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Problem 9. Find natural frequencies and principal coordinates of the two-degrees-of-freedom vibrating system: a) b) Problem 9. Find natural frequencies and principal coordinates of the two-degre...
The number of degrees of freedom of a vibrating system depends on
The number of degrees of freedom of a vibrating system depends on the number of masses, springs and dashpots in the system. the number of masses and degrees of freedom of each mass the number of masses and constraints of each mass the number of coordinates used to describe the position of each mass
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
Determine the natural frequencies of the two-degree-of-freedom mechanical system of Figure P6.37 6.37 Determine the natural...
Determine the natural frequencies of the two-degree-of-freedom
mechanical system of Figure P6.37
6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. N N 2 x 10 3 x 10 10 2 kg 3 kg FIG. P6.37
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0...
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of moti...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww-
For the system shown in Figure 5, a. How many degrees of freedom...
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and iden...
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and identify any nodes for each mode. (d) Demonstrate mode shape orthogonality. (e) If F- and the motion is initiated by giving the mass whose displacement is a velocity of 0.2 m/s when in equilibrium, determine 0) and ,0 (f) Determine the steady-state solution for both *)...
6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. 2 x...
6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. 2 x 10 3 x 10 1 x 105N 2 kg 3 kg FIG. P6.37
Determine the natural frequencies and vibration modes of the two degree of freedom rectilinear system shown...
Determine the natural frequencies and vibration modes of the two
degree of freedom rectilinear system shown in the following
figure.
please detail all the steps
ans:
k m, ww m2 DCL LEE LFF Оn1 — 0 k(m1+m2) Wn2 7ш.Тш X1 X2 -т, — Х, ( X2 X1 т2
vibrations The given equation represents an undamped forced two degrees of freedom system. (a) Decouple the...
vibrations
The given equation represents an undamped forced two degrees of freedom system. (a) Decouple the equation and find the generalized mass [Ml; stiffiess [K]; force |F) while the generalized coordinates are, (a).(b) Determine the steady state response. ,6 -21 (31 2.
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
Determine the natural frequencies of the two-degree-of-freedom
mechanical system of Figure P6.37
6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. N N 2 x 10 3 x 10 10 2 kg 3 kg FIG. P6.37
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww-
For the system shown in Figure 5, a. How many degrees of freedom...
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and identify any nodes for each mode. (d) Demonstrate mode shape orthogonality. (e) If F- and the motion is initiated by giving the mass whose displacement is a velocity of 0.2 m/s when in equilibrium, determine 0) and ,0 (f) Determine the steady-state solution for both *)...
6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. 2 x 10 3 x 10 1 x 105N 2 kg 3 kg FIG. P6.37
Determine the natural frequencies and vibration modes of the two
degree of freedom rectilinear system shown in the following
figure.
please detail all the steps
ans:
k m, ww m2 DCL LEE LFF Оn1 — 0 k(m1+m2) Wn2 7ш.Тш X1 X2 -т, — Х, ( X2 X1 т2
vibrations
The given equation represents an undamped forced two degrees of freedom system. (a) Decouple the equation and find the generalized mass [Ml; stiffiess [K]; force |F) while the generalized coordinates are, (a).(b) Determine the steady state response. ,6 -21 (31 2.
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