###### Structural Dynamics and Vibration in Practice: An Engineering Handbook

60 SOLVED PROBLEMS

Question: 8.3

## Use the component mode synthesis, free interface, method to find the normal modes of the single system formed when the two uniform cantilever beams, R and S, of lengths L and 2L, respectively, as shown in Fig. 8.2, are subsequently rigidly joined at the free ends. The two cantilevers have the same ...

We shall need the following relationships: From Eq...
Question: C.1

## The noise measured in the vicinity of a jet engine is shown in Table C3, expressed as dB re. 20 μPa in standard third-octave bands.(a) Find the overall sound pressure level (OASPL) of the noise in dB re. 20 μPa.(b) Express the spectrum given in Table C3 in the form of power spectral density,(PSD) ...

Part (a) To add dB levels, they must first be expr...
Question: 12.1

## The main landing gear sketched in Fig. 12.2 is fitted with two wheels, on a live axle, and has two sets of disk brakes. These were sometimes found to lock when the brakes were applied firmly at very low speeds, resulting in a skid, during which severe fore and-aft vibration of the gear occurred if ...

Part (a): From Eq. (12.10), the effective non-dime...
Question: 11.3

## (a) Find the optimum damping for a springless vibration absorber where the absorber mass is one-half of the mass of the main system. Use Eq.(11.15) to plot the nondimensional response of the optimized system, and compare it with non-optimized cases.(b) Compare the optimized response above with that ...

Part (a): The mass ratio \mu = m_{2} / m_{1...
Question: 11.2

## In Fig. 11.10, the mass m1 and spring k1 represent a single-DOF system with low inherent damping. Its response z1, due to the applied force, F0, is found to be excessive. The obvious solution of adding a damper in parallel with k1 is found not to be feasible in this case, and it is proposed to add ...

Part (a): The value of the mass ratio, \mu ...
Question: B.1

## Use the area-moment method to derive the flexibility matrix for the cantilever beam shown in Fig. B2 at (a), where EI is constant over the length of the beam. ...

The flexibility influence coefficient matrix is de...
Question: 11.1

## Figure 11.3 shows a proposed vibration-isolated shelf, to be fitted at a location in a high performance aircraft, where the environmental vibration is broad-band random. The measured PSD levels, in the vertical direction, are all enveloped by the values shown in Table 11.1, which can therefore be ...

Part (a): From Eq. (10.44), the response PSD funct...
Question: 10.14

## It is desired to use a DFT program to measure the PSD of random pressure fluctuations generated by a jet engine, in the frequency band from 25 to 800 Hz. It is known from experience that in this case the spectrum will be fairly flat, so that it will be sufficient to plot it at 25 Hz intervals. A ...

Using a DFT with N = 2048 points, sampled at 2048 ...
Question: 10.13

## Extend the 10-point DFT calculation of Example 9.2, to illustrate the computation of:(a) the PSD function of x(t);(b) the ACF of x(t). ...

Part (a): Table 10.7 repeats the values of ...