Transient Dynamic Analysis

Understanding Transient Dynamic Analysis: A Critical Tool for Modern Engineering

In the demanding engineering environment of Atlantic Canada, where structures must withstand everything from severe winter storms to industrial vibrations, understanding how systems respond to time-varying loads is essential. Transient dynamic analysis represents one of the most sophisticated and valuable tools in the modern engineer's arsenal, enabling the prediction of structural behaviour under rapidly changing conditions that static analysis simply cannot capture.

Unlike steady-state or static analyses, transient dynamic analysis—sometimes called time-history analysis—examines how structures respond to loads that change over time. This includes impact events, blast loading, earthquake ground motions, wave impacts on offshore structures, and machinery startup sequences. For engineering firms operating in Nova Scotia and throughout the Maritime provinces, where industries range from ocean technology to manufacturing, mastering this analytical approach is fundamental to delivering safe, reliable designs.

The Fundamentals of Transient Dynamic Analysis

Transient dynamic analysis solves the complete equation of motion, including inertial and damping effects that vary throughout the analysis duration. The governing equation takes the form:

{ü} + {u̇} + {u} = {F(t)}

Where represents the mass matrix, the damping matrix, the stiffness matrix, {u} the displacement vector, and {F(t)} the time-dependent force vector. This equation must be solved at each time step throughout the analysis, making transient analysis computationally intensive but remarkably powerful.

Key Parameters and Considerations

Successful transient dynamic analysis requires careful attention to several critical parameters:

• Time Step Selection: The time increment must be small enough to capture the highest frequency response of interest. A common rule requires at least 10-20 time steps per period of the highest significant frequency, with typical values ranging from 0.0001 to 0.01 seconds depending on the application.

• Analysis Duration: The total analysis time must extend long enough to capture the complete transient response, including any subsequent free vibration decay. For impact analyses, this might be milliseconds; for seismic events, it could extend to 30-60 seconds.

• Damping Characterisation: Structural damping significantly affects response magnitude and decay rate. Typical damping ratios range from 1-2% for welded steel structures to 5-7% for bolted connections and concrete structures.

• Mass Distribution: Accurate mass representation, including both structural mass and any added masses from equipment, fluids, or operational loads, is crucial for proper inertial effects.

Solution Methods

Engineers employ two primary approaches for solving transient dynamic problems. Implicit methods, such as the Newmark-beta algorithm, allow larger time steps but require matrix factorisation at each step. Explicit methods, commonly used in impact and crash simulations, use smaller time steps but avoid matrix inversion, making them efficient for highly nonlinear problems with contact and material failure.

Applications in Maritime and Industrial Engineering

The diverse industrial landscape of Nova Scotia and Atlantic Canada presents numerous applications for transient dynamic analysis. Understanding these applications helps engineers select appropriate analysis methods and interpret results effectively.

Offshore and Marine Structures

Nova Scotia's extensive coastline and growing offshore industry create significant demand for marine structural analysis. Transient dynamic analysis proves essential for:

• Wave Slam Loading: When waves impact offshore platforms or vessel hulls, the resulting pressure pulses can reach 200-500 kPa over durations of 50-200 milliseconds. Transient analysis captures the structural response to these brief but intense loads.

• Vessel Berthing: Ship impacts on wharf structures during berthing operations involve energy absorption over 0.5-2 seconds. Analysis ensures fender systems and supporting structures can safely dissipate berthing energy without damage.

• Mooring Line Snap Loads: Dynamic tensioning and potential failure of mooring systems create shock loads that propagate through entire floating structures.

Industrial Equipment and Machinery

Manufacturing facilities throughout the Maritimes rely on heavy rotating equipment, presses, and material handling systems that generate significant dynamic loads:

• Press Operations: Forging and stamping presses can generate impact forces exceeding 10 MN over stroke times of 10-50 milliseconds, requiring foundation and structure analysis to prevent vibration transmission to sensitive equipment.

• Rotating Equipment Startup: Large motors and turbines pass through critical speeds during startup, temporarily exciting resonant frequencies. Analysis ensures structures can withstand these transient amplification periods.

• Emergency Shutdown Scenarios: Sudden equipment stops create reaction forces and torques that must be safely transmitted through supporting structures.

Seismic Analysis for Critical Infrastructure

While Atlantic Canada experiences lower seismic activity than western regions, the National Building Code of Canada still requires seismic design consideration. The 2020 seismic hazard model identifies peak ground accelerations of 0.09-0.15g for the 2% in 50-year probability level in parts of Nova Scotia. Time-history analysis using representative ground motion records provides more accurate response predictions than simplified equivalent static methods, particularly for irregular structures or critical facilities.

Modelling Techniques and Best Practices

Achieving accurate transient dynamic analysis results requires careful attention to modelling practices that differ from static analysis approaches.

Mesh Considerations

Dynamic analysis mesh requirements often exceed those for static analysis. The mesh must accurately capture wave propagation through the structure, requiring element sizes related to the wavelength of the highest frequency of interest. For steel structures responding to impact loads with frequency content up to 1,000 Hz, element sizes of 50-100 mm are often necessary in critical regions.

Boundary Conditions and Supports

Support flexibility significantly affects dynamic response. Fixed boundary conditions that adequately represent static behaviour may artificially constrain dynamic motion. Including foundation flexibility, with typical soil spring stiffnesses ranging from 20-200 MN/m for spread footings on Maritime soils, often improves correlation with measured responses.

Load Characterisation

Accurate load time-history definition is perhaps the most critical input for transient analysis. Engineers must characterise:

• Rise Time: How quickly the load reaches its peak value, with faster rise times exciting higher frequency response.

• Duration: The length of load application relative to the structure's natural periods determines whether the response is impulsive, dynamic, or quasi-static.

• Decay Characteristics: Whether loads terminate abruptly or decay gradually affects the subsequent free vibration response.

Nonlinear Effects

Many transient events involve nonlinear behaviour that linear analysis cannot capture. Material yielding during impact, gap closure in bolted connections, and contact between components all require nonlinear solution algorithms. While computationally expensive, nonlinear transient analysis provides realistic predictions of permanent deformation and energy dissipation.

Validation and Result Interpretation

Transient dynamic analysis results require careful interpretation and, where possible, validation against physical measurements or established benchmarks.

Response Metrics

Key output quantities from transient analysis include:

• Peak Displacement: Maximum structural movements, critical for ensuring adequate clearances and limiting non-structural damage.

• Peak Stress: Maximum stress values for fatigue assessment and comparison against material allowables. Dynamic stress concentrations can exceed static values by factors of 2-4 at resonant conditions.

• Acceleration Response: Critical for equipment qualification and human comfort assessment. Accelerations exceeding 0.5g are generally unacceptable for occupied structures.

• Support Reactions: Time-varying reaction forces for foundation and connection design.

Dynamic Amplification

One of the most important insights from transient analysis is the dynamic amplification factor (DAF)—the ratio of peak dynamic response to the equivalent static response. For loads with duration near the structure's natural period, DAFs can reach 1.5-2.0, while very short duration loads may produce DAFs below 1.0 due to the structure's inability to fully respond before the load passes.

Verification Approaches

Engineers should verify transient analysis results through:

• Energy Balance Checks: Comparing input energy with stored strain energy, kinetic energy, and dissipated energy throughout the analysis.

• Convergence Studies: Confirming that results stabilise with time step refinement and mesh density.

• Comparison with Simplified Methods: Checking peak responses against single-degree-of-freedom approximations or response spectrum methods.

Software Tools and Computational Requirements

Modern transient dynamic analysis relies on sophisticated finite element software capable of handling large models and extended time histories. Common platforms include ANSYS, Abaqus, LS-DYNA, and NASTRAN, each with particular strengths for different application types.

Hardware Considerations

Transient analysis computational demands often exceed those of static analysis by one to two orders of magnitude. A typical industrial machinery impact analysis might involve:

• 500,000 to 2,000,000 degrees of freedom

• 10,000 to 100,000 time steps

• Solution times of 4-24 hours on modern multi-core workstations

• Results files of 10-100 GB requiring careful data management

Cloud computing resources increasingly enable engineering firms to tackle large transient problems without maintaining dedicated high-performance computing infrastructure, an important consideration for firms serving Atlantic Canada's distributed industrial base.

Integration with Design Standards and Codes

Canadian engineering standards increasingly recognise the value of transient dynamic analysis for demonstrating code compliance. The National Building Code of Canada permits time-history analysis as an alternative to prescribed static or response spectrum methods, often enabling more economical designs for complex structures.

Industry-specific standards, including CSA standards for pressure equipment and offshore structures, reference dynamic analysis requirements for equipment subject to cyclic or impact loading. Understanding when transient analysis is required versus optional, and how to document results for regulatory review, represents an important aspect of professional engineering practice.

Partner with Experts in Dynamic Analysis

Transient dynamic analysis represents a powerful but complex engineering tool that can reveal critical insights into structural behaviour under time-varying loads. From protecting offshore installations against wave impacts to ensuring industrial machinery foundations perform reliably, these analyses form an essential part of comprehensive engineering design.

Sangster Engineering Ltd., based in Amherst, Nova Scotia, brings extensive experience in advanced structural analysis methods to clients throughout Atlantic Canada and beyond. Our engineering team combines sophisticated analytical capabilities with practical understanding of the unique challenges facing Maritime industries. Whether your project involves marine structures, industrial equipment, or critical infrastructure requiring dynamic assessment, we provide the technical expertise to ensure safe, efficient, and code-compliant designs.

Contact Sangster Engineering Ltd. today to discuss how transient dynamic analysis can benefit your next project. Our commitment to engineering excellence and client service makes us the trusted choice for complex analytical challenges in Nova Scotia and across the region.

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.