Embedded Beam Experiment

Vibration modes are specific patterns of oscillation that a physical system naturally adopts when disturbed. Each mode is associated with a natural frequency. These modes are essential in the dynamic analysis of structures and components, including rotating machinery.

In the engineering of rotating machinery, such as turbines, engines, and pumps, the analysis of vibration modes is crucial. These machines operate at high speeds and are subject to dynamic forces that can induce vibrations. Knowing the vibration modes and their natural frequencies allows engineers to predict and avoid resonances, which occur when the operating frequency coincides with a natural frequency, resulting in significant amplification of vibrations. These amplifications can lead to accelerated wear, mechanical failures, and, in extreme cases, the destruction of the machine.

Furthermore, modal analysis helps identify structural problems and optimize design to improve performance and safety. This is particularly important in industries such as aerospace, automotive, and power generation, where reliability and efficiency are critical.

Embedded Beam Experiment: Demonstration of the First Three Vibration Modes

To demonstrate the principles of vibration modes, an experiment can be conducted with an embedded beam, which is a structure fixed at one end and free at the other. This experiment is a practical and visual way to understand how structures vibrate and how their natural frequencies can be determined.

Experiment Setup

Below are the lists of equipment/materials needed for the experiment as well as the procedures to be executed.

• Required Equipment:

1. A beam made of suitable material (e.g., steel or aluminum).

2. A rigid support to fix one end of the beam.

3. Displacement sensors or accelerometers to measure the beam's response.

4. An exciter (such as an electromagnetic actuator) to apply varying forces to the beam.

5. A data acquisition system to record the sensor measurements.

• Procedure:

1. Fix one end of the beam to the rigid support, ensuring that the other end is free.

2. Place displacement sensors or accelerometers at strategic points along the beam.

3. Use the exciter to apply varying forces to the beam and induce vibrations.

4. Record the beam's responses using the data acquisition system.

Embedded Beam Experiment Video

Analysis of results

The measurements obtained from the sensors will be analyzed to determine the natural frequencies and modal shapes of the beam. For this experiment, the focus will be on the first three vibration modes:

• First Vibration Mode: This mode features a single smooth curvature along the beam, with the greatest amplitude at the free end.

• Second Vibration Mode: This mode exhibits a waveform with a node (point of zero oscillation) in the middle of the beam, dividing the beam into two vibrating sections.

• Third Vibration Mode: This mode presents two nodes, dividing the beam into three vibrating sections, with more complex curvature patterns.

By comparing the experimental measurements with theoretical predictions, it is possible to validate the mathematical models used to describe the vibrational behavior of the beam, ensuring the accuracy of analyses and safety in the design of structures and machinery.

Conclusion

Understanding vibration modes and their natural frequencies is vital for the analysis and design of rotating machinery and other structures. Experiments like the embedded beam provide valuable insights into vibrational behavior and help ensure that structures are designed to avoid harmful resonances, resulting in safer and more efficient systems.