ANALYSIS AND DESIGN OF MACHINE FOUNDATION

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Introduction

This document deals with vibration analysis and design of machine foundations subjected to dynamic load.

Richart and Lysmer's Model

Richart et al. (1970) idealised the foundation as a lumped mass supported on soil which is idealised as frequency independent springs which he described in term of soil parameter

dynamic shear modulus or shear wave velocity of the soil for circular footing when footings having equivalent circular radius. The Tables below shows the different values of spring and damping vlaues as per Richart and Lysmer.

In which, G = dynamic shar modulus of he soil and is given ; ν = Piosson's ratio of the soil; ρ_{s} = mass density of the soil; V_{s} = shear wave velocity of the soil obtained

from soil testing; g = acceleration due to gravity; m = mass of the machine and foundation; J = mass moment of inertia of the machine and foundation about the appropriate axes; K = equivalent spring stiffness of the soil; C = damping value of the soil; B = interia factor contributing to the damping factor; D = damping ratio of the soil; r = equivalent radius of a circular foundation; L = length of foundation, and B = width of the foundation.

Sketch

Table : Values of soil springs as per Richart and Lysmer (1970) model

SI No.

Direction

Spring value

Equivalent radius

Remarks

1

Vertical

This is in vertical Z direction

2

Horizontal

This induce sliding in horizontal X

2.1

This induce sliding in horizontal Y

3

Rocking

This produces roxking about Y axis

3.1

This produces roxking about X axis

4

Twisting

This produces twisting about vertical Z axis

Table : Values of soil damping as per Richart and Lysmer (1970) model

Mass ratio (B)

Damping ratio and Damping values

This damping value is in vertical Z direction

This damping value is in lateral X direction

Error, invalid left hand side in assignmentError, invalid left hand side in assignment

This damping value is in lateral Y direction

Error, invalid left hand side in assignmentError, invalid left hand side in assignmentError, invalid left hand side in assignment

This damping value is for rocking about Y direction

This damping value is for rocking about X direction

Error, invalid left hand side in assignmentError, invalid left hand side in assignmentError, invalid left hand side in assignmentError, invalid left hand side in assignment

This damping value is valid for twisting about vertical Z axis

Vertical Motion Considering damping of the Soil

For vertical direction the equation becomes that of a lumped mass having single degree of freedom when

By algebraically manipulating the expression, the form traditionally used by engineers is derived:

This form includes the damping ratio , the natural frequency , and the external forcing term . Consider only free vibration by setting

Download Analysis_and_Design_of_Machine_Foundations_1.mw

Good Morning Mapleprime Community,

Would anybody please help in the attached worksheet. I'm trying to use the new function in Maple that is the clicable method, but I was having problem in some of my output such as zeta_y and zeta_phi as this two equations are generating an error message.

Regards,

Moses

Hello there! Maple 2016.1 sometimes gets crasy about parsing input strings. I managed to capture this behaviour in the attached file. It looks like below. I am not sure what exactly triggers it. It just starts happening all of a sudden. What might be the cause...?

Error, incorrect syntax in parse: `;` unexpected (near 4th character of parsed string)

Error, invalid semantics "π"

Download test.mw

In workbook mode I use the Insert>>Paragaph>>Before Cursor to create a text block. I just want to type text into this block by way of comments on what preceded/follows. However, when I type parentheses or <> of (I expect) other stuff that Maple recognises as being parts of mathematical expressions Maple switches to italic and bold and starts generally interefering with my text. In the case of my title I get the result in the picture below. Is there any way to stop Maple doing this so I can type text?

Here is my Maple 16 code:

I expected to get outuput

a [a,b,c]

a [a,c,b]

But I get no output.

Why?

So I am trying to apply the Optimization function to a rather complicated problem I am currently working on, and having some trouble getting maple to cooporate. This is the part of the code that is giving me the error, with error included. All of the variables imputtet when calling OptimizeSpring are constants. If there is any other details I should add, please say so and I will add them promptly :) Thanks alot!

I suspect that it might be related to this suggestion, but I am not sure how to apply it http://www.mapleprimes.com/posts/95113-Optimization-Workaround-For-Operator-Form

HI,

wondered if anyone knows how to make proper use of the large operators pallete on the list of pallettes on the left. For example when using the contour integration symbol on the left how do you enter the delimiters.

I always get the error: "Error, unable to match delimiters". The help on this is not useful for this case.

Thanks.

Error, invalid piecewise

but

is OK.

Hi. I have this strange error.

Whenever I type D(f)(x) into the maple prompt, the program adds a whitespace between D(f) and (x), so I get the wrong output. I have to go back and delete the space manually. Here is a picture. http://prntscr.com/8vji4k

I type 'D(f)(x)' and the software displays 'D(f) (x) ' in the prompt, with the extra space.

I am using maple 2015 if that helps, but I think I had the same error with Maple 18

I did not add a space. I literally just entered f:=x->x^2 -3*x + 2; D(f)(x)

but the computer adds a space as I type D(f)(x).

Also I'm not sure why the space ruins the expression

What i am supposed to get is ' 2x - 3 '

Greetings,

I am a Maple 15 Student Edition user on both Windows and Linux. I wonder if it is possible to see the actual command send to Maple when I click on a particular entry in the right click context menu. If it is possible to do so, how can I have it displayed in document/worksheet mode? Does it matter if I am inputting in 1D or 2D?

Thanks in advance

i have the following equation:

1.003225155^(l)-((∫)[0]^1[((((0.6 r^2+1)^1.813666667)/((0.375 r^2+1)^2.666666667))^())^(l)r ⅆr)=0

and throws me the error:

Error, Got internal error in unknown : "invalid input: lhs received sattr, which is not valid for its 1st argument, expr"

do you know the meaning of the error and why this equation cant be solved for l?

i noticed members use such tags in their post very rarely in mapleprimes

and i am confused whether ?

there is a list of special html tags that are supported in "HTML Source Editor" of mapleprimes

that are compatible with it ? or all tags described in html5 or html4 are compatible ?

i just tested a few of those tags and they work excellent ...

Hi

I would like to display mathematical expressions on a plot.

I am using the following command on the code edit region of Maple 15 worksheet, intending to show the maths on a plot.

t := plots:-textplot([x, y, typeset(a[0]=1)], align = above): #where x and y are the position

plots[display]([p,t],labels=["X","Y"],font=["Times","Roman",20],labeldirections=[default,vertical],axis=[gridlines=10],caption=typeset(eta[12...

Hi,

is the series expansion for the following expression bugged in maple or am I missing some crucial thing of series?

series((1/epsilon-log(4)),epsilon=0);

results in epsilon^-1 -2 -2*ln(2)

for xmaple 16.01. The console version does not add the wrong term "-2".

Apparently it works here:

How does one change a previous Atomic setting back to non-Atomic? This seems so simple, but I can't find anyway to Undo this change.

Thanks,

I am using Maple 11. When I set up an equation, I can see an easy solution by visual inspection but when I have Maple solve the equation then use real numbers the results are different! What is going on?? I have uploaded my worksheet which shows the discrepancy.

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