## Dynamic & Vibration Analysis

## Products and structures including rockets, satellites, smartphones, high-rise buildings, helicopters, turbines, and more need to be designed and analyzed for dynamic and vibration loading. Our dynamic and vibration analysis

## Dynamic and vibration analysis differs from other structural analyses because the loading is changing with time. As a result, it is necessary to take into account time-dependent structural characteristics, such as resonance frequencies and inertia to correctly calculate the response.

## our capabilities

## Modal Analysis

If loads change with time, then one needs to be concerned about the resonance frequencies of your product or structure. A modal analysis is used to calculate the resonance frequencies, corresponding shapes, and mass participation. Mass participation helps to distinguish between modes that will cause failure and those that are negligible. The shapes help to understand which are important.

In order to understand how a structure reacts to vibration loads, modal analysis is required. This is why prior to every vibration analysis we obtain modal shapes of a structure.

## Harmonic loads

Harmonic loads change at a constant frequency. Products that must be designed for harmonic loads include helicopters (due to rotor down-wash), turbines for blade crossing excitations, flywheels, generators, and turbines due to rotor imbalance, and piston engine drive-trains due to the torque variation from compression to power strokes. All of these systems must be designed to avoid the coincidence of the harmonic load and inherent structure resonance frequencies. Steady-state operation at a point of coincidence between a harmonic load and structural resonance will cause rapid failure unless system damping is elevated.

As we perform our vibration analysis for harmonic loads, our first course of action is “frequency avoidance” within steady-state operation regimes. Frequency avoidance assessments include Campbell and Interference Diagrams. If frequency avoidance cannot be achieved in steady-state operating regimes, then the application of damping may be a solution. Squeeze film dampers at bearings and elastomeric isolators both add significant amounts of damping and often are able to shift the resonance frequencies of a structure to a more transient operating regime. These are knobs that are used only if necessary. By far the best approach is to avoid frequency coincidence.

## Random Vibration loads

Our vibration analysis services include analyzing random vibration loads on structures. Random vibration loads vary in frequency and magnitude. They exist on aircraft, rockets ships, and ground vehicles. Their source can be air turbulence or ground and water texture. They are represented as a frequency-dependent energy density spectrum. Any structural resonance within the spectrum will be excited by the vibration. Because the vibration magnitude varies, the resulting calculated stresses are given in terms of a normal distribution. 68% of the time stresses will be equal to or less than the 1 sigma level, etc… A corresponding fatigue analysis considers the normal distribution of random loading and the expected cycle count given the structural resonance frequencies and duration of exposure

## Shock Loads

Shock loads in practice are short-duration impulses generated by an impact, blast, or drop. Shock loads are defined in a couple of different ways. Historically most shock loads were defined as a sine or sawtooth-shaped acceleration pulse. This method worked great analytically. A transient dynamic analysis was capable of processing non-linear characteristics which are important for material allow ables. In the last decade, the industry leaders have opted for defining shock as a Shock Response Spectrum (SRS). Unfortunately, the analytical simulation of an SRS is a linear analysis.

That means linear elastic material properties under the type of infrequent loading that will cause acceptable permanent deformation. Any structure made out of a ductile material will survive. The problem is that the linear analysis result predicts stresses well above the ultimate strength of ductile materials. To avoid unnecessarily over-designing structures, ASR has developed an empirical formula for calculating the elastic strength allowable for ductile materials. Rest assured, we will not unnecessarily burden your structure because of inaccurate analytical tools

## Seismic loads

Buildings and large industrial equipment often must be shown to survive the seismic loads specified for their location. Seismic analysis can be performed with response spectrum or time history loading. Both methods provide similar stress results. However, only the time history method provides a visual of the movement of the structure under the seismic event. Whenever Time-History acceleration data is available, I always use it because seeing is believing and understanding. One cannot fix a problem unless it is understood.

## Impact Analysis

Impact analyses are used to simulate events, such as drop, crash, ballistics, ice, and bird strikes. These highly dynamic events are expensive to test and often difficult to design for. Simulations can add enormous clarity to the events that occur in milliseconds. We use LS-Dyna software to simulate impact events. This software handles metallic, composite, soft fabric, and fluid/gas materials. It is truly marvelous software. If you are burdened with impact requirements, do yourself a favor and find out what is really happening with a simulation.

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## Blast Analysis

Blast analyses involve the simulations of TNT, C4, or other explosives being detonated in proximity to a test article. It could be a vehicle, building, or protective wall. The analysis simulates the energy release and gas expansion shock wave and its impact upon anything included in the model. We use LS-Dyna software for blast simulations. The software has the ability to track the blast wave under micro sec increments. In addition, the test article can be metal, composite, concrete, fabric or a composite of materials. The simulation with shows how the test article fairs under the blast wave loading. If you are burdened with blast requirements, do yourself a favor and find out what is really happening with a simulation.

## Rotordynamics

Rotordynamics analyses simulate the special situations involved with relatively high-speed rotating equipment. All rotating equipment has an imbalance. It may be small, but it exists. This imbalance creates a 1/rev harmonic excitation load. Because of this load, anything with a rotating element can self-excite its resonance frequencies.

This is not a good situation and can rapidly run away to a structural failure. As a result, it is especially important to understand the resonance frequencies of rotating elements. As with all resonance problems, the first goal is frequency avoidance. Try to keep the resonance out of the operating range. If this is not possible, then the only solution is to control the resonance with damping. Squeeze film dampers at the bearings are often effective.

While most dynamic characteristics are linear, rotor dynamics with a high inertia rotor behave non-linearly. This is due to gyroscopic effects acting upon the rotor. Careful analysis of high inertia systems is necessary to ensure resonance frequencies stay out of the operating range. When the resonance frequencies change with speed due to gyroscopic effects, the familiar straight lines start to curve on Campbell diagrams.

Along with frequency avoidance, Rotordynamics is used to determine the structural response of a system to a sudden imbalance. Usually, that imbalance is the result of a lost blade. Suddenly the carefully minimized rotor imbalance is increased by magnitudes. An analysis is required to ensure the static and rotating structure can withstand the new loading long enough for the system to shut down.