1.2 Dynamic Impedance Versus Static Impedance

Understanding the fundamental distinction between static stiffness and dynamic stiffness is crucial in the field of structural engineering and mechanical systems analysis. Stiffness, a fundamental mechanical property, describes how a system or material responds to applied forces or displacements. However, the behavior of a system can differ significantly under static or dynamic loading conditions, giving rise to the concept of static stiffness and dynamic stiffness.

Figure 1.2a Single Degree of Freedom Static System (Load is applied statically, i.e. slowely)

Figure 1.2b Single Degree of Freedom Dynamic System (Load is applied dynamically, i.e. rapidly)

Impedance is a concept used in many fields, including physics and engineering. In systems with static loads, the static impedance can be expressed as a simple spring constant and a damper (Figure 1.2a). In a dynamical system, it's often associated with mechanical or electrical systems and refers to the measure of a system's opposition to motion when subjected to harmonic excitation. It can be defined as the complex ratio of the sinusoidal force (or voltage in an electrical system) applied to a system to the resulting velocity (or current in an electrical system) response. In a mechanical system represented by a mass spring system, it can be viewed as a box containing the spring and the damper. The spring represents the system stiffness and the damper represents the system damping (Figure 1.2b).

In a mechanical dynamical system, impedance depends on the frequency of the motion or excitation. Dynamic impedance is usually expressed as a complex number because it includes both the magnitude and phase information about the system's response. The real part of this complex number corresponds to the resistive (or "damping") characteristics of the system, while the imaginary part relates to the reactive (or "stiffness") characteristics.

In the context of mechanical systems, dynamic impedance can give valuable information about how a system will respond to vibrations. For instance, a system with high dynamic impedance at certain frequencies will not move much in response to forces at those frequencies, while a system with low dynamic impedance will have a large response.

Observations