Mechanical Vibration
Mechanical vibration is the oscillatory motion of a mechanical system about an equilibrium position, arising from elastic restoring forces and inertia. It occurs in structures, machines, and vehicles and can be free (natural), forced, or self-excited in nature. Understanding and controlling vibration is critical to prevent fatigue failure, noise generation, and resonance-induced catastrophic damage in engineering systems.
Key Formula
ω_n = sqrt(k / m)
LaTeX: \omega_n = \sqrt{\frac{k}{m}}
| Symbol | Meaning | Unit |
|---|---|---|
| \omega_n | Natural angular frequency | rad/s |
| k | Stiffness (spring constant) | N/m |
| m | Mass of the vibrating body | kg |
Worked Example
Problem
A machine component of mass 5 kg is mounted on a spring with stiffness k = 20,000 N/m. Calculate the natural frequency of vibration.
Solution
Step 1: Given m = 5 kg, k = 20,000 N/m. Step 2: Natural angular frequency: ω_n = √(k/m) = √(20,000/5) = √4,000 = 63.25 rad/s. Step 3: Natural frequency: f_n = ω_n / (2π) = 63.25 / 6.2832 = 10.07 Hz.
Answer
f_n ≈ 10.1 Hz
Types of Mechanical Vibration
| Type | Cause | Example | Control Method |
|---|---|---|---|
| Free vibration | Initial disturbance | Plucked guitar string | Damping materials |
| Forced vibration | External periodic force | Engine-mounted pump | Vibration isolation |
| Resonance | Forcing at natural freq. | Tacoma Narrows Bridge | Tuned mass dampers |
| Self-excited | Feedback from motion | Wheel shimmy | Structural modification |
| Random vibration | Irregular forces | Road vibration in cars | Active control |
Interactive Tools
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Related Terms
Vibration Damper
A vibration damper is a device that dissipates or absorbs vibrational energy from a mechanical system, reducing the amplitude of oscillation and suppressing resonance. Dampers operate by converting mechanical energy into heat through viscous friction, material hysteresis, or controlled mass tuning. They are widely used in automotive suspensions, civil structures, rotating machinery, and aerospace components to control excessive vibration and extend component life.
Fatigue Life
Fatigue life is the number of stress cycles that a material or component can endure at a given stress amplitude before fracture or failure occurs due to progressive crack initiation and propagation under cyclic loading. It is a critical design parameter for components subjected to repeated loading such as shafts, aircraft wings, and turbine blades. The S-N (Wöhler) curve relates the stress amplitude (S) to the number of cycles to failure (N) for a given material.
Composite Material
A composite material is an engineered material made from two or more constituent materials with significantly different physical or chemical properties, which remain distinct at the macroscopic level within the finished structure. The resulting composite typically exhibits superior performance characteristics — such as high strength-to-weight ratio, corrosion resistance, and tailored stiffness — compared to either constituent alone. Common composites include carbon fibre reinforced polymers (CFRP), glass fibre reinforced polymers (GFRP), and metal matrix composites (MMC).
From Latin "vibrare" meaning "to shake or brandish". The scientific study of vibration was formalised by mathematicians including Euler and Bernoulli in the 18th century, with systematic engineering analysis developed in the 19th and 20th centuries.