To determine the permissible and standardized parameters for vibrations and noise, it is primarily important to classify people’s (engineer-operators’) workplaces according to their working conditions. Vibrations that affect engineer-operators develop according to two categories: General and local. The effects of general vibration on a person can depend on the overall condition of the work environment, the support surface at the workplace, and whether the machine operator is seated or standing.

The primary objectives of this study are:

• To classify vibration types affecting human operators based on working conditions and sources.
• To determine permissible vibration velocity and acceleration levels using standardized analytical methods.
• To establish relationships between logarithmic vibration levels and their physical values.
• To develop tabulated reference standards for different categories of vibration exposure.

To define permissible noise levels in residential, industrial, and institutional environments.

General vibrations, based on their origin and purpose, can be divided into the following categories:

Category 1 - transportation vibrations, which affect a person when they operate vehicles such as: self-propelled and towed self-propelled machines; industrial and agricultural tractors; combines; trucks; mining rail transport and other similar machinery: graders; snow plows; scrapers, etc. Category 2 - Transport - technological vibrations transmitted to humans from machines and equipment such as: excavators; industrial and construction lifting equipment [1]; drilling machines; concrete pouring machines; and other similar operating equipment. Category 3 – Technological vibrations transmitted to humans from stationary machines such as: wood and metal processing equipment; pressing devices; casting machines; stationary electrical machines; drilling machines; pumping equipment and fans; chemical and petrochemical process equipment, etc. Vibrations of this category can also affect people in design offices and laboratories where the machines causing the vibrations are not directly present. According to direction, vibrations can be divided based on the orthogonal axes of coordinates (x₀, y₀, z₀). z₀ is vertical, when a person is seated or standing relative to the supporting surface — that is, in a vertical posture; x₀ and y₀ are horizontal, when a person is in a posture parallel to the supporting surface. According to spectral composition, vibrations can be classified as follows: narrowband, when the control parameters in a 1/3-octave band exceed those in the adjacent 1/3-octave band by 15 dB; broadband, which do not meet the above condition; low-frequency, when the maximum vibration levels are in the octave band from 1 to 4 Hz; mid-frequency, when they are from 8 to 16 Hz high frequency, when they are from 31.5 to 63 Hz. Vibrations affecting a person are classified according to their duration:

- relatively short-duration vibrations, when the vibration frequency exceeds 6 dB per second;

- relatively long-duration vibrations, when the vibration frequency is less than 6 dB per second. Non-continuous vibrations include intermittent vibrations, when human contact with the source of vibrations is interrupted for a certain period (the interruption interval is more than 1 second). Vibrations whose vibration velocity levels change continuously over time; impulse vibrations (for example, shocks), whose duration is at least 1 second. The hygienic assessment of vibrations affecting a person can be based on several convenient methods:

$L_c=20\lg \frac{v}{5\cdot {10}^{-8}}$

where v is the root mean square value of the vibration acceleration in m/s²; is the standard value of the vibration velocity, corresponding to the root mean square value when exposed to a sound tone with a frequency of 1000 Hz at a stress of 2,0∙10^-5 N/m². The relationship between the logarithmic levels of vibration velocities (in dB) and their corresponding values in m/s² is given in the first table [2].

The study adopts an analytical and standards-based approach to evaluate vibration and noise parameters. Vibration levels are assessed using root mean square (RMS) values of vibration velocity and acceleration, which are widely applied in vibration analysis and mechanical system evaluation [3,4]. The logarithmic levels of vibration are calculated using standard equations relating physical quantities to decibel (dB) scales [3].

Frequency-weighted analysis is performed across octave (1/1) and one-third octave (1/3) bands using weighting coefficients (K_i) corresponding to each frequency range. These coefficients are applied to determine corrected vibration values, ensuring compatibility with human sensitivity and standard measurement practices [4-6].

The evaluation includes:

· Classification of vibrations into general and local categories

· Analysis of spectral composition (low, medium, high frequency ranges)

· Calculation of equivalent energy exposure over time

· Use of tabulated standard values derived from recognized references

All parameters are analyzed in accordance with established engineering principles and aligned with internationally recognized standards such as ISO 2631-1 and vibration exposure guidelines [4,7,8].

The study presents a comprehensive set of tabulated values representing permissible vibration and noise parameters across different working conditions and frequency ranges. The results demonstrate clear relationships between vibration levels expressed in decibels and their corresponding physical quantities (m/s²), consistent with established vibration analysis principles [3,9].

The analysis indicates that:

Vibration intensity increases with frequency in specific operational ranges, as supported by standard vibration behavior models [3,9].

Transportation and technological vibrations exhibit distinct permissible limits depending on exposure duration, consistent with international standards [4,8].

Frequency-weighted coefficients significantly influence the corrected vibration values and exposure assessment [6,9].

Noise levels vary across environments, with stricter limits observed in medical and educational institutions compared to commercial areas, in line with environmental health guidelines [10,11].

The tabulated data (Tables 1–9) provide a structured reference framework for assessing vibration exposure and ensuring compliance with safety standards [4,7].

The values of the logarithmic levels of vibration accelerations are calculated using the formula.

$L_a=20\lg \frac{\alpha }{3\cdot {10}^{-4}},$

where a is the root mean square value of vibration acceleration in m/s²;

Given value is the basic value of vibration acceleration in m/s².

The ratio of the logarithmic levels of vibration accelerations (in dB) and their corresponding values in m/s² is given in the second table, [12].

The integral formation of the normalized parameters of vibration velocities and vibration accelerations is carried out using their corrected values.

$\tilde{v}=\sqrt{{\displaystyle \sum _{i=1}^n{\left(v_i{K}_i\right)}^2}}$

$L\tilde{v}=10\cdot \lg {\displaystyle \sum _{i=1}^n{10}^{0,1(L_{vi}/L_{Ki})}}$

where $L_{vi}$ - are the root mean square values of vibration velocities and vibration accelerations; n - is the number of the frequency band (1/3 or 1/1 octave); K_i, L_ki, - i - are the weighting coefficients of the i-th frequency band, K_i, and L_ki, the values of the, coefficients in 1/3 and 1/1 octaves are given in Table 3 [3].

When assessing vibrations by dose, the normalized parameter is the corrected value of the equivalent energy, which is determined by the formula [13].

$E_{ek}=\sqrt{\frac{v_k^2{T}_0}{T},}$

where T - is the minimum time interval, minutes; v_k - is the current corrected value of the vibration velocity over the time interval T₀, m/min. The permissible values of normalized parameters under different conditions, when the exposure of a person to vibration lasts on average 480 minutes, are given in Tables 5,6.

The results highlight the importance of standardized evaluation of vibration and noise parameters in engineering and occupational environments. The classification of vibrations into general and local types aligns with established theoretical and analytical models in vibration mechanics [3,13].

The use of logarithmic scaling provides an effective method for representing wide ranges of vibration magnitudes and is widely adopted in vibration analysis and signal processing [3,9]. However, careful attention must be given to the consistency of units and scientific notation to avoid misinterpretation.

Frequency-weighted analysis plays a crucial role in aligning measured vibration levels with human perception and physiological impact, as demonstrated in previous studies on vibration exposure and occupational health [6,7,14].

The observed variation in permissible limits across different environments underscores the need for context-specific standards. The results are consistent with internationally recognized frameworks such as ISO 2631-1 and related vibration exposure standards [4,5,8].

Furthermore, the noise exposure findings support established environmental and public health guidelines, particularly those outlined by global health authorities [10,11].

Maintaining allowable and standardized vibration noise parameters on the above-mentioned objects ensures both the safe operation of buildings and machinery, as well as the work of service personnel in an environmentally safe environment.

This study establishes a structured framework for determining permissible and standardized vibration and noise parameters across various operational environments. By integrating analytical methods, frequency-weighted evaluation, and tabulated reference data, the research provides a practical basis for assessing human exposure to vibration and noise.

The findings emphasize the importance of maintaining standardized limits to ensure occupational safety, protect human health, and enhance the reliability of engineering systems. Future work should focus on experimental validation and real-time monitoring techniques to further refine these standards and improve their applicability in dynamic environments.

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