Dynamics of Structures 3rd. Edition by Jagmohan L. Humar | 9780203112564 | 0415620864 | Holooly

Structural Analysis

Dynamics of Structures

252 SOLVED PROBLEMS

Question: 19.6

The beam in Example 19.5 is subjected to a vertical upward force P along d.o.f. 5 of component 2. What are the resulting vertical displacements at each node of the finite element mesh. ...

Verified Answer:

Referring to the d.o.f. of component 2 the force v...

Question: 16.P.5

The vibrations of the bar in Problem 16.4 are resisted by damping forces that are viscous in nature. Assuming that the distributed damping coefficient is proportional to the mass per unit length and that damping in the first mode is 5 % of critical, derive the damping ratios for the second and the ...

Verified Answer:

\begin{aligned}&\xi_{1}=0.05 \quad \xi_...

Question: 18.6

The plane frame shown in Figure E18.6a is modeled as a finite element system consisting of three elements, BA, BC, and CD. Columns BA and CD each have a length L, sectional moment of inertia I, and mass per unit length m. Beam BC is of length 2L, moment of inertia 2I, and mass per unit length 2m. ...

Verified Answer:

As shown in Figure E18.6a, the frame has three deg...

Question: 18.5

The simply supported beam of length L shown in Figure E18.5 is vibrating in the lateral direction. The beam is of uniform section, has flexural rigidity EI and mass per unit length m. It is divided into three finite element as shown in the figure, which also shows the global degrees of freedom. ...

Verified Answer:

The stiffness matrix for element

\mathrm{BC...

Question: 16.P.1

A simply supported beam of span L, mass per unit length m, and flexural rigidity EI vibrates under the following support motions. Obtain expressions for the displacement response of the beam. (a) Both the left and the right hand ends undergo identical lateral motions given by ug = A0 sin Ωt. (b) ...

Verified Answer:

(a)

u(x, t)=\frac{4 A_{0}}{\pi}\left(\Sigma...

Question: 18.P.11

The beam AB shown in Figure P18.11 is subjected to a distributed load that varies from p1 per unit length at A to p2 per unit length at B. Obtain the equivalent consistent loads at the two ends of the beam using (a) interpolation functions given in Equation 18.26, (b) interpolation functions given ...

Verified Answer:

\begin{aligned}&\text { (a) and (b) } \...

Question: 13.P.1

Using Rayleigh Ritz method and the following Ritz shapes obtain estimates of 2 frequencies and the associated mode shapes of the four-story frame shown in Figure 11.14. ...

Verified Answer:

\begin{aligned}\omega_{1} &=9.56 \math...

Question: 13.16

The two-degree-of-freedom system of Figure E13.16a is subjected to an applied force given by p = [1 1/2]g(t) where g(t) is the rectangular pulse function shown in Figure E13.16b. Obtain the response of the system by using a modal analysis through frequency domain. ...

Verified Answer:

The stiffness and mass matrices of the system are ...

Question: 8.12

Calculate the response of the tower in Example 8.9 to the loading shown there for the first 1.0 s using a numerical integration technique. Assume that damping in the system is 10% of critical and use h = 0.1 s. ...

Verified Answer:

We will obtain the response using (a) the constant...

Question: 6.P.3

An electric motor weighing 1160 N is attached to a floor beam which deflects 0.76 mm under the weight. The armature of the motor weighs 40 kg. As the motor is run up gradually to operating speed of 1600 RPM, it is observed that the maximum amplitude of oscillation is 2.5 mm, decreasing to 0.5 mm at ...

Verified Answer:

1467 N ·s/m, 0.805 mm

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