Mechanical Vibration Amplitude-Frequency Characteristic Analysis: Principles, Testing Methods, and A

Mechanical vibration amplitude-frequency characteristic analysis measures how the vibration response amplitude of a structure varies with excitation frequency, producing a frequency response curve that reveals natural frequencies, resonance peaks, and damping behavior. As a core technique in structural dynamics and reliability engineering, it is widely used to verify designs, avoid harmful resonance, and qualify components before delivery. This article explains the technical principles, sample types, measured parameters, testing methods, and typical applications of amplitude-frequency characteristic analysis.

Technical Overview

The amplitude-frequency characteristic of a mechanical system describes the relationship between the amplitude of the vibration response and the frequency of the excitation. When a structure is excited by a harmonic force or base motion, the response amplitude does not stay constant: it rises sharply whenever the excitation frequency approaches a natural frequency of the structure, producing a resonance peak. Plotting response amplitude (displacement, velocity, or acceleration) against excitation frequency yields the amplitude-frequency curve, which is the magnitude of the frequency response function (FRF) and the most direct graphical representation of the dynamic behavior of a machine or component.

Amplitude-frequency characteristic analysis therefore focuses on locating resonance peaks, quantifying the amplification at each resonance, and estimating the damping that limits peak amplitudes. The results support resonance avoidance, structural optimization, vibration qualification, and failure diagnosis. Key reference standards include the ISO 7626 series for experimental determination of mechanical mobility, ISO 16063 for vibration transducer calibration, ISO 18431 for digital signal processing of vibration data, ISO 10816 and ISO 20816 for machinery vibration severity assessment, IEC 60068-2-6 for sinusoidal vibration testing of equipment, ASTM E756 for measuring damping properties of materials, and the GB/T 11349 series for mechanical mobility measurement in Chinese national practice.

• Natural frequencies at which the structure responds with minimum excitation effort.
• Resonance frequencies and peak amplitudes of the response.
• Amplification factor Q and dynamic magnification at each resonance.
• Half-power bandwidth and the corresponding damping ratio.
• Transmissibility between the excitation point and the response point.
• Antiresonances, which help identify node locations and mounting behavior.

Testing Samples

Rotating Machinery Components

Rotors, shafts, impellers, fan wheels, gears, couplings, bearing housings, and motor armatures are analyzed to confirm that operating speeds, tooth-meshing frequencies, and blade-passing frequencies maintain an adequate margin from natural frequencies, and to support dynamic balancing and lateral critical speed assessment.

Structural and Machined Assemblies

Beams, plates, brackets, welded frames, cast housings, machine-tool spindles, and fixtures. Both free-free boundary conditions and as-installed mounting states are examined, because support stiffness can shift the amplitude-frequency curve significantly.

Automotive and Rail Transit Parts

Engine mounts, suspension springs and dampers, chassis brackets, body panels, exhaust hangers, battery enclosures, and interior trim components, typically evaluated with reference to automotive vibration test procedures such as JIS D 1601 and related OEM-style sine sweep specifications.

Electronic Assemblies and Packaging

Printed circuit board assemblies, electronic control units, connectors, sensor modules, and instrument housings. A resonance search is performed before sinusoidal or random vibration endurance testing per IEC 60068-2-6 and IEC 60068-2-64 to identify critical frequencies that may cause fatigue failure of solder joints or leads.

Material Specimens

Cantilever and sandwich beam coupons of damping materials, rubbers, composites, and viscoelastic treatments, characterized per ASTM E756 using the resonance curve (half-power bandwidth) method.

Testing Items

Depending on the engineering purpose, a typical amplitude-frequency characteristic test program measures and reports the following items:

• Amplitude-frequency response curves (FRF magnitude) at defined measurement points and directions.
• Natural frequencies of the first several modes within the specified frequency band.
• Resonance frequencies and peak response amplitudes in acceleration, velocity, or displacement units.
• Amplification factor Q and dynamic magnification ratio at each resonance.
• Damping ratio or loss factor derived from the half-power bandwidth.
• Transmissibility curves for vibration isolators, mounts, and mounted equipment.
• Mode shapes when the scope is extended to experimental modal analysis.
• Resonance dwell response, including strain measurements at fatigue-critical locations.

Testing Methods

Excitation Techniques

• Impact hammer excitation provides broadband input in a single strike and is the fastest method for modal screening, per ISO 7626-2 and GB/T 11349.
• Electrodynamic shaker excitation with step-sine or logarithmic swept-sine signals offers the highest frequency resolution around resonances and is the basis of the resonance search in IEC 60068-2-6.
• Broadband random and burst-chirp excitation enables averaged FRF estimation with excellent signal-to-noise ratio, processed per ISO 18431-2.
• Base excitation on a vibration table is used to measure transmissibility of isolators and mounted assemblies.

Sensors and Data Acquisition

IEPE piezoelectric accelerometers are attached by stud, adhesive, or wax in accordance with ISO 5348, ensuring the mounting resonance stays well above the analysis band. Force sensors between the shaker and the structure provide input signals for FRF computation, while non-contact laser Doppler vibrometers are preferred for lightweight structures where accelerometer mass loading would distort the amplitude-frequency curve. Anti-aliasing filtering, adequate dynamic range, and frequency resolution fine enough to resolve the half-power bandwidth of the narrowest peak are mandatory for valid measurements.

Signal Processing and Curve Analysis

Time records are transformed to the frequency domain by FFT analysis, and FRF estimators H1 or H2 are computed depending on the dominant noise location. Coherence is verified to exceed approximately 0.9 near resonances to confirm data quality. Natural frequencies are identified by peak picking, and single-degree-of-freedom circle or curve-fitting methods are applied around each resonance to extract frequency, amplitude, and damping consistently.

Damping Evaluation

The half-power bandwidth method is the standard approach: with resonance frequency fn and the frequencies f1 and f2 at which the response falls to the square root of one half, or minus 3 dB, of the peak value, the damping ratio is approximated by zeta = (f2 - f1) / (2 fn), and the amplification factor is Q = fn / (f2 - f1).

Typical Test Procedure

• Define the frequency band, boundary condition (soft free-free suspension or service-representative mounting), and acceptance criteria.
• Select the excitation method and configure shaker or hammer with force sensing.
• Install accelerometers or laser measurement points at pre-defined grid locations.
• Perform the sweep or impact sequence and record input and output signals.
• Verify coherence, repeatability, and absence of distortion or overload.
• Identify resonance peaks, compute Q values and damping ratios, and compare with limits.
• Optionally conduct resonance dwell testing at critical frequencies for endurance assessment.

Applications

• Resonance avoidance and speed margin verification for pumps, fans, compressors, motors, and other rotating equipment.
• Design verification and lightweighting, comparing prototype amplitude-frequency curves with finite element predictions and updating simulation models.
• Vibration isolation engineering, including mount selection and transmissibility verification for sensitive equipment.
• Environmental qualification of electronic assemblies, using resonance search results to plan dwell and endurance tests.
• Predictive maintenance, tracking downward shifts in natural frequency that indicate cracks, loosening, or wear in machinery.
• Material characterization of damping treatments, composites, and elastomers for noise and vibration reduction programs.
• Independent verification and certification support in accredited third-party laboratories, providing objective curves and pass or fail conclusions against defined acceptance criteria.

FAQ

What is the difference between natural frequency and resonance frequency?

In lightly damped structures the two are nearly identical. Strictly, the natural frequency is a property of the undamped system, while the resonance frequency observed as the peak of the amplitude-frequency curve is shifted slightly lower by damping. For most engineering purposes the difference is negligible.

Why does the amplitude-frequency curve show sharp peaks?

At a natural frequency, the input energy accumulates in the structure instead of being dissipated, and only damping limits the response. Low damping produces a high Q factor and therefore a tall, narrow peak, while high damping produces a low, broad peak.

How is damping obtained from the amplitude-frequency curve?

The half-power bandwidth method is most common. The frequencies on either side of the peak where the amplitude drops by 3 dB are measured, and the damping ratio is estimated as the bandwidth divided by twice the resonance frequency. For very light damping, decay or curve-fitting methods may be used instead for better accuracy.

What frequency range is usually tested?

Typical ranges are 5 Hz to 2 kHz for industrial equipment, automotive parts, and electronic assemblies, extended up to about 10 kHz for small precision components such as sensors and hard-drive or optical sub-assemblies. The range must cover all excitation frequencies the product will experience in service.

How should a sample be mounted for the test?

For intrinsic modal parameters, the sample is suspended softly to approximate free-free conditions. When installed behavior is of interest, the actual service mounting is reproduced rigidly and consistently. The chosen boundary condition must always be documented, because it directly shifts the measured frequencies and amplitudes.

What does the final test report include?

A complete report presents the test setup and boundary conditions, applicable standards, instrumentation with calibration traceability, amplitude-frequency curves for every measurement point, tables of natural frequencies with Q values and damping ratios, and conclusions against the specified acceptance criteria.