the damping factor ξ = 0.05, while exciting the mass-spring-damping system with just
an excitation force of f2 = 0.1 · e j·w·t [N] (initial velocities and initial displacements are set
zero). Explain the vibration behavior of the system in terms of amplitudes and frequencies,
when: (a) w = 10%wn1; (b) w = 50%wn1; (c) w = 90%wn1; (d) w = wn1; (e) w = 110%wn1;
(f) w = 90%wn2; (g) w = wn2; (h) w = 110%wn2; (i) w = 200%wn2;
10. Explain how the variation of such parameters could be useful in a case with a real machine?
• Create a program dof3-integration.m based on dof2-integration.m and answer the following
questions:
1. Make use of the beam theory, and show how to get the 9 stiffness coefficients k11, k12, k13,
k21, k22, k23, k31, k32 and k33.
2. Excite the mass-spring system with just an initial velocity at the first coordinate ( ˙y1ini )
(initial displacements and excitation forces are set zero). Describe the vibration behavior
of the points y1, y2 and y3.
3. Excite the mass-spring system with just an initial velocity at the second coordinate ( ˙y2ini )
(initial displacements and excitation forces are set zero). Describe the vibration behavior
of the points y1, y2 and y3.
59