Choosing Isolator Natural Period For Short And Long Shock Pulses

Shock isolation is not governed by a single rule such as use a softer mount or use a higher natural frequency for short pulses. The correct natural period depends on the shock input, payload fragility, allowable travel, damping, mounting configuration, and installation constraints. For short and long shock pulses, the central design variable is the relationship between pulse duration and isolator natural period, supported by Shock Response Spectrum (SRS) analysis and fixture-controlled validation.

This article presents a defensible selection workflow for OEM engineers and technical purchasing teams. It emphasizes quantitative screening, clear documentation, and validation evidence rather than generic rules of thumb.

Figure 1. Shock isolation selection requires the shock input, payload fragility, mounting configuration, and allowable travel to be evaluated together.

Define the Shock Input Before Selecting an Isolator

Isolator selection begins with a defined shock input, not with a catalog natural frequency. The input should be described as an acceleration-time history or as an enveloping pulse that bounds the expected service environment. At minimum, record:

• Peak acceleration (A_{pk})
• Pulse shape: half-sine, rectangular, triangular, exponential, complex transient, etc.
• Pulse duration (\tau) and the method used to define it
• Direction or axes of excitation
• Repetition rate, number of shocks, and sequence
• Mounting-plane input and any fixture or base impedance effects
• The governing standard, test method, or program requirement

The pulse duration must be defined consistently. Depending on the governing standard or test method, duration may be the zero-crossing width, the half-sine width, or the time above a specified threshold. Do not compare durations defined by different methods.

Where applicable, use the program-governing shock standard or test method. Common examples include MIL-STD-810 Method 516 for environmental shock testing and IEC 60068-2-27 for shock testing of equipment. For product fragility and packaging-related shock, ASTM D3332 and ASTM D4169 may be applicable depending on scope. The standard defines the input, tolerances, instrumentation, and acceptance criteria.

Standards must be cited by scope. For example, ASTM D999 addresses vibration testing of shipping containers, not mechanical shock. ISO 10846 addresses laboratory measurement of vibro-acoustic transfer properties of resilient elements, not general shock-isolation validation. Neither should be presented as a general shock-input definition or shock-isolation qualification standard.

Payload Mass, Fragility Limit, and Mount Quantity

The isolator must protect a specific payload with a specific fragility limit. Define:

• Payload mass (M) and center of gravity
• Fragility limit (A_{frag}), the maximum acceleration the payload can tolerate without damage
• Required safety factor (SF), so the design target is (A_{frag}/SF)
• Number of mounts (n), mounting locations, and load distribution
• Total isolator stiffness (k_{total})
• Damping ratio (\zeta)

For a linear system, the natural frequency and natural period are

[
f_n=\frac{1}{2\pi}\sqrt{\frac{k_{total}}{M}},
\qquad
T_n=\frac{1}{f_n}=\frac{2\pi}{\omega_n},
\qquad
\omega_n=\sqrt{\frac{k_{total}}{M}}.
]

For (n) identical mounts, (k_{total}=n k_{mount}). Mount quantity therefore changes both the system natural period and the load per mount. If the center of gravity is offset, the mounts will not share load equally; calculate per-mount static and dynamic loads using moment equilibrium rather than simple division.

The required attenuation is

[
R_a=\frac{A_{frag}/SF}{A_{pk}}.
]

If (R_a \ge 1), the input peak may already be below the fragility target, although rebound, resonance, and repeated shock still require review. If (R_a < 1), the isolator system must reduce the payload response below the fragility limit with margin.

Peak Acceleration, Pulse Shape, and Pulse Duration

Peak acceleration alone is insufficient. Two pulses with the same peak but different shapes and durations can produce very different payload responses. A rectangular pulse often contains more energy than a triangular pulse of the same peak and duration. A half-sine pulse is commonly used for impact and drop simulations. An exponentially decaying pulse may represent a different energy-release mechanism.

The dynamic response is governed primarily by the normalized ratio

[
\frac{\tau}{T_n},
]

together with damping (\zeta), pulse shape, and input amplitude. This ratio explains why short and long pulses require different design reasoning.

• Short-pulse regime, (\tau \ll T_n): The pulse acts approximately as a velocity impulse. A longer natural period, meaning a lower natural frequency, generally reduces transmitted acceleration but increases relative displacement. A stiffer isolator may reduce travel but transmits more acceleration.
• Transition regime, (\tau \approx T_n): Resonance and amplification are possible. This is often the most demanding region for fragility and travel. SRS analysis or time-domain simulation is required.
• Long-pulse regime, (\tau \gg T_n): The payload may follow the base quasi-statically, providing little isolation. To isolate a long pulse, the natural period must be sufficiently long relative to the pulse, which often demands large travel. If travel is constrained, damping, snubbers, or a change in the isolation concept may be required.

A common but misleading shortcut is to state that short pulses require a higher natural frequency. That is not generally true. A higher natural frequency can reduce relative displacement, but it usually increases transmitted acceleration. A lower natural frequency can reduce acceleration, but it increases travel demand. The correct choice depends on which limit is binding: payload fragility or available travel.

Relate Pulse Duration to the Isolator Natural Period

The isolator natural period should be selected by evaluating the payload response over a range of candidate (T_n) values. The goal is not to match the pulse duration directly, but to place the isolator response in an acceptable region of the shock response spectrum while satisfying travel and installation constraints.

For an impulsive short pulse, an initial estimate can be made from the velocity change. For a half-sine acceleration pulse of peak (A_{pk}) and duration (\tau),

[
\Delta v=\frac{2A_{pk}\tau}{\pi}.
]

For (\tau \ll T_n), the maximum relative displacement can be approximated for low damping as

[
x_{max}\approx \frac{\Delta v}{\omega_n},
]

and the approximate transmitted acceleration is

[
A_{payload}\approx \omega_n \Delta v.
]

These approximations are useful for early screening only. Final selection requires SRS or time-domain analysis using the actual pulse shape and damping.

Illustrative Short-Pulse Calculation

Consider a 50 kg payload with a fragility limit of (10g), subjected to a half-sine pulse with (A_{pk}=30g) and (\tau=8\,\text{ms}). The required attenuation is

[
R_a=\frac{10g}{30g}=0.33.
]

The velocity change is

[
\Delta v=\frac{2(30)(9.81)(0.008)}{\pi}\approx 1.50\,\text{m/s}.
]

For a candidate natural period (T_n=40\,\text{ms}), (\omega_n=2\pi/T_n\approx 157\,\text{rad/s}). The impulse estimate gives

[
x_{max}\approx \frac{1.50}{157}\approx 0.0096\,\text{m}=9.6\,\text{mm},
]

[
A_{payload}\approx 157(1.50)\approx 235\,\text{m/s}^2\approx 24g.
]

This exceeds the (10g) fragility limit. For (T_n=100\,\text{ms}), (\omega_n\approx 62.8\,\text{rad/s}):

[
x_{max}\approx \frac{1.50}{62.8}\approx 0.0239\,\text{m}=23.9\,\text{mm},
]

[
A_{payload}\approx 62.8(1.50)\approx 94.2\,\text{m/s}^2\approx 9.6g.
]

This candidate is near the fragility limit and would require additional margin and validation. It also requires more than 24 mm of relative travel before clearance and tolerance are added. The example shows the central trade-off: for a short impulsive pulse, a longer natural period can reduce transmitted acceleration, but it increases travel demand.

For long pulses, the same logic becomes more severe. If (T_n) is short relative to (\tau), the payload tends to follow the base and isolation is limited. If (T_n) is made much longer than (\tau), travel can become impractical. In such cases, the designer should evaluate damping, snubbing, stroke limiters, or a different mounting architecture rather than forcing an unrealistic low-frequency isolator.

Figure 2. The response depends on pulse duration relative to the isolator natural period, not on peak acceleration alone.

Use the Shock Response Spectrum to Set Attenuation Targets

The SRS is the primary screening tool for shock isolation. For a given input pulse and damping ratio, the SRS gives the maximum acceleration response of a single-degree-of-freedom system as a function of its natural period or frequency. The isolator natural period should be selected so that

[
S_a(T_n,\zeta)\leq \frac{A_{frag}}{SF},
]

where (S_a) is the acceleration response from the SRS and (SF) is the chosen safety factor.

The attenuation target is not simply a frequency ratio. It is a response limit. If the input SRS exceeds the payload fragility over the practical range of (T_n), the design is not closed. Options include:

• Increasing damping to reduce response peaks and travel
• Adding a snubber or stroke limiter to control extreme displacement
• Reducing input severity through packaging, handling, or system-level redesign
• Relocating sensitive components to a lower-response location
• Selecting a different isolation architecture

Avoid selecting a natural frequency that coincides with a prominent SRS peak. The objective is to place the isolator on a low-response region of the spectrum, not to align the natural frequency with the SRS peak. For steady-state vibration, isolation often requires the natural frequency to be below the excitation frequency. For shock, the transient SRS and pulse-duration ratio govern the response, and the same steady-state rule cannot be applied blindly.

Calculate Maximum Relative Displacement and Required Travel

Acceleration attenuation is only half of the design. The isolator must also have sufficient travel to accommodate the maximum relative displacement between the payload and the base. For a linear single-degree-of-freedom system, the relative displacement (x(t)) can be obtained from

[
\ddot{x}+2\zeta\omega_n\dot{x}+\omega_n^2x=-a_{base}(t),
]

where (a_{base}(t)) is the base acceleration input. Solve this equation by time-domain integration or use validated SRS-based approximations.

For each direction (i), including compression and extension as applicable, calculate the required travel as

where:

• (|x|_{\max,i}) is the maximum dynamic relative displacement in direction (i)
• (\delta_{\mathrm{static},i}) is the static deflection due to payload weight or steady preload acting in that direction; for vertical mounts, (\delta_{\mathrm{static}}) is generally positive in compression
• (c_{\mathrm{clearance},i}) is the clearance needed to prevent contact with adjacent structures
• (\varepsilon_{\mathrm{tolerance},i}) accounts for manufacturing, installation, and material tolerances

Check travel in both compression and extension directions. Also evaluate rebound. Excessive rebound can cause secondary impacts and should be controlled through damping, snubbing, or stroke limiting. A design that meets the acceleration target but bottoms out is not acceptable. If snubbers or stroke limiters are used, their impact behavior and resulting secondary shock should be included in the validation.

Figure 3. Acceleration attenuation and relative displacement must be evaluated together; allowable travel often controls the design.

Validate Fixture Input and Payload Response During Testing

Analysis must be confirmed by fixture-controlled validation. The test should measure:

• Base input acceleration at the mounting plane
• Payload acceleration at critical locations
• Relative displacement across the isolator
• Fixture dynamics, to confirm that the fixture does not distort the intended input
• Rebound and post-shock settling behavior

The measured input SRS should envelope the specified input SRS within the test tolerances. The measured payload response should remain below the fragility limit with the chosen safety factor. The measured relative displacement should remain within the available travel with clearance and tolerance.

A recommended validation record includes the specified input definition, test fixture configuration, instrumentation locations, measured input and response time histories, measured SRS, relative-displacement data, pass/fail criteria, and any deviations or nonconformances. Analysis and test should be traceable to the same input definition and acceptance criteria.

Documentation Checklist

A defensible isolator selection package should include:

• Shock input definition and source standard or program requirement
• Pulse shape, peak, duration definition, direction, and repetition
• Payload mass, center of gravity, fragility limit, and safety factor
• Mount quantity, locations, stiffness, and damping assumptions
• Candidate (T_n) sweep and SRS screening results
• Predicted payload acceleration versus fragility target
• Predicted relative displacement and required travel in each direction
• Rebound, snubbing, and stroke-limiter evaluation
• Fixture-controlled validation results and comparison with analysis
• Open risks, tolerances, and inspection or acceptance criteria

References

1. MIL-STD-810H, Method 516.8, Shock.
2. IEC 60068-2-27:2008, Environmental testing Part 2-27: Tests Test Ea and guidance: Shock.
3. ASTM D3332, Standard Test Methods for Mechanical-Shock Fragility of Products, Using Shock Machines.
4. ASTM D4169, Standard Practice for Performance Testing of Shipping Containers and Systems.
5. ASTM D999, Standard Test Methods for Vibration Testing of Shipping Containers vibration scope, not a general shock standard.
6. ISO 10846 series, Acoustics and vibration Laboratory measurement of vibro-acoustic transfer properties of resilient elements transfer-property measurement scope, not a general shock-isolation validation standard.