Modal Theory of Single Degree of Freedom System Dept. of Mechanical Engineering Yungpeng Wang 南臺科技大學 STUST.

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Modal Theory of Single Degree of Freedom System Dept. of Mechanical Engineering Yungpeng Wang 南臺科技大學 STUST

Introduction to Modal Theory 1. Theory 2. Laplace Domain Theory 3. Definition Of Terms 4. System Classifications 5. Analytical Model 6. Frequency Response Function Representation 7. Impulse Response Function Representation 8. Change of Physical Parameters 9. Estimating Partial Fraction Parameters 南臺科技大學 STUST

Theory 1. Equation of Motion: Single degree of freedom system, 2 nd order differential equation. 2. Response (Solution) of Single Degree of Freedom System: Transient portion, Steady state portion 南臺科技大學 STUST

Laplace Domain Theory 1. (System) Impedance. 2. (System) Transfer Function 南臺科技大學 STUST

Definition Of Terms 南臺科技大學 STUST 1. Critical Damping 2. Damping Ratio

System Classifications 南臺科技大學 STUST 1. Overdamped system:  1 > 1 2. Critically damped system:  1 > 1 3. Underdamped system:  1 > 1

Analytical Model 南臺科技大學 STUST 1. Scalar Polynomial: M, C, K 2. Partial Fraction: Poles, Residues

Frequency Response Function Representation 南臺科技大學 STUST 1. From an experimental point of view, when one talks about measuring a transfer function, the frequency response function is actually being measured.

Change of Physical Parameters 南臺科技大學 STUST 1. Change of Stiffness 2. Change of Damping Coefficient 3. Change of Mass

Estimating Partial Fraction Parameters 南臺科技大學 STUST 1. Estimating damped natural frequency 2. Estimating damping ratio and damping factor: Half-power bandwidth method 3. Estimating residue