Short Answer:

Base excitation is a type of vibration that occurs when the base or support of a mechanical system moves or vibrates, causing the entire system to oscillate. Instead of an external force being applied directly to the mass, the vibration is introduced through the motion of the base.

In simple terms, base excitation happens when the foundation or support of a structure moves due to external causes such as an earthquake, road roughness, or machine vibration. The system then responds to this movement depending on its mass, stiffness, and damping characteristics.

Detailed Explanation :

Base Excitation

Base excitation is an important concept in the study of mechanical vibrations. It refers to the condition in which the vibration of a mechanical system is caused by the motion of its base or support rather than a direct external force applied to the mass. This type of vibration is commonly observed in real-world applications such as vehicles moving on uneven roads, buildings during earthquakes, and machines mounted on vibrating surfaces.

When the base of a structure moves, the connected parts like mass, spring, and damper experience a relative motion. The vibration of the base transfers energy to the system, resulting in oscillations. The motion of the base can be vertical, horizontal, or angular, depending on the type of system and excitation source.

Let us consider a simple model to understand this concept. A single-degree-of-freedom (SDOF) system with a mass  , spring stiffness  , and damping coefficient   is mounted on a vibrating base. If the displacement of the base is represented as   and that of the mass as  , then the relative displacement between the mass and the base is  .
The equation of motion for base excitation is written as:

This equation shows that the base motion acts as the source of vibration for the system. When the base moves, it causes a reaction in the attached mass due to the spring and damping forces.

The response of the system depends on the characteristics of the excitation and the properties of the system such as natural frequency and damping. The most common form of base excitation is harmonic base motion, represented as:

Where,

•  = amplitude of base motion,
•  = angular frequency of excitation.

Substituting this into the equation of motion gives the complete expression for the system’s response, which helps engineers determine how the mass moves relative to the base.

Physical Examples of Base Excitation

1. Vehicle Suspension Systems:
   When a vehicle moves on a rough or uneven road, the road surface acts as a vibrating base. The vibrations from the road are transmitted to the tires and then to the vehicle body. The suspension system acts as the spring and damper, controlling how much of the base motion (road vibration) is transmitted to passengers.
2. Buildings During Earthquakes:
   In this case, the ground acts as the base, and when it moves during an earthquake, it excites the building structure. The vibration response of the building depends on its natural frequency and damping. If the natural frequency matches the earthquake frequency, resonance may occur, leading to severe damage.
3. Machines on Vibrating Platforms:
   Machines mounted on platforms or floors that experience vibrations (for example, from nearby equipment) are also subjected to base excitation. The vibration from the base can affect the precision, performance, and life of the machine.

Response to Base Excitation

The system’s response to base excitation depends on several factors:

• Frequency Ratio ( ):
  The ratio of the excitation frequency to the natural frequency determines whether the system amplifies or isolates vibration.
  • For  , the motion of the mass follows the base closely.
  • For  , vibration isolation occurs, and the relative motion of the mass is smaller than the base motion.
• Damping Ratio ( ):
  Damping helps reduce vibration amplitude and prevents resonance. Higher damping reduces the peak response near resonance but can slightly increase response at higher frequencies.

The transmissibility ratio is also used to analyze base excitation, as it shows how much of the base motion is transmitted to the system. This is similar to the study of vibration isolation systems, where base motion is the main cause of vibration.

Importance of Base Excitation Analysis

Base excitation analysis is critical in designing systems that must resist or isolate vibrations transmitted through their support structures. Engineers use this analysis to ensure stability and safety in:

• Earthquake-resistant building design
• Vehicle suspension systems
• Machine foundation design
• Aerospace and ship structures

This analysis helps prevent excessive vibrations that can cause fatigue, noise, or even structural failure.

Conclusion:

Base excitation refers to the vibration of a system caused by the motion of its base or support. It is commonly seen in vehicles, buildings, and machines subjected to ground or surface motion. The response of a system to base excitation depends on its natural frequency, damping, and the frequency of the base motion. Studying base excitation helps engineers design systems that effectively minimize vibration transmission and improve performance, comfort, and safety.