Structural dynamics

The structural dynamics is concerned with the calculation and assessment of dynamically loaded structures.

In contrast to the structural analysis the dimension of time or the frequency is taken into account in the task of structural dynamics. This is the construction in principle necessary when time varying forces acting on a structure and the structure also, due to its construction, the possibility ( swinging ) to respond to these agents. The acting forces can be directly on a building act ( force excitation ) or on the ground in a building registered (load case, the " Fußpunktanregung ").

Theory

Apart from the usual in the static stiffness matrix of a mass matrix for the consideration of inertial forces is needed in the dynamics. Furthermore, it is taken into account in the control system damping. This can be done in different ways. Classic is the consideration by means of a damping matrix ( viscous characteristic, that is proportional to the vibration velocity ). A material damping ( = internal damping due to less frictional processes ) can be considered in complex form, is where the " loss factor " to the static stiffness modulus of the material under consideration slammed (so-called hysteretic damping).

Through the damping mass and the matrix is ​​a (linear) system of equations (linear ) differential equations.

Solution strategies

The following solutions are available:

• Solution in the frequency domain ( as a function of the time)
• Solution in the time domain ( time step integration)
• Modal analysis (identifying natural frequencies, mode shapes )

For the selection of the solution path, it is important to know the load occurring closer. Dynamic loads can generally be divided into:

• Harmonic loads
• Transient loads ( variable in time, such as on - and decaying )
• Pulse excitation

Furthermore, the periodicity of a load in problem solving can help. The same is true for purely randomly distributed loads ( noise).

Computational tools / methods

Widespread is the solution baudynamischer problems using finite element method / calculation ( FEM). This method, however, comes in all sorts of boundaries:

• Wave radiation in the half space

Or suitable elements, which provide the energy radiation to infinity.

• The knowledge alone of natural frequencies can only disclose critical frequency ranges. However, a complete system calculation assumes precise knowledge of the attenuation characteristics, damping sizes and excitation characteristics.

• Ways to parameter variation and result processing are so far mostly been restricted.

: Amongst other things,

• Multi-body simulations
• Continuous systems
• Implicit FE approaches
• Commercial FE models as a sub-
• Transform modeling for continua (eg soil: model for half-space, layered half space, etc.)
• Semi-empirical models; generally adapt on measurement data ( see below)

Advantages of these computational models are the extremely short computation times that allow rapid variation analysis and show the result as a function of the ( fuzzy ) input values.

Areas of responsibility in practice

General:

• Earthquake
• Wind on slender structures (eg towers, chimneys, long-span bridges)
• Shocks (eg ) residential buildings to rail lines )

In Germany:

• Train vibrations
• Vibrations from construction operations (eg sheet piles - shaking in )
• Industrial vibration (car and heavy industry )
• Execution extremely immissionsempfindlicher systems (eg scanning electron microscope)
• Storage emitting machines (vibrating foundation, such as Elastic support of presses or mills )
• Secondary airborne sound problems ( sound radiation of vibrating structures, such as the railway bridge)

In practice, the Baudynamiker addition to the above-mentioned computational solution strategies must be familiar in the field of vibration measurements. Dynamic measurements are essential for the collection of input data and for the understanding of the system.