# Vibration

What is Vibration?

Vibration is a force which oscillates about some specified reference point. Vibration is commonly expressed in terms of frequency such as cycles per second (cps), Hertz (Hz), cycles per minute (cpm) or (rpm) and strokes per minute (spm). This is the number of oscillations which occurs in that time period. The amplitude is the magnitude or distance of travel of the force.

What is Isolation?

Isolation is a reduction in the capacity of a system to respond to an excitation. This is attained through various techniques designed to decouplle the vibration of the mounting surface from the component itself.

The predominant technique used is tuned mass spring dampers such as air bladders, mechanical springs and compliant material such as sorbethane. To a lesser extent, active vibration cancellation is also used.

What is Natural Frequency?

Natural frequency is defined as the number of cycles of oscillation that occurs in a time period when moved from its normal position and allowed to vibrate freely.

What is Resonance?

Resonance occurs when the frequency of excitation is equal to the natural frequency of the system. When this happens, the amplitude of vibration increases and is only limited by the amount of damping present in the system.

For example, in any given room there may be structures in the walls, floor, ceiling and even furniture which could resonate with certain frequencies in the music. This leads to unwanted phase and frequency response distortions which color and impair tonality. This is also known as sympathetic vibration.

What is Free Vibration?

Free vibration is the natural response of a structure to some impact or displacement. The response is completely determined by the properties of the structure and its vibration can be understood by examining the structure’s mechanical properties. For example, when you pluck a string of a guitar, it vibrates at the tuned frequency and generates the desired sound. The frequency of the tone is a function of the tension in the string and is not related to the plucking technique.

What is Forced Vibration?

Forced Vibration is the response of a structure to a repetitive forcing function that causes the structure to vibrate at the frequency of the excitation. For example, the rear view mirror on a car will always vibrate at the frequency associated with the engine’s RPMs. In forced vibration, there is a relationship between the amplitude of the forcing function and the corresponding vibration level. The relationship is dictated by the properties of the structure.

What is Sinusoidal Vibration?

Sinusoidal vibration is a special class of vibration. The structure is excited by a forcing function that is a pure tone with a single frequency. Sinusoidal vibration is not very common in nature, but it provides an excellent engineering tool that enables us to understand complex vibrations by breaking them down into simple, one-tone vibrations. The motion of any point on the structure can be described as a sinusoidal function of time.

What is Random Vibration?

Random vibration is very common in nature. The vibration you feel when driving a car results from a complex combination of the rough road surface, engine vibration, wind striking the car’s exterior, etc. Instead of trying to quantify each of these effects, they are commonly described by using statistical parameters. Random vibration quantifies the average vibration level over time across a frequency spectrum.

What is a Mechanical Wave?

Vibrations can be considered to be mechanical waves. These waves are generated by artificial and natural sources and they are propagating through mechanical structures via different paths.&nbsp; Mechanical waves generated by traffic and internal machinery propagate through the ground to the supporting elements of a building. For static reasons the joint connection between the ground and the supporting elements is designed in a rigid manner. Therefore most of the incoming wave is transmitted to the building. Following the propagation path the wave excites the floor and walls. Finally all structures inside the building, e.g. source components, amplification, pre-amplification and loudspeakers, will be excited by the structure borne sound as well. Depending on the excitation frequency and the material of the wall the structure borne sound can be transferred into air borne sound as a secondary transmission path.

What are Building Vibrations?

From the engineer’s point of view, buildings are mechanical structures assembled by plates, shells, beams and rods. As with any mechanical structure, buildings vibrate due to the presence of vibration generating sources. Wind excitation causes a low frequency tilting of the building with high vibration amplitudes (up to 500µm/s) in the horizontal direction. The upper floors are especially affected by wind excitation. Planes and heavy traffic in surrounding area result in building vibration of small to mid size amplitudes (typical values are 5 – 100µm/s). The related excitation frequencies are typically in the range of 5 to 100Hz. Seismic excitation causes vibration over an entire building in vertical and horizontal direction, e.g. twisting. The corresponding excitation frequency is very low (0.5 – 10Hz) whereas the amplitudes are varying from small to extremely large values.

Internal machinery, e.g. elevators and air condition systems may generate local vibrations. Local vibrations are limited to a substructure of a building, e.g. a single floor. The related amplitudes are high in the near field of these sources (up to 200µm/s), but they are decreasing rapidly with the distance. The excitation frequencies are very different, depending on the type of internal machinery but as a general rule they are more focused to higher values (10Hz and higher).

What is Vibration in an Audio Room?

The vibration level inside an audio room depends on many different parameters. The location of the audio room inside the house has a major influence. Audio Rooms on higher or suspended floors suffer much more from most vibration sources than those located in basements which usually have slab or foundation flooring.

Furthermore the vibration level in an audio room increases near higher traffic areas. The type of equipment inside an audio room and the number of people will have an effect as well. Door slams, kitchen equipment, HVAC units and foot traffic also cause quite a bit of vibration problems.

How do you Measure Vibration?

Depending on the type of vibration, different measurements methods have to be used. The two main classes of vibration measurements are time domain and frequency domain.

Time domain analysis starts by analyzing the signal as a function of time. An oscilloscope, data acquisition device, or signal analyzer can be used to acquire the signal. The plot of vibration versus time provides information that helps characterize the behavior of the structure. If behavior can be characterized by measuring the maximum vibration (or peak) level, or finding the period, (time between zero crossings), or estimating the decay rate (the amount of time for the envelope to decay to near zero). These parameters are the typical results of time domain analysis.

Time domain measurements are useful for the analysis of transient vibration phenomenon and for long term vibration inspection. Transient vibration problems are often related to impacts and other non deterministic impulse type sources. As a result of the impact the vibration amplitude strongly depends on the time, e.g. the decay process until the mechanical system comes to rest again. The long term vibration inspection is used to investigate the presence of vibration sources over a specified time period. The time period varies between several minutes up to days or weeks. The target of long term inspection is to predict the presence or absence of vibration sources in order to optimize the use of sensitive equipment.

Frequency analysis also provides valuable information about structural vibration. Any time history signal can be transformed into the frequency domain. The most common mathematical technique for transforming time signals into the frequency domain is called the Fourier Transform. The math is complex, but today’s signal analyzers race through it automatically, in real-time. Fourier Transform theory says that any periodic signal can be represented by a series of pure sine tones. In structural analysis, usually time waveforms are measured and their Fourier Transforms computed. The Fast Fourier Transform (FFT) is a computationally optimized version of the Fourier Transform.

Frequency domain measurements are useful for steady state vibration. To obtain the frequency domain the measured time signal (displacement, velocity, acceleration) has to be transformed by the Fast Fourier Transformation (FFT). The resulting data shows the vibration amplitude with respect to the frequency.

What is Vibration Isolation?

The isolation, in structures, of those vibrations or motions that are classified as mechanical vibration; involves the control of the supporting structure, the placement and arrangement of isolators, and control of the internal construction of the equipment to be protected.

What is Passive Vibration Isolation?

Passive vibration isolation systems consist essentially of a mass, spring and damper (dash-pot). The equipment and gears have joints with surrounding objects (the supporting joint – with the support; the unsupporting joint – the pipe duct or cable).

What is Active Vibration Isolation?

Active vibration isolation systems contain, along with the spring, a feedback circuit which consists of a piezoelectric accelerometer, a controller and an electromagnetic transducer. The acceleration (vibration) signal is processed by a control circuit and amplifier. It then feeds the electromagnetic actuator, which amplifies the signal. As a result of such a feedback system, a considerably stronger suppression of vibrations is achieved compared to ordinary damping.

What is Damping?

Damping is a dissipation of energy in an oscillating system. Damping limits the maximum amplitude of an&nbsp; isolator’s natural frequency.

What is Structural Damping?

Structural damping reduces the vibration of resonating surfaces that radiate noise. Damping is accomplished by affixing a material directly to the vibratory surface. This material converts the mechanical vibration energy into to a minimal amount of heat energy.

What is Subframe Isolation?

Another technique used to increase isolation is to use an isolated subframe. This splits the system with an additional mass/spring/damper system. This doubles the high frequency attenuation roll off, at the cost of introducing additional low frequency modes which may cause the low frequency behavior to deteriorate. This is commonly used in the rear suspensions of cars with Independent Rear Suspension (IRS), and in the front subframes of some cars. Above 42 Hz the compliantly mounted subframe is superior, but below that frequency the bolted in subframe is better.

Passive versus Active Isolation

Passive isolation always exhibits amplification within the resonance and the isolation for higher frequencies decreases because of the viscous damping. Another advantage of an active isolation system compared to a passive stage is the short settling time. The passive system needs a long time to come to rest again. In the case of the active system the vibration decays much faster because the active system reacts with its actuators. The actuators are generating forces which counteract the movement of the isolated mass.