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# Dynamic Response to Harmonic Loads

#### The SPACE GASS harmonic response module analyses the effect of time or frequency dependent load sources vibrating in a regular sinusoidal fashion. Typical harmonic load sources include vibrating machines such as crushers, pumps or vibrating tables, footfall excitation caused by people walking, running or jumping, vehicular excitation caused by moving traffic, imbalance in rotating parts of a machine, etc.

• Analysis types are:
• Time sampling (time-history response)
Evaluates the response of the structure over a period of time
• Frequency sampling (resonance response)
Evaluates the response of the structure over a range of frequencies
• Problem types are:
• Base displacements
• Base velocities
• Base accelerations
• Frequencies and phases can be defined for each load source.
• Loads with different frequencies and phases can be combined.
• User-defined factor vs frequency tables can be used with frequency sampling.
• Harmonic, transient, spectral and static analysis results can be combined.
• Damping can be Modal or Rayleigh.
• You can specify the number of calculation steps and the time or frequency range.
• The structure can be animated to see how it responds to the harmonic loads.
• Graphs of displacements, velocities and accelerations vs time (time sampling) or vs frequency (frequency sampling) are available.
• Displacements, forces, moments, stresses and reactions are available for each time or frequency step. Operating the module simply involves you defining your vibrating load sources, creating some harmonic load cases and then running the analysis. Once analysed, you can animate the model to see how it responds to the harmonic loads or you can generate graphs of displacements, velocities or accelerations vs time (for time sampling) or vs frequency (for frequency sampling). From there you can convert any of the time or frequency steps to load cases that contain displacements, forces, moments, stresses and reactions, just like you would get from a static analysis.

### Harmonic Load Cases

Each harmonic load case is defined by a source load case (for applied load problem types), problem type, mass case, base excitation (for base problem types), factor, frequency and phase. You can combine loads with different frequencies or phases by defining multiple lines in the datasheet that share the same harmonic load case number. ### Problem Types

Harmonic response problem types are:

• Base displacements
• Base velocities
• Base accelerations

Applied loads are typically used to model the effect on the structure of vibrating machines such as a vibrating screen, crusher, pump, motor or any out of balance rotating or oscillating mass. They can also be used to model the effect of walking excitation or vehicular traffic.

Base displacements, velocities or accelerations can be used to model the effect of the support nodes vibrating in-phase such as you might get with a car's suspension or a structure mounted on a vibrating platform.

### Analysis

A harmonic analysis lets you choose the list of load cases to be analysed, the modes to be considered, the damping settings, the time range (for time sampling) or frequency range (for frequency sampling) and the number of time or frequency steps.

Each time or frequency step represents a snapshot of the structure's response to the harmonic loads. Put together, they show the complete structural response and can be represented as an animation or as time-based or frequency-based graphs. ### Damping

The process by which free vibration steadily diminishes in amplitude is called damping. In actual structures, the damping mechanisms include friction at steel connections, opening and closing of micro-cracks in concrete, fireproofing, and friction between the structure itself and non-structural elements such as partition walls.

SPACE GASS allows you to disable damping or specify it as "Modal" or "Rayleigh". Modal damping uses a constant damping ratio for each dynamic mode, whereas Rayleigh damping uses a combination of mass-proportional and stiffness-proportional damping. ### Factor vs Frequency Table

When using frequency sampling, if the magnitude of the load source depends on its vibration frequency then you can define a factor vs frequency table that takes this into account. For example, a mass m rotating around a circle of radius r at a frequency of f has a dynamic force equal to ma = mr(2πf)2 and, as the frequency changes, the dynamic force changes in proportion to f2. This can be defined in the function editor as a simple equation and then transferred into the factor vs frequency table. ### Time or Frequency Sampling

#### Time Sampling

You should choose time sampling if you want to see how the structure responds to the vibrating load sources over a user-defined period of time. You can then generate time-based graphs of displacements, velocities or accelerations for any node or direction. Time sampling is normally used if you know the frequencies and phases of your loads and you want to see their effect on your structure. #### Frequency Sampling

You should choose frequency sampling if you want to see how the structure responds to a range of user-defined frequencies. You can then generate frequency-based graphs (resonance curves) of displacements, velocities or accelerations for any node or direction. Frequency sampling is useful if you want to see which frequencies cause maximum excitation (resonance) of your structure. ### Animation

The harmonic animation shows a realistic representation of how the structure responds to the harmonic loads. You can change the speed and amplitude of the animation on-the-fly by using the controller at the bottom. ### Reports

Reports that summarize the harmonic response results for each load case list the maximum translations, velocities and accelerations together with the time or frequency step at which they occur. ### Creating Result Load Cases

You can convert any of the harmonic time or frequency steps into load cases that contain displacements, forces, moments, stresses and reactions, just like you would get from a static analysis. They can then be used to generate bending moment diagrams, shear force diagrams, stress diagrams, etc. or used in any of the SPACE GASS steel or RC concrete design modules. 