“Modes” are a major topic in the study of vibration of dynamic systems. A (hopefully) minimally controversial and carefully constructed definition is provided here.
Modes go by several names. You might have heard any of the following used in this context:
- Modes
- Vibrational modes
- Structural modes
- Elastic modes
- Normal, natural, or real modes
These generally refer to the same thing, provided damping can be ignored. If damping is sufficiently low, then the difference in meaning between these terms is minor. And it usually is, thus the near interchangable use of these terms.
Let’s seek a clear, concise definition for our basic term “mode”, starting with a familiar textbook reference:
The word mode generally refers to both the natural frequency and its corresponding mode shape. A mode shape is a mathematical description of a deflection. It forms a pattern that describes the shape of vibration if the system were to vibrate only at the corresponding natural frequency.
Inman, Engineering Vibration, 2014
Perhaps we can adjust this slightly:
The word mode generally refers to both the natural frequency and its corresponding mode shape. A mode shape is a mathematical description of a deflection that provides the relative displacements of each of the physical coordinates when the system vibrates at the mode’s corresponding natural frequency.
Modes are a property, not a response quantity. More philosophically, modes are about a balance of mass and stiffness properties. Stiffness is a means to store potential (or strain) energy, but there is also kinetic energy associated with the motion of mass. Motion at a natural frequency is a balance between these energies.
Modal analysis is a means to predict modes from know mass distributions and stiffness (e.g. material) properties using FEA. These are called normal modes. It can’t be overstated how much insight into the dynamic response or stability that a modal analysis provides, or how much using modes in other analysis reduces analysis complexity. Side note – modes are properties of all real structures, and there are an infinite amount of modes for a real continuous structure. When we employ finite element analysis, we discretize structure into a number of degrees of freedom. The number of DOF sets the limit on the number of modes that analysis can recover, the important influence of modeling choices notwithstanding.
Modal testing is a means to determine modal properties of a structure with specific vibration testing methods. It is employed to validate techniques of modal analysis. Modal testing also exposes damping properties that can arise from material and construction methods and is not generally possible to predict analytically. An entire industry centered around modal testing. Like modal analysis, much knowledge and skill is attributed to this field.
A fun reference on aircraft modes can be read in reference [3].
Other modes types not in family with the prior list:
- Aeroelastic modes. Aeroelastic modes are structural modes influenced by aerodynamics, which can lead to coupling of modes and potential significant changes to a mode’s frequency, shape, and damping levels. Modes not influenced by aerodynamics are typically labeled “vacuum (vacuo) modes” or “wind off modes”.
- Rigid body modes. There are no relative displacements between any points in the body (structure), in contrast with elastic modes. Examples of rigid body modes include pitching (R2 motion) or heaving (T3 motion).
- Control surface modes. A subset of modes associated with rotation of a control surfaces about its hingeline. This is an elastic mode. In some contexts, like for loads analysis, this can instead refer to rigid unit deflection of the control surface for the determination of control surface increments that are part of trim analysis.
One mode type in particular is not in family with the prior list.
References
- Inman, D. J. (2014). Engineering vibration (4th ed.). Pearson.
- Beam_mode_3.gif: The original uploader was Lzyvzl at English Wikipedia. derivative work: Jahobr, CC BY-SA 3.0, via Wikimedia Commons
- Oliver Herrero, M., Arévalo Lozano, F., & Climent Máñez, H. (2017). Aircraft normal modes… Friend or foe? An Airbus answer. Paper presented at the 6th CEAS Air & Space Conference (CEAS 2017), Bucharest, Romania. Retrieved from https://www.fzt.haw-hamburg.de/pers/Scholz/ewade/2017/CEAS2017/960-final.pdf