**2. Mechanical vibration**

#### **2.1 General characteristics**

Mechanical vibration is a physical agent of wave nature. It can be produced by different devices, such as a refrigerator engine, a motor vehicle engine, an air conditioner, and others. A vibrating platform is one of such examples. In all the examples provided, the device is outside the person's body, but if the person is in contact with it, the mechanical vibration is transmitted to the person [11, 12]. As shown in **Figure 1**, the waveforms of mechanical vibrations produced by different devices, can be deterministic (**Figure 1A**) or random in nature.

The mechanical vibration, that is generated in a vibrating platform [11, 12] or portable [10] devices, is characterized by the sinusoidal form, and this deterministic approach has particular interest for everything that will be covered in this book chapter on vibration therapy.

#### **2.2 Mechanical vibration as a daily stimulus**

It is very important to highlight that mechanical vibration is a natural stimulus that is part of the daily life of all living beings and is periodically added to the organism during movements [11, 12]. It is closely associated with the physiological responses of all organisms, including human being. The addition of mechanical vibration happens in a wide number of routine situations [11], such as walking, running, playing, being in a car or public transport, or doing a domestic activity, such as using a vacuum cleaner for cleaning or a fruit extractor while making a juice. Likewise, in professional activities such as driving a car, truck, train, or using dental equipment, mechanical vibration is transmitted to the individual that is in contact with the device that is producing the referred vibration [13, 14]. In addition, several structures of the human body naturally produce mechanical vibrations, such as the heart, digestive system, the shortening and stretching of muscle fibers, vessels of the vascular system, the vibrational energy of electrons in a chemical bond, or the vibration of molecules in the cellular metabolism. Likewise, many of the organic functions depend on mechanical vibrations at different levels of anatomical structures [12, 15, 16]. Of course, in general, this addition of mechanical vibration is

#### **Figure 1.**

*Different waveforms related to mechanical vibration.*

not fully perceived by the person, but when a movement is performed, mechanical vibration is added to the body. However, in some activities like walking or running, when the foot contacts the floor, mechanical vibration is more easily perceived. It may be relevant to consider that this addition of mechanical vibration would be the trigger for organic functions to take place and for the person to live with physical and mental health [12, 16].

When, for several reasons, the person cannot add mechanical vibration to the body, the mechanical vibration generated by a device can be transmitted to the person in contact with it. This procedure corresponds to a clinical intervention called vibration therapy [10–12].

#### **2.3 Biomechanical characteristics of mechanical vibration**

Vibration therapy, which is considered in this chapter, uses mechanical vibration, which is a physical agent that transports energy and is characterized by a displacement in relation to an equilibrium position with an oscillatory, sinusoidal, and deterministic movement, as shown in **Figure 2**.

In this case, biomechanical parameters such as frequency, amplitude, and peakto-peak displacement can be conveniently adjusted depending on the outcome to be achieved and the individual's clinical conditions. These parameters need to be considered when designing a vibration therapy intervention protocol [8].

Frequency (f) is expressed in Hertz (Hz) and represents the number of cycles in one unit of time, for example, the second. Peak-to-peak displacement (D) is the measure of the perpendicular extension between the largest and smallest displacement of mechanical vibration expressed in millimeters (mm). The amplitude represents half the peak-to-peak displacement and is also expressed in mm. These parameters are represented in **Figure 3**. The path of the mechanical stimulus between the successive points Z1 and Z2, defines the cycle developed by the vibration. The number of cycles performed in the unit of time is the frequency [8, 11, 12]. An important observation is that at Z2, the stimulus begins again to have the same characteristics as point Z1.

The distance comprised by the straight-line segment between points Z1 and Z2, measured, for example, in mm, is defined as the wavelength of the mechanical

**Figure 2.** *Sinusoidal waveforms related to mechanical vibration.*

**Figure 3.** *Representation of a sinusoidal mechanical vibration.*

stimulus. This corresponds to the projection of the entire cycle on the propagation plane. It is important to consider that in the International System of Measurements, the wavelength value would be expressed in meters. Considering the perpendicular measure between the highest point or the lowest point (x1) of the mechanical vibration and the propagation plane or the lowest point (x2) is the amplitude. The perpendicular of the point X1 up to the level of the x2 is the displacement peakto-peak. The value of the displacement peak-to-peak corresponds to twice the amplitude [17].

The peak acceleration (Ap) of mechanical vibration depends on the frequency and the peak-to-peak displacement and is normally expressed in multiples of gravity (xg). The peak acceleration can be determined using accelerometers, or according to the equation Ap = 2 x π2 x f2 x D [17]. Peak acceleration allows defining the intensity or magnitude of mechanical vibration and of the vibration therapy.

Two mechanical vibrations, with the same frequency, with displacement with correspondences in points X1 and x2, are said to be in phase. On the other hand, when these coincidences do not occur, the two stimuli are out of phase. These considerations are relevant, in the same way, the stimulus generated in the platform has its own amplitude, the medium being crossed also presents mechanical vibration.
