Modal Analysis for Vibration Problems

Understanding Modal Analysis: The Foundation of Vibration Problem Solving

Vibration problems represent one of the most challenging issues facing industrial facilities, infrastructure, and mechanical systems throughout Atlantic Canada. From the fish processing plants along Nova Scotia's coastline to the pulp and paper mills of New Brunswick, unwanted vibrations can lead to equipment failure, structural damage, reduced productivity, and safety hazards. Modal analysis stands as the most powerful engineering tool available for understanding, diagnosing, and resolving these complex vibration challenges.

Modal analysis is a dynamic testing and analytical method used to determine the inherent dynamic characteristics of a structure or mechanical system. These characteristics—known as modal parameters—include natural frequencies, damping ratios, and mode shapes. By understanding how a structure naturally wants to vibrate, engineers can identify the root causes of vibration problems and develop targeted solutions that address the source rather than merely treating symptoms.

For facilities operating in the Maritime provinces, where harsh environmental conditions, aging infrastructure, and the constant presence of dynamic loading from wind, waves, and industrial processes create unique challenges, modal analysis provides the scientific foundation necessary for effective vibration management.

The Science Behind Modal Parameters

Natural Frequencies

Every structure, from a simple beam to a complex industrial facility, possesses natural frequencies at which it prefers to vibrate. These frequencies are determined by the structure's mass distribution, stiffness properties, and boundary conditions. When external forces excite a structure at or near these natural frequencies, resonance occurs, causing dramatically amplified vibration responses that can be 10 to 100 times greater than the static response.

In practical terms, a structure might have a natural frequency of 25 Hz. If nearby rotating equipment operates at 1,500 RPM (also 25 Hz), the resulting resonance can cause catastrophic vibration levels. Modal analysis identifies these critical frequencies, typically ranging from 0.5 Hz for large civil structures to several thousand Hz for precision machinery components.

Mode Shapes

Mode shapes describe the deformation pattern a structure exhibits when vibrating at each natural frequency. Understanding mode shapes is crucial because they reveal which parts of a structure experience the greatest displacement and stress during resonant vibration. A cantilever beam, for example, exhibits distinctly different mode shapes at its first, second, and third natural frequencies—each with different nodal points and maximum displacement locations.

For industrial equipment common in Nova Scotia's manufacturing sector, mode shapes help engineers identify optimal locations for adding mass, stiffness, or damping to modify problematic vibration behaviour. They also guide the placement of vibration isolation systems and help predict how structural modifications will affect overall dynamic response.

Damping Ratios

Damping represents the mechanism by which vibration energy dissipates from a system. The damping ratio, typically expressed as a percentage of critical damping, indicates how quickly vibrations decay after excitation ceases. Steel structures typically exhibit damping ratios of 1-2%, while concrete structures range from 2-5%, and systems with elastomeric components may reach 5-10% or higher.

Low damping ratios mean that resonant vibrations can build to very high amplitudes, while higher damping limits peak response. Modal analysis quantifies these damping values, enabling engineers to determine whether additional damping treatments are necessary and to predict the effectiveness of proposed solutions.

Experimental Modal Analysis Techniques

Impact Testing Methods

Impact testing, also known as bump testing, represents the most common experimental modal analysis technique. This method uses an instrumented impact hammer to apply a controlled, broadband force input to the structure while accelerometers measure the resulting vibration response. The force and response signals are processed using Fast Fourier Transform (FFT) algorithms to generate Frequency Response Functions (FRFs) that contain the modal information.

Modern impact hammers are available with various tip materials and head masses to suit different applications:

• Soft rubber tips: Excite frequencies from 0-100 Hz, suitable for large civil structures

• Medium polymer tips: Excite frequencies from 0-500 Hz, appropriate for industrial machinery

• Hard steel tips: Excite frequencies from 0-5,000 Hz, used for precision components

• Hammer masses: Range from 100 grams for small components to 12 kg sledge-type hammers for heavy industrial equipment

For structures throughout the Maritimes, impact testing offers significant advantages: it requires minimal setup time, causes no damage to the structure, and can be performed during brief operational shutdowns—an important consideration for facilities that operate continuously.

Shaker Excitation Methods

When impact testing cannot provide sufficient energy input, or when more controlled excitation is required, electrodynamic or hydraulic shakers offer an alternative approach. Shakers can apply sinusoidal, random, or swept-sine excitation patterns, providing greater control over the frequency content and amplitude of the input force.

Shaker testing is particularly valuable for large structures such as bridges, offshore platforms, and tall buildings, where impact methods cannot adequately excite lower-frequency modes. In Nova Scotia, where numerous bridges and marine structures require periodic assessment, shaker-based modal analysis provides essential data for structural health monitoring programmes.

Operational Modal Analysis

Operational Modal Analysis (OMA), also called output-only modal analysis, extracts modal parameters using only response measurements while the structure operates under ambient or operational excitation. This technique is invaluable when structures cannot be shut down for testing or when artificial excitation is impractical.

OMA relies on the assumption that operational forces are broadband and randomly distributed, allowing advanced signal processing algorithms to separate structural modes from the response data. For continuously operating facilities—such as power plants, water treatment facilities, and manufacturing operations common throughout Atlantic Canada—OMA enables modal characterisation without production interruption.

Applications in Industrial Problem Solving

Rotating Machinery Vibration

Rotating equipment represents the most common source of industrial vibration problems. Pumps, fans, motors, compressors, and turbines all generate periodic forces at frequencies related to their rotational speed and number of rotating elements. When these forcing frequencies coincide with structural natural frequencies, severe resonance conditions develop.

Modal analysis of rotating machinery support structures typically reveals natural frequencies in the 15-150 Hz range—precisely where many industrial machines operate. For a pump running at 1,800 RPM (30 Hz) with a six-vane impeller, the vane pass frequency of 180 Hz may excite piping system resonances. Modal analysis identifies these coincidences and guides solutions such as:

• Adding mass to lower natural frequencies below the forcing frequency range

• Increasing stiffness to raise natural frequencies above forcing frequencies

• Installing tuned mass dampers or dynamic vibration absorbers

• Modifying operating speeds to avoid resonance conditions

• Implementing vibration isolation systems to decouple equipment from supporting structures

Piping System Vibration

Piping systems in process plants, marine vessels, and building mechanical systems frequently experience vibration problems due to flow-induced excitation, mechanical excitation from connected equipment, and acoustic resonance. The complex geometry of piping systems—with multiple branches, supports, and connected components—creates numerous natural frequencies and mode shapes that must be understood for effective vibration control.

Modal analysis of piping systems typically involves measuring at 50-200 locations to capture the three-dimensional vibration behaviour. Results guide the optimal placement of additional supports, the selection of support types (rigid versus resilient), and the identification of spans requiring modification. For the extensive piping networks found in Nova Scotia's food processing and energy sectors, systematic modal analysis prevents costly failures and ensures regulatory compliance.

Structural Floor Vibration

Modern industrial and commercial buildings increasingly experience floor vibration problems due to lightweight construction methods, long spans, and sensitive equipment requirements. Walking-induced vibrations, mechanical equipment, and external sources such as traffic can create unacceptable vibration levels for precision manufacturing, laboratory operations, and occupant comfort.

Modal analysis of floor systems identifies natural frequencies (typically 4-15 Hz for problematic floors) and mode shapes that indicate which floor regions are most susceptible to vibration. This information guides decisions about structural modifications, equipment placement, and vibration isolation requirements. For research facilities, medical centres, and precision manufacturing operations throughout the Atlantic provinces, floor vibration assessment ensures operational requirements are met.

Finite Element Correlation and Model Updating

Modal analysis serves a crucial role in validating and refining Finite Element Analysis (FEA) models. Theoretical predictions from FEA models can differ significantly from actual structural behaviour due to modelling assumptions, uncertain material properties, and unknown boundary conditions. Experimental modal analysis provides the benchmark data necessary to correlate and update FEA models for accurate dynamic predictions.

The correlation process compares experimental and analytical natural frequencies, mode shapes, and damping values. Quantitative metrics such as Modal Assurance Criterion (MAC) values indicate the degree of correlation between experimental and analytical mode shapes, with values above 0.90 generally indicating good agreement. When discrepancies exist, model updating techniques systematically adjust FEA parameters to improve correlation.

For engineering projects in Atlantic Canada, correlated FEA models provide validated tools for evaluating proposed modifications, predicting performance under different operating conditions, and assessing structural integrity. This combination of experimental and analytical methods delivers the highest confidence in engineering solutions.

Industry Standards and Best Practices

Modal analysis procedures and vibration criteria are governed by numerous industry standards that ensure consistent, reliable results. Key standards relevant to Canadian engineering practice include:

• ISO 7626: Vibration and shock — Experimental determination of mechanical mobility

• ISO 10816: Mechanical vibration — Evaluation of machine vibration by measurements on non-rotating parts

• CSA S6: Canadian Highway Bridge Design Code, including dynamic load provisions

• AISC Design Guide 11: Vibrations of Steel-Framed Structural Systems Due to Human Activity

• API 610/617/618: Vibration standards for centrifugal pumps, compressors, and reciprocating equipment

Adherence to these standards ensures that modal analysis results are defensible, comparable across different projects, and aligned with regulatory requirements. Professional engineers conducting modal analysis must be familiar with applicable standards and their proper implementation.

Selecting the Right Approach for Your Application

The selection of modal analysis methods depends on numerous factors specific to each application. Key considerations include:

• Structure size and complexity: Simple components may require only 10-20 measurement points, while complex industrial systems may need 500 or more

• Frequency range of interest: Determines sensor selection, sampling parameters, and excitation methods

• Operational constraints: Availability of shutdown periods influences the choice between conventional testing and operational modal analysis

• Accuracy requirements: High-precision applications demand more extensive testing protocols and higher-quality instrumentation

• Budget and schedule: Testing scope must balance technical requirements with practical constraints

Experienced engineering judgement is essential for designing modal analysis programmes that deliver actionable results within project constraints. Understanding both the theoretical foundations and practical limitations of various techniques ensures that the selected approach addresses the specific vibration problem at hand.

Partner with Experts for Your Vibration Challenges

Vibration problems rarely resolve themselves, and incomplete or incorrect diagnoses often lead to ineffective solutions that waste resources while problems persist or worsen. Modal analysis provides the scientific foundation necessary for understanding vibration behaviour and developing targeted, cost-effective solutions.

At Sangster Engineering Ltd., our team brings extensive experience in modal analysis and vibration problem solving to clients throughout Nova Scotia and Atlantic Canada. From industrial facilities in Amherst to marine operations along the coast, we provide comprehensive vibration analysis services that identify root causes and deliver practical solutions.

Whether you're experiencing equipment reliability issues, structural vibration concerns, or need to validate designs before construction, our professional engineers can help. We combine advanced testing capabilities with proven analytical methods to solve even the most challenging vibration problems.

Contact Sangster Engineering Ltd. today to discuss your vibration challenges and learn how modal analysis can provide the answers you need. Our team is ready to help you protect your assets, improve operational reliability, and achieve your performance objectives.

Partner with Sangster Engineering

At Sangster Engineering Ltd. in Amherst, Nova Scotia, we bring decades of engineering experience to every project. Serving clients across Atlantic Canada and beyond.

Contact us today to discuss your engineering needs.