Understanding the Frequency Ratio in Machine Foundations

The question asks about the specific range for the frequency ratio that should be avoided according to Indian Standards (IS) codes for machine foundations. The frequency ratio is a critical parameter in the design of foundations, especially for machines that operate at specific frequencies.

The frequency ratio is defined as the ratio of the operating frequency of the machine to the natural frequency of the soil-foundation system. Mathematically, it can be represented as:

Frequency Ratio = $ \frac{f_{op}}{f_{nat}} $

where:

• $f_{op}$ is the operating frequency of the machine (in Hz or cycles per second).
• $f_{nat}$ is the natural frequency of the soil-foundation system (in Hz or cycles per second).

Significance of Frequency Ratio and Resonance

The primary concern when dealing with the frequency ratio is the phenomenon of resonance. Resonance occurs when the operating frequency of the machine ($f_{op}$) is close to or equal to the natural frequency of the soil-foundation system ($f_{nat}$). When resonance occurs (i.e., the frequency ratio is close to 1), the amplitudes of vibration can become excessively large, potentially leading to:

• Increased stress on the foundation and surrounding soil.
• Damage to the machine or the structure.
• Discomfort for occupants or operational issues.

To avoid these detrimental effects, design codes typically specify ranges that should be avoided to ensure the system operates well below or significantly above the natural frequency.

IS Code Recommendations for Frequency Ratio

Indian Standard codes, such as IS 2974 (Parts 1-5) related to foundations for machinery, provide guidelines to ensure safe and stable operation. These codes recommend avoiding frequencies that could excite the natural frequencies of the system. Specifically, to prevent resonance and excessive vibrations, the frequency ratio ($ \frac{f_{op}}{f_{nat}} $) should ideally be kept outside a certain range around 1.

Based on standard engineering practice and IS code recommendations for machine foundations, the range of the frequency ratio that poses a risk of resonance and should generally be avoided is between 0.5 and 1.5. Operating within this range can lead to significant amplification of vibrations.

Analysis of Provided Options

Let's look at the given options in the context of IS code recommendations:

• Option 1: 0.5 to 1.5
• Option 2: 1.0 to 2.5
• Option 3: 1.5 to 3.0
• Option 4: 3.0 to 6.0

The IS code guidelines suggest that the frequency ratio should not fall within the range where resonance is likely to occur. This problematic range is typically considered to be close to 1. Therefore, the range 0.5 to 1.5 is the one that should be avoided as per standard practices informed by IS codes to prevent excessive vibrations.