The following is a brief description of the four analyses.
A special kind of dynamic loading better known as impulsive can be analyzed in the time analysis. Impulsive loads are generally relatively short on duration, therefore, they are assumed to have an infinite period. These types of loads are frequently important in the design of certain classes of structural systems (e.g. vehicles such as trucks or automobiles). Dynamic Time Analysis can be used to obtain the steady state as well as the transient response of the system.
There are some types of load condition, which make an analysis more convenient to perform in the frequency domain. The frequency domain is superior to the time domain approach when the forcing load is periodic. A periodic loading exhibits the same time variation successively for a large number of cycles. The simple periodic loading has a sinusoidal variation also known as simple harmonic. Simple harmonic loading is characteristic of unbalanced-mass effects in rotating machinery. Other example of periodic loading are those caused by hydrodynamic pressure generated by a propeller at the stern of a ship or by inertial effects in reciprocating machinery, which are frequently more complex. However, by means of a Fourier analysis any periodic loading can be represented as the sum of a series of simple harmonic components.
Random vibration is exactly what the name describes, vibrations that occur randomly. Driving down the road makes a car vibrate. It is never known when the car will hit a bump in the road because it occurs randomly. This is different from the vibration caused by an engine or a tire rotating in regular cycles which is easier to analyze using dynamic frequency response.
Dynamic Shock analysis is based on the response of a single degree of freedom system. This technique usually provides maximum response of the system when excited with a given shock load. This is usually used for earthquake analysis.