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Live Template

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templateTest

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Problem


Modal time-history

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analysis

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is

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well-suited

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for

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the

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modeling

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and

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analysis

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of

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human-induced

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vibrations

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which

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result

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from

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such

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impacts

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as

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pedestrian

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footfalls.

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Guidelines

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are

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presented

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in

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this

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test

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problem.

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Please

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note

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that

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these

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parameters

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are

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not

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intended

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to

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be

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realistic.

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It

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is

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up

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to

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the

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engineer

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to

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determine

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load

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magnitude,

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stride

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length,

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load

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frequency,

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and

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other

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input

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values.

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Human-induced

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vibrations

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may

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be

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modeled

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as

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follows:

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  1. Define

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  1. a

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  1. load

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  1. case

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  1. for

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  1. each

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  1. footfall

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  1. location,

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  1. and

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  1. for

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  1. convenience,

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  1. name

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  1. each

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  1. according

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  1. to

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  1. the

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  1. loading

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  1. sequence,

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  1. such

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  1. as

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  1. Step

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  1. 1,

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  1. Step

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  1. 2,

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  1. etc.

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  1. For

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  1. example,

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  1. 100

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  1. footfall

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  1. locations

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  1. would

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  1. require

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  1. 100

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  1. load

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  1. cases.

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  1. For each load case,

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  1. apply

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  1. a

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  1. point

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  1. load

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  1. in

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  1. the

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  1. location

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  1. of

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  1. the

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  1. corresponding

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  1. footfall.

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  1. It

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  1. may

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  1. be

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  1. convenient

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  1. to

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  1. use

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  1. a

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  1. unit

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  1. load,

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  1. then

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  1. adjust

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  1. magnitude

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  1. when

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  1. setting

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  1. the

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  1. scale

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  1. factor.

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  1. Define a single time-history

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  1. function

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  1. which

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  1. will

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  1. represent

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  1. the

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  1. footfall

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  1. sequence.

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  1. If

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  1. a

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  1. unit

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  1. load

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  1. is

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  1. applied

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  1. to

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  1. each

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  1. load

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  1. case,

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  1. set

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  1. the

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  1. magnitude

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  1. in

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  1. the

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  1. function

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  1. definition.

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  1. Additional

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  1. functions

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  1. may

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  1. be

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  1. defined

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  1. to

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  1. consider

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  1. multiple

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  1. impulse-function

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  1. shapes.

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  1. Define a time-history

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  1. analysis

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  1. case

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  1. from

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  1. the

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  1. following

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  1. options:

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    • Modal time history based on Eigen modes, where a sufficient number of modes should be captured for the given structure.

    • Modal time history based on Ritz modes, which may be a better option as far as analysis goes, though Ritz formulation requires as many modes as there are footfall locations and load cases, since each position must be considered as a starting load vector. For example, 100 footfalls require 100 modes.

    • Direct-integration time history, which is not based on modes, but rather a step-by-step process. Direct integration typically demands more time, but if a large number of modes are necessary for modal analysis, direct integration may be more viable.

  1. Add each footfall load case to the Loads Applied section (Figure 1), and specify the impulse function, scale factor, and arrival time. The timing of load sequence should be carefully considered and calculated, since arrival time and the application of impact is critical to dynamic response. Ensure that sufficient time steps are provided in the Time Step Data section to cover the duration of the time history.


Image Added

Figure 1 - Loads Applied

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