### Solid Dynamics Problem Solving

The problems of the dynamics are:

- modal analysis
- harmonic analysis
- transient analysis
- spectral analysis
- explicit dynamics analysis

**Modal analysis** (or analysis of free oscillations) carried out to determine natural (resonance) frequencies and mode shapes details and constructions.

*Natural vibration frequency* corresponds to the expected resonant frequency of the structure.

*Mode shape* shows how the relative deformation (displacement) will experience a structure in the event of resonance in the respective natural frequency. Knowing the expected mode shape at a natural frequency can be, for example, set an additional securing or support structure in the area corresponding to the peak of the mode shape, resulting in an effective change in the spectral properties of the product.

**Harmonic analysis** is used to find the steady reaction (response) of linear systems loaded with sinusoidal forces. Determines the responsiveness of the system at several frequencies and plotted the amplitude-frequency characteristics. Maximum response found on the schedule will correspond the maximum stresses in the structure. Harmonic analysis designed for finding the maximum levels steady vibration. Transients are not evaluated in this kind of analysis.

Maximum response to harmonic effects achieved when the frequency coincides with the natural frequencies of the structure. Therefore, prior to the harmonic analysis, modal analysis should be carried out to determine the natural frequencies.

**Transient analysis **(sometimes referred to as the analysis of the time) designed for finding the dynamic response of the system under the action of some time-dependent loads. This type of analysis is used to determine the time dependence of displacements, strains, stresses and forces in the system as a reaction to some combination of static, transient and harmonic forces. Calculation of the time scale means that the effects of inertia and damping are important.

**Spectral analysis** Spectral analysis is the calculation of displacements and stresses in the structure using the results of modal analysis. This type of analysis is mostly used instead of timing analysis (transient) to determine the response structure under the influence of accidental loads or time dependent loads, such as an earthquake or wind load, the load on the sea waves, the impact of a jet engine, and so further.

**Explicit dynamics analysis** it based on the solution of differential equations in partial derivatives, expressing conservation laws of mass, momentum and energy with the use of time integration explicitly. This analysis is used to highly nonlinear processes occurring in small intervals of time, such as high-speed and low-speed bumps, explosive load, highly nonlinear plastic deformation, the problem of contact being destroyed.