Getaran: Perbedaan antara revisi

=== Getaran bebas dengan redaman ===

 

 

Bila peredaman diperhitungkan, berarti gaya peredam juga berlaku pada massa selain gaya yang disebabkan oleh peregangan pegas. Bila bergerak dalam [[fluida]] benda akan mendapatkan peredaman karena kekentalan fluida. Gaya akibat kekentalan ini sebanding dengan kecepatan benda. Konstanta akibat kekentalan (viskositas) ''c'' ini dinamakan koefisien peredam, dengan satuan N s/m (SI)

:<math>\phi= \arctan {\left (\frac{2 \zeta r}{1-r^2} \right)} </math>

 

 

The plot of these functions, called "the frequency response of the system", presents one of the most important features in forced vibration. In a lightly damped system when the forcing frequency nears the natural frequency (<math>r \approx 1 </math>) the amplitude of the vibration can get extremely high. This phenomenon is called '''[[mechanical resonance|resonance]]''' (subsequently the natural frequency of a system is often referred to as the resonant frequency). In rotor bearing systems any rotational speed that excites a resonant frequency is referred to as a [[critical speed]].

In a previous section only a simple harmonic force was applied to the model, but this can be extended considerably using two powerful mathematical tools. The first is the [[Fourier transform]] that takes a signal as a function of time ([[time domain]]) and breaks it down into its harmonic components as a function of frequency ([[frequency domain]]). For example, let us apply a force to the mass-spring-damper model that repeats the following cycle--a force equal to 1 [[newton]] for 0.5 second and then no force for 0.5 second. This type of force has the shape of a 1 Hz [[square wave]].

 

 

The Fourier transform of the square wave generates a [[frequency spectrum]] that presents the magnitude of the harmonics that make up the square wave (the phase is also generated, but is typically of less concern and therefore is often not plotted). The Fourier transform can also be used to analyze non-[[periodic function|periodic]] functions such as transients (e.g. impulses) and random functions. With the advent of the modern computer the Fourier transform is almost always computed using the [[Fast Fourier Transform]] (FFT) computer algorithm in combination with a [[window function]].

 

For example, let us calculate the FRF for a mass-spring-damper system with a mass of 1 kg, spring stiffness of 1.93 N/mm and a damping ratio of 0.1. The values of the spring and mass give a natural frequency of 7 Hz for this specific system. If we apply the 1 Hz square wave from earlier we can calculate the predicted vibration of the mass. The figure illustrates the resulting vibration. It happens in this example that the fourth harmonic of the square wave falls at 7 Hz. The frequency response of the mass-spring-damper therefore outputs a high 7 Hz vibration even though the input force had a relatively low 7 Hz harmonic. This example highlights that the resulting vibration is dependent on both the forcing function and the system that the force is applied to.

 

The figure also shows the time domain representation of the resulting vibration. This is done by performing an inverse Fourier Transform that converts frequency domain data to time domain. In practice, this is rarely done because the frequency spectrum provides all the necessary information.

* {{en}}[http://structdynviblab.mcgill.ca/index.html Structural Dynamics and Vibration Laboratory of McGill University]

* {{en}}[http://web.mat.bham.ac.uk/C.J.Sangwin/Teaching/CircWaves/waves.html Normal vibration modes of a circular membrane]

 

[[Kategori:Mekanika]]

[[fa:ارتعاش]]

[[fr:Vibration]]

[[is:Titringur]]

[[it:Vibrazione]]

[[ja:振動運動]]

[[pt:Vibração]]

[[ru:Виброизоляция]]

[[sv:Vibration]]