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# Base Excitation

The Base excitation boundary condition allows to specify a base motion acceleration in a harmonic structural simulation. The acceleration is applied to all the faces that are constrained by means of a Fixed support boundary condition.

The parameters of the boundary condition to be defined are:

1. Direction: Vector pointing in the direction of the initial acceleration. The vector is represented through its x, y, and z components in the global frame of reference.
2. Acceleration: Scale factor for the acceleration vector, giving the magnitude of the acceleration. Can be specified as a constant value, or as a function of frequency using a table through the specify value button.
3. Phase angle: Allows to input different loads which are not synchronized, or in other terms, when the peak value of the different loads do not occur at the same time. The value ($$\varphi$$) for the angle can be related to the excitation frequency ($$f$$) and the time delay between the peaks ($$\delta$$) of two loads:

$$\varphi = 2 \pi f \delta$$

Assignments

Notice that this boundary condition, unlike the other ones, does not contain an assignment box. The base acceleration is applied to all the faces assigned to the Fixed support boundary condition. Thus, it is necessary to first define the fixed supports, then create the base excitation.

## Supported Analysis Types

The following analysis types support the usage of this boundary condition:

## Compatible Boundary Conditions

The base motion boundary condition can be used in combination, exclusively, with the following boundary conditions:

This exclusivity implies that boundary conditions not listed above can not be used in combination with the base motion, and trying to do so will result in an error message.

## Relative Frame of Reference

It is assumed that a rigid body motion is imposed to the fixed faces, due to the harmonic base excitation. Thus, the total displacement at any point in the structure can be expressed as the sum of a relative displacement with respect to the base and the rigid body motion of the base. The situation is illustrated in Figure 2:

Analytically, this can be expressed as:

$$X_T(t) = X_B(t) + X_R(t)$$

Which, due to the assumption of linearity in the harmonic analysis, also extends to the velocities and accelerations:

$$\dot{X}_T(t) = \dot{X}_B(t) + \dot{X}_R(t)$$

$$\ddot{X}_T(t) = \ddot{X}_B(t) + \ddot{X}_R(t)$$

In other words: one places the model in a frame of reference relative to the moving base, and the above corrections have to be performed in order to retrieve the motion with respect to an inertial frame of reference.

Moreover, all the displacements, velocities and accelerations in the result fields of a simulation under this boundary condition are expressed in the frame of reference relative to the base, and not in an inertial frame of reference. Thus, one has to be careful when comparing the results with other data, for example to experiments sampled with an accelerometer, where the registered values are total and not relative to the base motion.

## Application Notes

This boundary condition is intended to evaluate the inertial effects of a structure subject to harmonic base motion, transmitted through the points of support. Some examples of such cases are:

• Shaker table testing