Mechanical Vibrations

Mechanical vibrations are mechanical oscillations that arise when the equilibrium state of a physical system is disturbed and are typically defined as periodic motions. These vibrations become more pronounced under the influence of external forces close to the system’s natural frequencies and can directly affect its performance, safety, and durability.

Basic Concepts of Mechanical Vibrations

Types of Vibrations

Mechanical vibrations can be classified into different types based on the direction and nature of motion:

• Free Vibrations: Vibrations that occur without any external force, driven solely by the system’s internal energy.
• Forced Vibrations: Vibrations that arise when a periodic external force is applied to the system.
• Damped Vibrations: Vibrations in which energy loss occurs during oscillation, leading to the attenuation of the system’s motion.

Key Parameters

The main parameters used in the analysis of vibrations are:

• Natural Frequency (ω₀): The frequency at which the system oscillates when no external force is applied.
• Damping Ratio (ζ): A measure of the energy dissipation within the system.
• Frequency Response Function (FRF): Describes the relationship between the system’s response and the frequency of an external force.

Analysis of Mechanical Vibrations

Mathematical Models

The analysis of mechanical systems typically employs second-order differential equations that incorporate parameters such as mass, damping ratio, and stiffness. For example, the equation of motion for a mass-spring-damper (MSD) system can be expressed as:

Modal Analysis

Modal analysis is a technique used to determine a system’s natural frequencies, mode shapes, and damping ratios. This analysis is particularly important for understanding the vibration behavior of complex structures. Experimental modal analysis measures the system’s response and uses software to analyze these parameters. For instance, a platform based on LabVIEW software has been developed for experimental modal analysis. This software identifies modal parameters using the system’s frequency response functions and compares them with experimental data for validation.

Isolation and Control of Mechanical Vibrations

Passive Isolation Methods

Passive isolation is achieved by adding elements to a system to prevent or reduce the transmission of vibrations. These elements include metal springs, rubber mounts, and flexible materials. In particular, metal-rubber composite structures are preferred in industrial applications for vibration isolation. The design of such elements can be optimized using finite element analysis (FEA).

Active Isolation Methods

Active isolation employs sensors to detect vibrations and actuators to respond to them in real time. These systems can adapt instantly to changing vibration conditions and offer high efficiency. For example, electromagnetic dampers can convert vibrational energy into electrical energy, making them suitable for energy harvesting applications.

Applications of Mechanical Vibrations

Industrial Applications

Vibrations in industrial machinery can shorten equipment lifespan and increase maintenance costs. Therefore, monitoring and controlling vibrations is essential. For instance, vibration signals from asynchronous motors can be measured to detect faults. Analyzing these signals is an effective method for early fault diagnosis in such systems.

Structural Vibrations

Structures such as buildings and bridges can vibrate due to environmental factors and external forces like traffic. These vibrations can affect structural safety and occupant comfort. Modal analysis and vibration measurements are used to understand the vibration behavior of structures.

Vehicle Vibrations

Vibrations in vehicles directly impact driver and passenger comfort. In particular, road surface irregularities, the vehicle’s suspension system, and interior design collectively determine the magnitude of these vibrations. Therefore, vibration analysis of vehicles is crucial for enhancing driver comfort.

Mechanical vibrations are a common phenomenon in engineering systems with significant effects on performance, safety, and durability. Consequently, the analysis, control, and isolation of vibrations constitute a fundamental area of research and application in engineering disciplines. Thanks to advancing technologies and analytical methods, mechanical vibrations can now be managed more effectively.