Material fundamentals · Elasticity
Dynamic Young’s modulus
What does “stiff wood” actually describe?
Young’s modulus links normal stress to axial strain. In vibration testing, a dynamic modulus describes the elastic part of the response under the stated frequency and measurement model.
Try the interactive demoStart with something familiar
Pull a short strip and a long strip of the same material. The long one stretches farther under equal force. That does not mean its material has become softer: the object’s size has changed.
L
Same E, force and area
L × 2
Same E, force and area
Notice what changes
Force spread over area is called stress. Extension divided by original length is called strain. These let us compare differently sized specimens on a common basis.
Understand why
Young’s modulus compares stress with strain in the elastic range. A larger value means more stress is needed for the same relative stretch. It is not a breaking-load measurement.
Connect it to wood and making
Dynamic tests infer the response during vibration. Wood direction, test frequency and the model must accompany the result. Plate stiffness then combines this property with thickness and arching.
Put names to the ideas
Material property, not spring stiffness
E is measured in Pa, commonly GPa for wood. For a uniform axial bar, object stiffness is k = EA/L. Changing length or area changes k even when E is unchanged.
Dynamic is a test condition
A complex modulus E* = E′ + iE″ separates storage and loss response under harmonic loading. Resonance-derived E′ and a static bending modulus are not interchangeable without checking the protocol.
Direction is essential
Wood has different longitudinal, radial and tangential moduli. A longitudinal bending test estimates a relevant directional modulus, not every elastic constant of a violin plate.
σ = force/area, ε = extension/original length, and E = σ/ε. E′ is the storage part in a dynamic test: the part associated with recoverable elastic response rather than loss.
A worked example
Two bars with the same E and length but twice the cross-sectional area have twice the axial stiffness. In bending, thickness has a stronger geometric effect through the second moment of area.
Explore it yourself
When recording a modulus, attach the direction, static or dynamic method, geometry, frequency and environmental conditions.
- c
- 5345 m/s
- E′/ρ
- 28.57 10⁶ m²/s²
- R
- 12.73 m⁴/(kg·s)
- Z
- 2.24 MRayl
- Q ≈ 1/η
- 100.0
- ACE
- 1273 m⁴/(kg·s)
E′ + ρ → c → R, Z η → Q → ACE