Vibration Structural Interaction

Overview

Vibration structural interaction analyzes dynamic coupling between HVAC equipment vibration and building structural response. Equipment rotating and reciprocating components generate periodic forces exciting structural systems at specific frequencies. When excitation frequency approaches structural natural frequency, resonance amplifies vibration magnitudes substantially, creating occupant discomfort, equipment misalignment, and potential structural fatigue. Proper structural coordination prevents resonance conditions through frequency separation, damping enhancement, and vibration isolation.

Resonance Frequency Avoidance

Resonance occurs when excitation frequency matches structural natural frequency, causing amplitude magnification limited only by system damping. Structural members including floor systems, beams, and suspended ceilings possess natural frequencies determined by mass, stiffness, and boundary conditions.

The fundamental natural frequency for simply-supported beams: f_n = (π/2L²) × √(EI/m)

Where:

• L = span length
• E = elastic modulus
• I = moment of inertia
• m = mass per unit length

Composite floor systems exhibit natural frequencies typically 3-12 Hz depending on span, construction, and live load. Concrete on metal deck construction provides higher stiffness and frequency than bar joist with concrete topping. Equipment operating frequencies should differ from structural natural frequencies by factor of at least √2 (41%) to avoid resonance amplification region.

Variable frequency drives permit equipment operation at multiple speeds, creating potential for resonance at specific frequency combinations. Frequency sweeps during commissioning identify resonance conditions for avoidance through VFD programming restrictions or structural modification.

Structural Damping Characteristics

Structural damping dissipates vibrational energy, limiting resonance amplitude and accelerating vibration decay. Damping ratio ζ represents ratio of actual damping to critical damping. Typical structural damping ratios:

Low damping ratios permit substantial amplification at resonance. Magnification factor at resonance equals Q = 1/(2ζ). Steel structure with ζ = 0.02 exhibits magnification factor Q = 25, amplifying small excitation forces into large structural response.

Vibration isolation effectiveness depends on frequency ratio and damping. Undamped systems transmit vibration efficiently near resonance but provide excellent isolation at high frequency ratios. Damping reduces resonance amplification but degrades high-frequency isolation. Optimal damping balances resonance control against isolation performance.

Floor Deflection Limits

Floor deflection under equipment static load affects equipment leveling, piping alignment, and conduit strain. Excessive deflection complicates equipment installation and indicates inadequate structural stiffness. Deflection limits ensure proper equipment operation and acceptable dynamic response.

Typical deflection criteria:

• L/360 maximum under live load for general office areas
• L/480 for floors supporting sensitive equipment
• L/600 or 0.25 inches maximum for floors under rotating equipment
• L/1000 for precision machinery and measurement equipment

Where L represents beam or slab span in inches. These limits address both equipment function and occupant perception of floor motion.

Equipment-induced deflection combines static deflection from equipment weight plus dynamic deflection from operating forces. Dynamic deflection depends on force magnitude, frequency, structural properties, and damping. Resonance conditions can produce dynamic deflection exceeding static deflection by an order of magnitude.

Equipment Isolation Design

Vibration isolation systems reduce force transmission from equipment to structure using compliant mounts with natural frequency below operating frequency. Isolation efficiency improves as frequency ratio (operating frequency / isolator natural frequency) increases above √2.

Spring isolators provide low natural frequency (2-8 Hz) suitable for equipment operating above 10 Hz. Mount selection considers:

• Equipment weight and center of gravity
• Operating frequency range
• Required deflection (deflection = 248/fn² inches)
• Seismic restraint requirements
• Environmental conditions (temperature, corrosion)

Equipment with variable operating frequency requires isolation with natural frequency below minimum operating speed. VFD-controlled fans starting from zero speed require soft starting or temporary isolation bypass preventing excitation at isolator natural frequency.

Inertia bases combine equipment and mounting base as single rigid body on isolation mounts. The combined system natural frequency:

f_n = (1/(2π)) × √(k/m)

Where k is total isolator stiffness and m is combined equipment plus base mass. Inertia bases lower center of gravity, improve stability, and reduce rocking modes.

Structural Amplification Factors

Structural amplification describes vibration magnitude increase from input force due to structural resonance and dynamic characteristics. Dynamic amplification factor (DAF) relates dynamic to static response:

DAF = 1 / √[(1 - (f/fn)²)² + (2ζf/fn)²]

Where f is excitation frequency, fn is natural frequency, and ζ is damping ratio.

At resonance (f = fn), DAF reduces to Q = 1/(2ζ). Low-damped steel structures exhibit Q = 20-50, amplifying forces substantially. Operating equipment at resonance generates vibration 20-50 times greater than far-from-resonance operation with identical force magnitude.

Multiple modes contribute to structural response. Floor systems possess fundamental mode plus higher harmonics at integer multiples of fundamental frequency. Equipment harmonic forces can excite higher modes even when operating frequency differs from fundamental. Complete analysis considers all significant modes and harmonic force components.

Floor Vibration Criteria

Occupant sensitivity to floor vibration depends on frequency and amplitude. Human perception threshold varies with frequency, most sensitive at 4-8 Hz where internal organ resonances occur. Vibration criteria establish limits preventing occupant complaints and equipment malfunction.

International Standards Organization (ISO) criteria classify vibration according to environment type:

• Office environments: VC-B (100 μm/s RMS, 4-80 Hz)
• Residential: VC-A (50 μm/s RMS)
• Operating rooms: VC-C (200 μm/s RMS)
• Laboratories: VC-D to VC-E (400-800 μm/s RMS)

Generic criteria include:

• 5000 micro-inches peak-to-peak displacement for perceptibility threshold
• Velocity RMS < 2000 micro-inches/sec for acceptable office environment
• One-third octave band analysis for detailed frequency-dependent assessment

Modal Analysis and Frequency Response

Modal analysis identifies structural natural frequencies, mode shapes, and modal damping through analytical or experimental methods. Finite element analysis (FEA) calculates mode frequencies and shapes from structural geometry, material properties, and boundary conditions. Experimental modal analysis uses impact testing or shaker excitation with response measurement at multiple locations.

Mode shapes describe spatial displacement patterns at natural frequencies. First mode typically exhibits simple single-hump deflection. Higher modes show multiple displacement peaks and nodes. Equipment location at mode shape node minimizes excitation of that particular mode.

Frequency response functions (FRF) relate structural response to input force as function of frequency. FRF measurements identify resonance frequencies through response peaks. Multiple FRF measurements at different locations characterize complete structural dynamic behavior.

Mitigation Strategies

Resonance mitigation employs frequency separation, damping enhancement, or mass tuning:

Frequency Separation: Modify equipment operating speed or structural stiffness creating adequate frequency ratio. Increase structural stiffness through added framing members, decreased spans, or increased member sizes. Constrain equipment operating speeds outside resonance range through VFD programming.

Damping Enhancement: Add viscoelastic damping materials, constrained layer damping, or tuned mass dampers increasing structural damping. Damping reduces resonance amplification but requires careful material selection and installation for effectiveness.

Mass Tuning: Add mass to structure lowering natural frequency away from excitation frequency. Most practical when structural frequency exceeds equipment operating frequency. Added mass must account for additional static load on structural capacity.

Vibration Isolation: Break transmission path through compliant mounts between equipment and structure. Effective for equipment operating well above isolator natural frequency. Coordinate with seismic restraint requirements to prevent isolation system damage during earthquakes.

Testing and Verification

Post-installation vibration testing verifies acceptable structural response. Measurements during equipment operation at all operating conditions identify resonance, excessive vibration, or inadequate isolation. Compare measured levels with acceptance criteria and design predictions.

Test procedure includes:

1. Baseline measurements with equipment off establishing ambient vibration
2. Startup transient measurements capturing resonance passage during acceleration
3. Steady-state measurements at all normal operating speeds
4. Impact testing determining structural natural frequencies
5. Isolation transmissibility measurements verifying isolation system performance

Accelerometers measure vibration as acceleration (g), velocity (ips), or displacement (mils) depending on frequency range and criteria. Triaxial measurements capture three-dimensional vibration characteristics. Frequency analysis using FFT identifies discrete frequency components and harmonics.