Vibration analysis
Basic vibration analysis can be understood by studying the model simple mass-spring-damper. Complex structures such as the car body can be modelled as "sum" model of mass-spring-damper. This Model is an example of a simple harmonic oscillator
Vibration
Vibration analysis
Free vibration without silencer
In the simplest model of the attenuation is considered negligible, and there is no outside force affecting mass (free vibration).
In these circumstances the prevailing style in the spring the long stretch comparable to Fs x according to Hooke's law, or when it is formulated mathematically:
Fs =-k x
with the k is the spring constant.
According to Newton's second law force posed is proportional to the acceleration of the mass:
Σ F = ma = m {x} = m {d ^ 2 x}: {dt ^ 2} =
Since F = Fs, we get the following ordinary differential equation:
m {x} + k x = 0.
Simple harmonic motion-spring system
If we assume that we start the vibration system with spring-loaded so far A stretch and then release it, the above equations solution describing the mass movements are:
x (t) = A 2cos (2pi. fn. t)
This solution suggests that the mass will oscillate in simple harmonic motion having an amplitude of A frequency and fn fn number is one of the most important quantities in vibration analysis, and called the undamped natural frequency. For a simple mass-spring system, the fn is defined as:
fn = {1: {2pi}}. root {k: m}
Note: the angular frequency ω (ω = 2πf) and units of radians per second is often used in equations because it simplifies the equations, but the magnitude is usually converted into a "standard" frequency (units of Hz) when stating the frequency of the system.
When the mass and stiffness (a k) Note the frequency of vibration of the system will be determined using the formula above.
Vibration
Vibration analysis
Free vibration with damping
When the attenuation is taken into account, means style silencer also applies on a mass in addition to the force caused by stretching the spring. When moving in a fluid object will get attenuation due to the viscosity of the fluid. The style of this viscosity is proportional to the speed of objects. Due to constant viscosity (viscosity) c is a coefficient with units of reducer, N s/m (SI)
The solution to this equation depends on the magnitude of the damping. When damping is small enough, the system will still vibrate, but will eventually stop. This State is called less mute, and is most cases get attention in the analysis of the vibration. When the attenuation is enlarged so that it reaches the point when the system is no longer oscillates we reach a point of critical damping. When the attenuation is added through this critical point of the system referred to in the State through the mute.
To characterize the amount of attenuation in the system used a ratio called the damping ratio. This ratio is the ratio between the actual amount of attenuation attenuation is required to reach the point of critical damping.
Damped natural frequency less than the undamped natural frequency, however, for many practical cases the damping ratio is relatively small, and hence the difference is negligible. Therefore the damped and undamped description is often not mentioned when declaring natural frequency.
