In a vehicle design it is quite paramount to determine the vibration factor based on a number of specifications. The dynamics of a vehicle need to be discussed clearly so as to avoid vibrations which are undesired in roadside structures as well as for other elements in the vehicles [1]-[3]. The designer focuses on the vibrations developed or transferred from the road to the car body structures based on the road surface. Another aspect, thoroughly, discussed is the vibro-acoustic which considers the possibilities of vibration and acoustic signals in diagnosing and researching. One of the greatest effects is the resonance vibration with amplifies the vibration response more than the level of deflection, strain and stress caused when static loading is placed. The vehicle system payload parameters determine the material properties such as mass, stiffness, damping attributes, boundary conditions of the structure [4].

The data collected in this research focuses on the internal combustion engine and the design of the vehicle. The amount of vibration caused to the system is estimated to be within the 3-axis rotational velocity [5]. The speed of rotation may range from 750 rpm to 3000 rpm. In studying the vibration of the vehicle, the vehicle suspension and car body are defined and data collected is recorded in orthogonal axes; in the X, Y, and Z. To determine the measurement point section and vibration propagation from engine to human being, the following section is developed [6], 

• To determine the vehicle suspension in relation to the vibration of the system.
• To determine the vibration parameters using MATLAB implementation.

m : Mass (kg) F : Force (N)

k : Spring stiffness (N/m) c : Damping coefficient (Ns/m)

P : Pressure ( : Density (

CFD : Computational Fluid Dynamics FEA : Finite Element Analysis

CAD : Computer Aided Design CAM : Computer Aided Manufacturing

Most vehicles are fitted with shock absorbers which take up the effect of the uncertainties of the road surface during driving. The connection of the chassis of the vehicle to the wheels defines the suspension system. The wheels of a vehicle are affected by the unevenness of the road surface during motion. The designers adjust the mass, spring coefficient and the damping coefficient to determine the best suspension mode of a suspension system [7]. The vehicle has a damping element that gives a high damping at low frequencies so as to obtain the duty cycle and vibration constants.  

The vibration frequency is given as a function of the road roughness and the vehicle speed. The frequency is generated from the ground level roughness and it determines the horizontal speed of the vehicle [8]. The governing equations of motion for a vehicle under constant vibrations are, 

The acceleration is given as, 

The damping ratio is obtained as, 

To determine the critical damping ratio constant and the ratio of the vehicle displacement in the vertical direction to the road roughness as, 

The vibration signals are caused as a result of an excitation force obtained externally and affecting the working procedure of the internal combustion engine. The data was collected as shown using the ADXL sensor and a data acquisition unit.

Nomenclature

The first stage involves the collection of data from a real life experiment where data is obtained when driving at particular speeds on different road surfaces. The results and observations were collected and discussed. Based on the speeds used in the different sections of the road, it was found that the revolutions per minute of the vehicle lay in the range 750 rpm to 3000 rpm. This research paper seeks to determine the vibration accelerations at specific courses of time [9]. The measurements were recorded using the ADXL sensor and saved using a data acquisition unit connected to a computer system. The data is obtained from the three orthogonal axes on separate modes. The information is compared so as to determine which direction of the vibration propagation is parent.

The software used for data analysis in this research work is the MATLAB R2018b software. The data is further analysed using frequency and time functions or methods such as the short time Fourier transform. The STFT method is quite simple to implement although it is a constant time-frequency resolution that affects the analysis precision for different object dynamics [5]. It is, therefore, quite important to find a balance between the window width and the time or frequency resolution for the different applications. The STFT analyses are the coefficients that have dependence such as,

It is important to choose a suitable rectangular window for the window shift factor, b, so as to improve the frequency resolution as it is performed in the FFT analysis. To determine the vertical acceleration data measured from the travelling passenger seat section,  

About 512 samples are taken for this vibration acceleration data set. The total time taken to record was 223.165 seconds. 

The number of harmonics is equated to the number of samples per cycle. For the linear systems, the Fourier data is obtained by computing the value of the harmonics, 

The data is collected as shown in the graphical illustration as shown below. The data collected is loaded into MATLAB using the importdata() function. The data values for the vibration acceleration in different time scores were plotted for all the orthogonal axes [3]. The information took into consideration the position of the driver as stipulated in the standards AS 2670.1-2001. An evaluation of the entire human exposure to the vehicle suspension and vibration dynamics was performed.  

For a continuous time signal, the controller compares the output signal to the input or the reference signal. The reference signal in this instance is the data collected. The output is passed through a filter to remove the white Gaussian noise caused by disturbances in the environment during data collection. It is possible to convert the ADXL sensor data into a vibration acceleration equation using 512 data point samples from the entire data population [9]. Filtering the data using a low pass filter, the cut-off frequency is obtained. To represent a transfer function as a polar, it’s possible to combine the Fourier transform information into one graph such that, 

The Australian transport agency has standards used in determining specifications of the mechanical vibration and shock human effects that must be adhered to or which a driver must comply. The guideline has specific requirements, the continuous and shock-induced vibration in buildings for the effects of vibration and rotational motion on the passenger and crew comfort in a fixed-guide way transport systems [3]. The information discussed and the data analysis carried out in this research work is based on the SO 2041:1990, ISO 5805:1997 and ISO 8041: 1990 as the Australian Standards. The acoustics considerations of the signals and vibration parameters are guided by the AS/NZS 4476:1997 guideline. It focuses on the filtering within the octave band and fractional octave band. The root mean square method of assessing vibration has been shown for the underestimated effects of vibration with substantial peaks. The vehicles are found to have different applications and as a result they encounter different forms of vibrations [5]. For instance, a 4×4 drive vehicle in the remote arid areas requires different shock absorbers and filters as compared to a vehicle designed for urban roads. There are a lot of factors that are considered in the vibration of machines and its subsequent dynamics. A filter is used to remove the high frequency and low frequency harmonics from the system using a low pass and high pass filter respectively [8]. When the output is found to be oscillatory, it may have harmonics which may affect the comfort of the passengers or driver in the car. It is quite a complex affair to determine the vibration dynamics at design level hence tests are carried out on different road surfaces. 

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