# Periodic Excitation

Contents

## Concept

FEM-Design allows for calculation of periodically harmonic vibrations of dynamic effects, such as

- the centrifugal substitution load of an unbalanced mass rotating in a plane (e.g. ceiling fan),
- piston machine, which is the load calculated from the acceleration-deceleration mass on a given line.

The calculations are performed by the *Modal analysis* method using the periodic excited vibrations with harmonic sinus and/or cosine functions. The loads are assumed to be harmonic, so they are considered in the function of time (*t*) as: F(t) = Fr*cos(ωt) or Fr*sin(ωt), where *Fr* is the amplitude of the load function, *ω = 2*π*f*, and *f* is the excitation frequency.

There is a horizontal and a vertical load (e.g., in *x’-y ’*coordinate system) or just horizontal. What is considered horizontal or vertical is only decided when specifying the combination of periodic excitation.

## Restriction

Restrictions on periodic excitation dynamic analysis:

- No non-linear calculation (uplift, crack, plastic, nonlinear soil) is available.
- Diaphragm is not applicable.
- Only force loads are considered.
- The self-frequency calculation always runs before the periodic excitation calculation.

## Load cases

In case of a rotating mass, the horizontal and vertical loads must be specified in two separate load cases. There may be more than one of these pairs, but they can not be included in the same dynamic combination. In case of a piston, one load case is sufficient but it can only host loads that act together at the same time.

This is how the horizontal and vertical directions are recognized:

- If the mass rotates around the global
*Y*axis, then the horizontal direction is*X*, and the vertical direction is*Z*. - If the mass rotates around the global
*Z*axis (e.g.ceiling fan), then the horizontal direction is*X*, the vertical direction is*Y*. - In case of a mass moving on a line, there is only a horizontal direction.

## Dynamic combinations

One or maximum two related load cases can be included in a dynamic combination that should be created in the *Periodic excitation* dialog. Definition of the required frequency value (*f*), scaling factor and harmonic function (*cos* or *sin*) correspondence for the load combination is also required. The value of *f* should preferably be the same for both load cases in a combination.

## Dynamic analysis

The *Periodic excitation *calculation is based on a modal analysis, which means that FEM-Design will automatically run that *Eigenfrequency* calculation as an initial algorithm*. *The periodic excitation calculation requires several input parameters that can be found upon clicking on Setup button:

** delta t**: the step of saving the result; its recommended value is one tenth of the shortest vibration time (T

_{min}/10)

** t end:** the end time of saving the result; its recommended value is 5*T

_{max}, since only the stabilized part is calculated. This means that even the shape with the highest vibration time will be drawn with 5 full waves.

** Damping type**:

*Rayleigh*or

*Kelvin-Voigt*

** Damping factors**:

*Alpha*,

*Beta*and

*Ksi*

## Results

*Periodic excitation* results are available for defined calculated time points of dynamic combinations.

Maximum values can be selected as well:

absolute maximum of all calculated time points,*Maximum (abs)*:: positive maximum of all calculated time points,*Maximum +*: negative maximum of all calculated time points.*Maximum -*

The latter two are only available for *Internal forces* and *Reactions*.

**Dynamical translational displacement**

**Bar internal force, My’**

**Nodal acceleration / Displacement / Normalized dynamic factor**

These result types can be retrieved for each selected *Result point* as *Detailed results*: the result components (x, y, z) can be displayed individually or together as a function of time.

**Modal participation factor**

Modal participation factors are available for the whole structure in % and per dynamic combination and vibration shape, as horizontal (cos) and vertical (sin) factors.

## Documentation

All the Periodic excitation results can be listed in a tabular form and send to *Documentation *or external files.