Understanding Structural Vibrations Without External Excitation

When a structure vibrates after an initial disturbance, and there is no ongoing external force applying energy to sustain the motion, this type of vibration is known as Free vibrations. Let's explore the different types of vibrations to understand why this is the correct answer.

Defining Types of Vibrations

• Free vibrations: These occur when a structure is displaced from its equilibrium position and then released. The vibration continues naturally due to the internal restoring forces without any external periodic force acting on it. The frequency of this vibration is called the natural frequency.
• Forced vibrations: These happen when an external periodic force or excitation is applied to the structure. The structure then vibrates at the frequency of the applied external force, not necessarily its natural frequency. Examples include vibrations caused by machinery or wind.
• Natural vibrations: This term is often used interchangeably with free vibrations. It refers to the vibration of a system at its own natural frequency (or frequencies) of oscillation, without any damping or external driving force. The natural frequency, often denoted as $\omega_n$ (for undamped systems), depends on the structure's mass and stiffness properties.
• Damped vibrations: This describes vibrations where the amplitude gradually decreases over time. This reduction in amplitude is caused by energy dissipation mechanisms like friction or air resistance within the structure. Damped vibrations can occur during both free and forced vibration scenarios, but the key characteristic is the decay of motion.

Analysis of Vibration Conditions

The question specifically states that the structure vibrates "without any external dynamic excitation." This condition directly matches the definition of free vibrations. While natural vibrations occur at the natural frequency, the phenomenon described is the vibration itself occurring without external input. Forced vibrations require external excitation. Damped vibrations describe the decay of amplitude, which is a characteristic that can accompany free vibrations but doesn't define the condition of no external force.

Consider a simple example: pulling a bell and releasing it. It rings (vibrates) due to its internal properties. This is free vibration. If you continuously hit the bell with a hammer rhythmically, it would be forced vibration. The ringing sound of the bell eventually fades because of damping, but the initial ringing after release, without further hits, is primarily classified as free vibration.

Conclusion

Based on the condition of vibrating "without any external dynamic excitation," the correct classification of the vibration is Free vibrations.