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# in optistruct, if there is fatigue failure due to random vibration, the number of fatigue cycles of random vibration is evaluated by multiplying the vibration duration and another parameter called

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### Mohammed

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get in optistruct, if there is fatigue failure due to random vibration, the number of fatigue cycles of random vibration is evaluated by multiplying the vibration duration and another parameter called from screen.

## Learn Dynamic Analysis with Altair OptiStruct Final RP

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## Learn Dynamic Analysis with Altair OptiStruct_Final_RP

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Ciência dos Materiais

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frequency is defined as the cumulative sum of the

area under the Power Spectral Density function up to the specified frequency. Based

on the equation for yRMS obtained in the previous section, the RMS value of a response

61

for a particular degree of freedom x is calculated in the range of excitation

frequencies, [0, fn ] as follows:

(𝑆𝑥(𝑓))𝑅𝑀𝑆 = √2 ∫ 𝑆𝑥(𝑓) 𝑑𝑓 𝑓𝑛 0

In HyperView, the RMS values are displayed for a Random Response Analysis in a

drop-down menu with excitation frequencies. Each selection within this menu

displays the sum of cumulative RMS values for the particular response at all previous

excitation frequencies (which is the area under the response curve up to the loading

frequency of interest. The RMS over frequencies option can be selected to obtain the

RMS value of the response in the entire frequency range.

Auto-correlation Function Output for degree of freedom "x"

The RANDT1 Bulk Data Entry can be used to specify the lag time ( τ ) used in the

calculation of the Auto-correlation function for each response for a particular degree

of freedom, x.

The auto-correlation function and the power spectral density are Fourier transforms

of each other. Therefore, the auto-correlation function of a response Sx(f) can be

described as follows:

62

𝐴𝑥(𝜏) = 2 ∫ 𝑆𝑥(𝑓) 𝑒𝑥𝑝(𝑖2𝜋𝑓) 𝑑𝑓

𝑓𝑛 0

The Auto-correlation Function is calculated for each time lag value in the

specified RANDT1 set over the entire frequency range [0, fn ].

Number of Positive Zero Crossing

Random non-deterministic excitation loading on a structure can lead to fatigue

failure. The number of fatigue cycles of random vibration is evaluated by multiplying

the vibration duration and another parameter called maximum number of positive

zero crossing. The maximum number of positive zero crossing is calculated as shown

in the following equation:

𝑃𝐶 = ( ∫ 𝑓2𝑆𝑥(𝑓) ⅆ𝑓 𝑓𝑛 0 ∫ 𝑆𝑥(𝑓) ⅆ𝑓 𝑓𝑛 0 ) 0⋅5

If XYPLOT, XYPEAK or XYPUNCH, output requests are used, the root mean square

value and the maximum number of positive crossing calculated at each excitation

frequency will be exported to the *. peak file.

63

5.1 Card Image Used for Defining Power Spectral

Density as A Tabular Function

TABRND1

Defines power spectral density as a tabular function of frequency for use in random

analysis. Referenced on the RANDPS entry.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

TABRND1 ID XAXIS YAXIS FLAT

F1 G1 F2 G2 F3 G3 F4 G4

Where

ID Table Identification Number

XAXIS Specifies a linear or logarithmic interpolation of the X-Axis

YAXIS Specifies a linear or logarithmic interpolation of the Y-Axis

FLAT Specifies the handling method for y values outside the specified range

of x-values in the table.

=0 If an x-value input is outside the range of x-values specified on the

table, the corresponding y-value look up is performed using linear

extrapolation from the two start or two end points.

=1 if an x-value input is outside the range of x-values specified on the

table, the corresponding y-value is equal to the start or end point,

respectively

Fi Frequency value in cycle per unit time, must be in ascending or

descending order but not both

Gi Power Spectral Density

64 RANDPS

Defines load set power spectral density factors for use in random analysis having the

frequency dependent form 𝑆𝑗𝐾(𝐹) = (𝑋 + 𝑖𝑌) 𝐺(𝐹)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

RANDPS SID J K X Y TID

Where

SID Random analysis set identification number

J Subcase Identification number of excited load set

K Subcase identification number of applied load set

X, Y Components of Complex Number

TID A TABRNDi entry identification number which defines G(F)

RANDT1

Defines time lag constants for use in random analysis autocorrelation function

computation.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

RANDT1 SID N T0 TMAX

Where

SID Random analysis set identification number

N Number of time lag intervals

T0 Starting time lag

TMAX Maximum time lag

65

5.2 Tutorial: Random Response Analysis

This tutorial demonstrates how to import an existing FE model, apply boundary

conditions, and perform a random frequency response analysis on a flat plate.

OptiStruct is used to investigate the Peak Displacement in z-direction and extreme

fiber bending stress at undamped Natural Frequency (at the center of the plate)

The z-rotation and x, y translations are fixed for all the nodes, z translation is fixed

along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is

fixed along the edge y=0 and y=10. A steady state random forcing with uniform power

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## Fatigue life evaluated by using MSM and vibration fatigue technique.

Download Table | Fatigue life evaluated by using MSM and vibration fatigue technique. from publication: Fatigue life evaluation of mechanical components using vibration fatigue analysis technique | Unit brackets attached on a cross member and subjected to random loads often fail due to self-vibration. To prevent such failures, it is necessary to understand the fatigue failure mode and to evaluate the fatigue life using test or analysis techniques. The objective of this... | Fatigue, Failure and Prevention | ResearchGate, the professional network for scientists.

Table 3 - uploaded by Seong-In Moon

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## Fatigue life evaluated by using MSM and vibration fatigue technique.

Source publication

Fatigue life evaluation of mechanical components using vibration fatigue analysis technique

Article Full-text available Mar 2011 Seong-In Moon Il-Je Cho David Yoon

Unit brackets attached on a cross member and subjected to random loads often fail due to self-vibration. To prevent such failures, it is necessary to understand the fatigue failure mode and to evaluate the fatigue life using test or analysis techniques. The objective of this study is to develop test specifications for components, which are applicab...

## Context in source publication

Context 1

... equivalent PSD and transfer function presented in Figs. 8 and 9 were used for the fatigue analysis. Fig. 10 shows contour plots of fatigue damage and the fatigue life was presented in Table 3 with that calculated by MSM (Mode Superposition Method). The MSM technique estimated the tested fatigue life well within the difference of 13%. ...

View in full-text

## Citations

... Furthermore, the battery brackets are studied by a means of single-axis acceleration test approach [15]. Therefore, conducting investigations on the amplitude and frequency of the vibration to which batteries are exposed is vital to understanding how the mechanical vibration affects electronic and electrical components and how to avoid or hinder the loss of electrical continuity and the housing structural failure, which is a common well-known cause of failure [15][16][17][18][19]. It has been demonstrated that structural failure with sustained and excessive motion inevitably happens if a system vibration happens at the same frequency as its natural frequency [16]. ...

... Therefore, conducting investigations on the amplitude and frequency of the vibration to which batteries are exposed is vital to understanding how the mechanical vibration affects electronic and electrical components and how to avoid or hinder the loss of electrical continuity and the housing structural failure, which is a common well-known cause of failure [15][16][17][18][19]. It has been demonstrated that structural failure with sustained and excessive motion inevitably happens if a system vibration happens at the same frequency as its natural frequency [16]. Some studies are dedicated to studying individual single-cell responses to vibration while some referred to considering the whole battery pack. ...

Modal Analysis of a Lithium-Ion Battery for Electric Vehicles

Article Full-text available Jul 2022

Nicholas Gordon Garafolo

Manindra Varma KoricherlaShihao Wen

Roja Esmaeeli

The battery pack in electric vehicles is subjected to road-induced vibration and this vibration is one of the potential causes of battery pack failure, especially once the road-induced frequency is close to the natural frequency of the battery when resonance occurs in the cells. If resonance occurs, it may cause notable structural damage and deformation of cells in the battery pack. In this study, the natural frequencies and mode shapes of a commercial pouch lithium-ion battery (LIB) are investigated experimentally using a laser scanning vibrometer, and the effects of the battery supporting methods in the battery pack are presented. For this purpose, a test setup to hold the LIB on the shaker is designed. A numerical analysis using COMSOL Multiphysics software is performed to confirm that the natural frequency of the designed test setup is much higher than that of the battery cell. The experimental results show that the first natural frequency in the two-side supported and three-side supported battery is about 310 Hz and 470 Hz, respectively. Although these frequencies are more than the road-induced vibration frequencies, it is recommended that the pouch LIBs are supported from three sides in battery packs. The voltage of the LIB is also monitored during all experiments. It is observed that the battery voltage is not affected by applying mechanical vibration to the battery.

... Seong-in Moon et cl. [7] proposed a methodology to decide the optimum vibration fatigue test, which gives an equivalent failure mode with driving test condition, through a series of vibration fatigue analyses by changing acceleration directions and magnitudes. Arshad et cl. ...

... Then, it was observed that under the effects of structural resonance frequency, a vehicle would also experience failure, even though the load was much smaller than the general fatigue load, and this contributed to the occurrence of vibration fatigue problems (or dynamic fatigue problems) [20]. Fatigue is defined as the progressive and localized structural damage caused by repeated loads [7,11]. In the beginning, only static fatigue analysis that doesn't consider the inertial effects has attracted much attention. ...

... where n e gp and ωp i are respectively the number of Gauss points and their weights in element Ω e of the parent domain. contact mechanics [55][56][57][58][59], fluid mechanics [60][61][62], structural optimization [63][64][65][66][67][68][69][70][71][72][73][74], shell analysis [18,[75][76][77][78][79], damage and fracture mechanics [7,11,80], structural vibration analysis [81][82][83][84][85][86]. In the following, I will mainly present the IGA in the algorithm, structural optimization, shell, and vibration analysis. ...

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Mohammed 4 day ago

Guys, does anyone know the answer?