Aluminum Case Vibration Isolation and Transmissibility

Vibration isolation engineering is the discipline that prevents externally transmitted vibration from damaging enclosed equipment, while also controlling internal vibration from being transmitted to the case exterior. The aluminum case, its internal suspension or foam cushioning system, and the enclosed equipment form a spring-mass-damper system whose transmissibility must be engineered to protect sensitive components across the 5-2000 Hz vibration spectrum. Engineered isolation systems achieve 70-95% vibration reduction above the isolation region, complying with MIL-STD-810H 519.7, ASTM D4169, ISTA 3A/3E/3H, ISO 8318, and ISO 13355 standards.

Spring-Mass-Damper System Fundamentals

The simplest vibration isolation model is a single degree of freedom (SDOF) spring-mass-damper system. The equation of motion for a mass m on a spring k with damper c, subjected to base excitation y(t) = Y*sin(omega*t), is: m*x_ddot + c*(x_dot – y_dot) + k*(x – y) = 0, where x is the mass displacement. The natural frequency is omega_n = sqrt(k/m), the damping ratio is zeta = c / (2*sqrt(k*m)), and the frequency ratio is r = omega / omega_n.

The static deflection of an isolator under equipment weight is delta = m*g / k = g / omega_n^2. This provides a convenient way to estimate natural frequency from static deflection: f_n = (1/2pi) * sqrt(g/delta) = (1/2pi) * sqrt(9.81/delta). Larger static deflection means lower natural frequency and better low-frequency isolation, but requires more space and allows more equipment movement.

Transmissibility and Isolation Efficiency

Transmissibility is the ratio of transmitted force/displacement to input force/displacement. For a base-excited SDOF system, the absolute transmissibility is: T = sqrt((1 + (2*zeta*r)^2) / ((1 – r^2)^2 + (2*zeta*r)^2)). At r=0, T=1 (no isolation). At r=1 (resonance), T peaks at Q = 1/(2*zeta) for low damping. At r=sqrt(2), T=1 regardless of damping. For r>sqrt(2), T<1 and the system provides isolation. Isolation efficiency is eta = (1 – T) * 100%.

At resonance (r=1), the transmissibility peaks at Q = 1 / (2 * zeta). This is the resonance amplification factor—the ratio of output to input at the natural frequency. Low damping means high amplification (rubber zeta=0.05, Q=10), which is dangerous if the excitation frequency coincides with the natural frequency. Higher damping (wire rope zeta=0.25, Q=2) reduces resonance amplification but also reduces isolation effectiveness at high frequency ratios.

Isolator Materials and Selection

Vibration isolators for aluminum cases use elastomeric, metallic, or pneumatic elements. The selection depends on required natural frequency, damping, load capacity, environmental conditions, and space constraints. Elastomeric isolators (rubber, silicone) are most common for their low cost and moderate performance. Wire rope isolators offer excellent resonance control and environmental durability. Pneumatic isolators provide the lowest natural frequencies for ultra-low frequency isolation.

Random Vibration: PSD and GRMS

Real-world transport vibration is random (non-deterministic) and is characterized by Power Spectral Density (PSD) in g2/Hz. The overall vibration intensity is the Root Mean Square acceleration: GRMS = sqrt(integral of PSD(f) df). Random vibration testing uses shaped PSD profiles to simulate specific transport environments. The case must withstand the specified PSD level without equipment damage or structural fatigue.

Vibration testing applies excitation sequentially along three orthogonal axes (vertical Z, longitudinal X, lateral Y). Each axis test duration is typically 1-4 hours. The case is bolted to the shaker table through its base or transport frame. Multi-axis simultaneous excitation (6-DOF) is used for high-fidelity simulation but requires specialized equipment.

Related Reading

• Aluminum Case Vibration and Shock Isolation Engineering:
• Aluminum Case Vibration Isolation Engineering: Transmissibility