Service overview
Stress, vibration, fatigue, nonlinear and composite structural simulation and design optimisation. This service is part of that division and is scoped individually around what you need to learn, decide or publish.
Every structure has natural frequencies at which it vibrates freely, each with a characteristic mode shape. When an excitation, such as an unbalanced rotor or a periodic load, approaches a natural frequency, the response can be amplified dramatically. Modal and vibration analysis finds those frequencies and predicts the response so that resonance can be avoided or controlled.
The analysis connects directly with testing. Experimental modal analysis measures the same frequencies and shapes from a real structure, and the comparison reveals whether the model's stiffness, mass and boundary conditions are right. Mismatch is common and informative, which makes this a field where simulation and experiment are naturally used together.
If you plan to publish the outcome, see manuscript & publication support, for example computational & simulation manuscripts or original research article writing.
What this service covers
Problems this service can address
- Resonance risks near operating frequencies
- Mismatch between model and measured natural frequencies
- Unclear damping assumptions
Methods and analytical approaches
- Eigenvalue (modal) analysis
- Harmonic, random and transient response analysis
- Model updating against test data
- Damping estimation approaches
Applications
- Rotating machinery and supports
- Lightweight structures
- Vibration-control studies
Relevant engineering disciplines
Scope, inputs and deliverables
Scope of work
- Definition of the physics, geometry and quantities of interest
- Model set-up with verification and, where data allow, validation
- Parametric or sensitivity studies agreed at scoping
- Results and documentation suitable for reports or publication
- Feasibility check on: geometry, mass and stiffness data
Typical inputs required from you
- Geometry, mass and stiffness data
- Excitation description
- Measured frequencies or accelerations
Deliverables
- Frequency and mode-shape tables
- Response results versus excitation
- Resonance-avoidance observations
Highly specialised requests are first checked for feasibility from this information. Please do not send confidential data through the public form; describe it first and agree secure transfer afterwards.
Project workflow and method
- 01Enquiry and requirement assessment
- 02Technical scoping and proposal
- 03Execution
- 04Quality review and delivery, with an agreed round of revisions
Read the full project workflow.
In depth: how the work is done
Eigenvalue (modal) analysis
Modal analysis solves an eigenvalue problem for the undamped structure, giving natural frequencies and mode shapes that depend only on mass and stiffness distribution and boundary conditions. Free-free and constrained analyses serve different purposes. Mode shapes indicate where the structure moves most, guiding sensor placement and design modifications. The number of modes required depends on the frequency range of excitation and on the participation of each mode in the response.
Harmonic, random and transient response
Harmonic response analysis computes steady-state response to sinusoidal excitation across a frequency range and shows resonance peaks. Random vibration analysis uses power spectral densities to compute statistical response to broadband excitation such as road or acoustic loading. Transient analysis follows the response to time-varying loads such as impacts. Each requires damping, which is the least well-known part of the model and often has the biggest influence on peak response.
Damping estimation
Damping in real structures comes from material, joints, friction and surrounding fluid, and it is difficult to predict from first principles. Estimates come from tests, using half-power bandwidth or decay methods, or from literature for similar structures. Modal damping ratios are typically assigned per mode, and their effect on the response is tested by varying them. Sensitivity to damping is highlighted because small errors change resonance peak amplitude markedly.
Model updating against test data
When measured frequencies and mode shapes are available, the model can be updated by adjusting uncertain parameters, such as joint stiffness or boundary conditions, to improve agreement. Mode correlation metrics, such as the modal assurance criterion, compare shapes quantitatively. Updating must be physically justified; adjusting parameters beyond plausible ranges merely hides model errors. The remaining discrepancy is reported honestly.
Design implications and vibration control
Results are translated into practical actions: shifting natural frequencies away from excitation by changing stiffness or mass, adding damping, isolating the source or adding tuned absorbers. We evaluate the effect of such modifications and their robustness to variations in parameters, such as temperature or loading, that change frequencies. The goal is a design that is not just tuned at one nominal condition but tolerant of realistic variation.
Quality control and good practice
Quality-control approach
- Verification: mesh, time-step and solver sensitivity are examined before results are reported.
- Validation: results are compared with measurements or reference solutions where these exist, and the absence of such data is stated.
- Boundary conditions and material or fluid properties are recorded with their sources.
- Sensitivity to the least certain inputs is shown or explained.
Common pitfalls this service helps avoid
- Wrong boundary conditions. Natural frequencies are very sensitive to how a structure is supported, and idealised supports shift them.
- Assuming damping values. Peak response scales inversely with damping, so a guessed value can mean large errors.
- Too few modes in the response calculation. Truncating the modal set can omit contributions that matter at the frequency of interest.
- Matching frequencies but not shapes. Agreement in natural frequency alone does not show that the model captures the real dynamics.
What good reporting looks like
A vibration report describes the structure, mass and stiffness representation, boundary conditions, modal results with frequencies and mode shape plots, the excitation considered, the response results with the damping assumptions, comparison with test data and correlation metrics where available, model updating steps and parameter changes with justification, and design recommendations. It lists the uncertainties, especially damping and boundary conditions, and how they affect the conclusions.
An illustrative scenario
Hypothetical example written for explanation. It is not a client case, a result or a testimonial.
Imagine a researcher analysing a lightweight support frame beneath a motor. The model predicts a natural frequency close to the running speed, and the harmonic response shows a large peak with the assumed damping. Measured data from a tap test show the real frequency is somewhat lower, which model updating attributes to joint flexibility at the base. After updating, the frequency match is good, and a stiffening rib is evaluated, which moves the frequency away from the running speed with an acceptable margin even when damping is varied.
Questions to settle before you begin
- Which excitation frequencies are present?
- How is the structure really supported?
- What damping data can I use?
- Do I have measured natural frequencies or mode shapes?
- What margin from resonance is acceptable?
Key terms
- Natural frequency
- A frequency at which a structure vibrates freely after being disturbed.
- Mode shape
- The deformation pattern associated with a natural frequency.
- Damping ratio
- A measure of energy dissipation relative to critical damping.
- Power spectral density
- The distribution of signal power over frequency used to describe random loading.
- Modal assurance criterion
- A measure of similarity between two mode shapes.
Working together on Finite Element Analysis (FEA) & Structural Engineering projects
Structural and FEA engagements begin by clarifying what must be predicted, such as stress, stiffness, frequency or life, and which loads and supports are known. We ask for geometry, material data, load cases, connection details and any test measurements. A hand calculation or benchmark is prepared alongside the finite element model to cross-check it. Reports show mesh convergence, state assumptions about supports and materials, and give margins with their uncertainty. The work is research-level analysis and does not replace code-based design checks or certification by licensed professionals.
Frequently asked questions
Can you update my model to match test data?
Yes. Model updating adjusts uncertain parameters within physical limits. We report what was changed and why.
Can you analyse rotating machinery?
Modal and response analysis of supports and casings is possible. Rotor-dynamic analysis with gyroscopic effects can be discussed if in scope.
Do I need test data?
Not necessarily, but test data improve credibility considerably. Without them, results are labelled as unvalidated predictions.
Can you suggest how to avoid resonance?
Yes, by identifying which modes are excited and proposing modifications, with an assessment of their robustness.
Do you perform experimental modal testing?
The service analyses models and data you supply. Testing itself would need to be carried out by a suitable laboratory.
How is this service scoped and priced?
After your enquiry we review what you need, ask for missing information and send a written scope and quotation. Price depends on complexity, deliverables and timeline. See the project workflow.