Structural dynamics

The Structural Dynamics deals with the calculation and assessment dynamic be congested buildings .

In contrast to the structural analysis , the dimension of time or frequency is taken into account in the area of ​​structural dynamics . In the construction sector, this is in principle necessary when temporally variable forces act on a structure and at the same time the structure offers the possibility of reacting (oscillating) to these influences due to its construction. The acting forces can act directly on a structure (force excitation) or also be entered in a structure via the subsurface (load case of "base point excitation"). The structural dynamics is part of the structural dynamics, which in German is often referred to as dynamics and deals with the mechanical properties of moving components of all kinds. In the English-speaking world, the term structural dynamics is used precisely to distinguish between structure, flow and electrodynamics.

theory

In addition to the stiffness matrix common in statics, a mass matrix is ​​required in dynamics to take into account the forces of inertia. In addition, the system damping must usually be taken into account. This can be done in different ways. The classic approach is to use a damping matrix (viscous characteristic, i.e. proportional to the vibration velocity). Material damping (= internal damping due to small friction processes) can be taken into account in a complex form, with the "loss factor" being added to the static modulus of stiffness of the material in question (so-called hysteretic damping).

The mass and damping matrix turns a (linear) system of equations into a (linear) differential equation system.

Solution strategies

The following possible solutions are available:

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

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

• Harmonic loads
• Transient loads (variable over time, e.g. increasing and decreasing)
• Impulse excitation

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

Computational tools / methods

The solution of structural dynamics problems using the finite element method / calculation (FEM) is widespread. However, this method has many limitations:

• Wave radiation in half space

requires either very large calculation models until the wave emitted to infinity has subsided; otherwise there are reflections that affect the result

or suitable elements that can map the energy radiation into infinity.

• Knowing only about natural frequencies can only reveal critical frequency ranges. A complete system calculation, however, requires precise knowledge of the damping characteristics, damping quantities and the excitation characteristics.

• Options for parameter variation and processing of results are mostly very limited up to now.

So-called replacement models (simple models) are usually much more suitable for short-term problem solutions. However, they require the user (= creator of a model) to have a sound knowledge of building dynamics.

Among other things, are used

• Multi-body simulations
• Continuous systems
• Implied FE approaches
• Commercial FE models as a substructure
• Transformed modeling for continua (e.g. floor: model for half-space, layered half-space, etc.)
• Semi-empirical models; generally adapt via measurement data (see below)

The advantages of these calculation models are the extremely short calculation times, which enable rapid variant analyzes and show that the results are dependent on the (fuzzy) input values.

Areas of responsibility in practice

Vibrations are caused by:

• earthquake
• Effect of wind on slender structures (e.g. towers, chimneys, wide-span bridges)
• trains passing on railway lines
• Construction operation (e.g. vibrating sheet piles )
• Industrial vibrations from machines (e.g. in heavy industry )

Special tasks:

• Execution of extremely immission-sensitive systems (e.g. scanning electron microscope)
• Bearing of emitting machines (vibrating foundation, e.g. elastic bearing of presses or mills)
• Reduction of secondary airborne noise (noise radiation from vibrating structures, e.g. railway bridge)

Vibrations can often be reduced by using materials with a high level of internal damping . The attenuation is expressed in the loss factor µ of the material.

Structural dynamics engineers also take vibration measurements, which serve as the basis for calculation and system understanding.

literature

• Helmut Kramer: Applied Structural Dynamics. Basics and examples for study and practice . Ernst & Sohn, Berlin 2007, ISBN 978-3-433-01823-1 .
• Lothar Stempniewski, Björn Haag: Building dynamics practice. Bauwerk Verlag, Berlin 2010, ISBN 978-3-89932-264-4 .