What is Natural Frequency?
Every system, assembly or component vibrates in some specific frequency in the absence of external load and damping- this vibration frequency is commonly known as Natural frequency or Eigen Frequency. For the various natural frequencies for a given component, it exhibits changes in the shape- it is called mode shapes. If the system moves in a sinusoidal manner with the same frequency-it is termed as normal mode. When these components are a part of a vibrating system and their natural frequency matches with the induced frequency, the vibration tends to amplify and resonance takes place, where the amplitude will higher and the component is weaker. The value at which the resonance takes place is called resonance frequency.
When the system’s induced frequency matches or closer to the natural frequency of the component, the component exhibits high amplitude, low stiffness and may even cause failures and cracks. The natural frequency and Induced frequencies are completely different concepts. The natural frequency of an elastic component is similar to a mass and spring concept of discussion and is defined by mass(m) and stiffness(k) of that component. This stiffness varies with shape, material, constraint etc.
What is Modal Analysis?
Modal Analysis in Finite element analysis (FEA) plays a vital role to determine the dynamic nature of the system or component and to find its natural frequencies. The dynamic nature of the system-determines the system’s response to the induced vibration and dynamic forces. For any system in a vibrational environment, the induced vibration is maintained not to match or gets closer to the natural frequency of the system, if not the vibrational amplitude increases drastically and stiffness falls drastically to vibrate in the mode shapes of the components and is called resonance. Resonance result in sudden failure and cracks.
- For any component, that is a part of a vibrational system- it is necessary to know that the natural frequency and is maintained away from the √2 of the natural frequency of that component for proper working and avoid sudden failure.
- For systems that involve human resources, it is mandatory to have natural frequency and induced vibration above 11Hz for safety precautions – Human body parts have a natural frequency band 4-6 Hz and 7.5Hz in an average.
- Natural frequency and resonance affect the stability of the structure and skyscrapers during wind-induced vibration and seismic conditions. The structural stiffness is lifted-up to a certain extent that it does it match the induced vibrational band.
Case 1: Structural collapse of Tacoma bridge – resonance with Aerodynamic Flutter
As we discussed the aerodynamic fluttering in our blog, COMPUTATIONAL FLUID DYNAMICS FOR PRODUCT DEVELOPMENT- WHAT, WHY AND HOW? – the induced frequency of the aerodynamic fluttering resonates with the natural frequency of the bridge results in large amplitude of vibration and deformation causing a sudden collapse of that large structure
Case 2: Skyscrapers and Dampers
Skyscrapers like Burj Khalifa, Taipei 101, 121-story Shanghai Tower are constant harassed by the wind-induced vibrations. They are incorporated with tuned mass damper setup to dampen the vibration amplitude and frequency with in a definite band and protect the structure from resonance and swaying
Case 3: Casing Modal study
Graphler Technology solutions worked on this case to find the root cause of sudden failure in the component with cracks propagating in a definite pattern. The failure occurred due to the resonance with the induced vibration in a specific scenario – where some fasteners lost its grip over the component.
Conclusion :
Graphler Technology, one of the fastest growing product design companies in India. Our FEA Consulting Services holds great promise for the Model Analysis, .We have a team of experts specialized in CFD Analysis Services, 3D CAD Design and 3D Modelling Services in India.
