When considering buildings, it is important to identify the natural frequencies of beams. The implication will...

When considering buildings, it is important to identify the natural frequencies of beams. The implication will be that rotating equipment (e.g. pumps, compressors, washing machines, etc.) are selected so that the natural frequency of the beam is not excited thus brining the entire structure into resonance and causing damage.

A beam will have an infinite number of natural frequencies. The natural frequencies of a beam are the roots of a characteristic equation (which can be obtained using various analytical methods). Consider a beam whose characteristic equation is given by:

cos(0.1012x)cosh(0.1012x)=1

where x is the natural frequency in Hz.

Problem :

Use the Newton-Raphson method to find the natural frequency of the beam near 46 Hz.

Expert Solution

genius_generous answered 2 years ago

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