What Is the Dynamic Complex Shear Modulus & Loss Factor tan(δ) Calculator?
Complex modulus describes the complete viscoelastic resistance of materials under harmonic oscillation.
How Does the Dynamic Complex Shear Modulus & Loss Factor tan(δ) Calculator Work?
Storage modulus G′ stores energy elastically; loss modulus G″ dissipates energy into heat.
Dynamic Complex Shear Modulus & Loss Factor tan(δ) Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
|G^*| = \sqrt{(G')^2 + (G'')^2}, \quad \tan(\delta) = \frac{G''}{G'}, \quad \delta = \arctan\left(\frac{G''}{G'}\right)
Complex modulus magnitude and loss tangent damping factor.
How to Use the Dynamic Complex Shear Modulus & Loss Factor tan(δ) Calculator
- Input storage modulus G′ and loss modulus G″ from DMA or rheometer tests.
Step-by-Step Example Calculation
Viscoelastic Damping Layer
Input Values:
storageModulusGPrimePa:4000000
lossModulusGDoublePrimePa:3000000
Worked Steps: Evaluates complex modulus |G*| = 5.0 MPa, loss factor tan(delta) = 0.75, and phase angle = 36.87°.
Understanding Your Result
Reveals tan(delta) damping capacity and overall stiffness magnitude |G*|.
Factors That Affect the Result
- Peak tan(delta) corresponds to maximum vibration damping and acoustic absorption.
When Should You Use This Calculator?
- Designing engine vibration isolators, tire treads, and viscoelastic acoustic dampers.
Assumptions & Limitations
- Applies to linear viscoelastic regime at constant harmonic frequency.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard ASTM D4065 / ISO 6721 dynamic mechanical analysis formulation.