Vibration Analysis

In the realm of physics and engineering, understanding the dynamics of in-plane and out-of-plane motions is essential, as these movements significantly impact the behavior of systems and materials. Out-of-plane motion refers to displacements or changes occurring parallel to the optical axis, whereas in-plane motion involves movements within the plane perpendicular to the sensor’s optical axis. When these motions are periodic, they are classified as vibrations. Analyzing how a structure responds to external stimuli is crucial for ensuring product functionality, making vibration analysis a critical component in fields such as MEMS, microfluidics, and material science.

The Fourier Transform is an essential mathematical tool for vibration analysis, enabling a detailed examination of the frequency components of a signal. By breaking down complex vibrations into their fundamental frequencies—much like discerning individual notes in a musical chord—the Fourier Transform allows us to analyze key vibration characteristics such as amplitude, phase, and frequency. This technique is particularly powerful in identifying structural resonances, which occur when a structure vibrates in harmony with external forces at its natural frequency. Understanding these resonances is crucial for diagnosing potential issues in mechanical systems, ensuring their stability and longevity.

Another widely used technique for vibration analysis is lock-in amplification, which excels in data collection efficiency, especially when compared to the Fourier Transform that may not fully utilize all gathered data. A single-phase lock-in amplifier is capable of extracting both the phase and amplitude of an input signal, even amidst significant noise, by using the principle of demodulation. This process involves multiplying the input signal by a reference signal. However, it only measures the component of the signal that is in phase with the reference, potentially missing the quadrature component, which is 90 degrees out of phase.

In contrast, a dual-phase lock-in amplifier captures both the in-phase and quadrature components, providing a more comprehensive analysis of the signal’s amplitude and phase variations. After demodulation, the input signal’s oscillatory nature is removed, leaving a DC offset that contains the desired information about the signal’s phase and amplitude. A low-pass filter then isolates this DC component.

For a dual-phase lock-in amplifier, these DC offsets are mathematically expressed as:

DC_sin = Amplitude · cos(Phase_Shift)

DC_cos = Amplitude · sin(Phase_Shift)

To fully characterize a vibrational mode, we compute the phase and amplitude using these simple yet powerful trigonometric relationships:

Amplitude_input = √(DC²_sin + DC²_cos)

Phase_input = arctan(DC_cos / DC_sin)

This approach provides a detailed and accurate characterization of vibrational signals, making it a powerful tool for vibration analysis.

The aforementioned techniques can be employed interchangeably; however, Fourier Transform often serves as the foundational step in decomposing a signal to identify critical resonant frequencies, or eigenfrequencies. The process begins by exciting a sample, which can be achieved mechanically through a shaker stage, electrically via modulated voltage, or passively by leveraging phenomena such as Brownian motion. Structures naturally amplify external stimuli at specific frequencies—these are the resonances. By employing a Michelson interferometer, time-domain data is acquired, and upon applying Fourier Transformation, these resonances become apparent as distinct peaks in the vibrational analysis.

When integrated with scanning capabilities, this technique can be expanded to 2D and 3D analyses, enabling the direct visualization of vibrational modes across two or three dimensions—a process known as modal analysis.

Modal analysis is a technique that captures and visualizes the vibration modes of a structure in two dimensions, providing a comprehensive view of its motion. This analysis reveals areas of maximum amplitude, as well as stationary points, known as nodes. The distribution and number of these nodes define the specific vibration mode, which is a key aspect of vibrometry. By mapping these modes, scanning vibrometry offers valuable insights into the dynamic behavior of structures.

At SmarAct, we have the capability to perform quantitative measurements of out-of-plane vibrations utilizing a variety of methods, thanks to the precise displacement data we obtain through Michelson interferometry. This technique allows us to directly measure the extent of vibrations.

While Michelson Interferometers are highly effective for quantifying out-of-plane displacements, in-plane motion analysis requires a different approach due to the inherent limitations of phase-based measurement techniques. Since in-plane movement does not produce phase differences, an alternative method is employed. In this context, the reflection signal, specifically the radius of the Lissajous graph, is utilized to monitor horizontal movements. The in-plane analysis is further refined using the knife-edge method, which evaluates how an object’s movement influences signal intensity.