# Dynamic structure analysis

The vibration behavior of a structure or building consists of two basic components:

**excitation frequency****natural frequency**of the structure (system answer)

The range in which natural frequency and excitation frequency overlap or are very close to each other is particularly critical. At this point a so-called dynamic elevation occurs, which can be harmful for a structure. This condition should be avoided if possible.

The natural frequency of a structure can be determined with a calculation model and modal analysis modal analysis by means of a tuned nnalysis software. A model (3D, surface or framework model) is implemented by the structure to be examined. The stiffness ratios and mass distribution are important in this context.

For stock structures, in-situ measurement is recommended. The excitation of the structure is recorded in the form of displacements, velocities or accelerations. By evaluating the measured quantities and a subsequent **Fast Fourier Transformation (FFT)** it is possible to split the digital signal into its frequency components. Frequency analysis enables the dynamic properties of a vibrating system to be identified by the input and output signal. The excitation of the structure from outside represents the input signal. The resulting vibrations are referred to as output signals. By using different signal analysis functions, it is possible to identify certain frequencies at which stronger vibrations (resonance) of the system occur.

If the natural frequencies of the structure have been identified and the frequency range of the excitation is known, the assessment of the susceptibility of the structure to resonance can take place. In order to be able to better assess a superposition of exciter frequency and natural frequency, the so-called **Campell diagram** is generally used. This makes it possible to compare the frequency ranges for the excitation and the determined natural frequencies of the structure. The Campell chart shows relatively quickly in which areas resonances can occur and at which frequencies the structure can be at risk.

# Dynamic amplication factors

The starting point of a dynamic structural analysis is often modal analysis or eigenfrequency analysis. This determines the influence of vibrations on a structure. The natural frequencies and the corresponding eigenforms of the structure are calculated. The natural frequency of a structure susceptible to vibration is the frequency with which the system can vibrate as its own form after a single excitation. If a weakly damped structure is excited from the outside with this frequency (excitation frequency), high amplitudes can occur. This is referred to as resonance effects.

After the preceding modal analysis, the calculation of a structure in the time domain is carried out, which is called dynamic structural analysis. This can usually only be carried out with numerical calculation methods. Unsteady or shock-like loads such as, for example, transient or shock loads are applied on the strukture or component, like:

- earth quakeen
- wind
- wave and current

The following time-dependent parameters can then be calculated:

- Internal forces
- Stress
- Strains
- Displacements / Rotations
- Forces at boundary conditions / suppoerting forces

# Services

The SKI Ingenieurges. mbH can offer structural and dynamic structural analyzes within the framework of structural design and structural assessment. These essentially comprise the following structural analyzes:

- Abstracting structure by a suitable model
- Determination of mass distribution
- Natural frequency analysis of the structure (modal analysis)
- In-situ measurements of the support structure
- Fast Fourier Transformation (FFT) of the measurement results
- Determination of natural frequencies
- Analysis and assessment of the frequency spectrum
- Assessment and definition of appropriate measures to reduce the resonance risk
- Calculation of buildings under earthquake stress
- Structural analyses of components by means of defined acceleration
- Design of structural loads due to wind, wave and current
- Time domain analyses