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Mechanics Corner

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A Journal of Applied Mechanics and Mathematics by DrD

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A Community Built On False Values -- An Opinion Piece

A Community Built on False Values This may well prove to be the least popular thing I ever post on this blog because what I have to say may offend many. I do not say it with the intent to offend, but because I am compelled to give a warning. One of the most interesting things that has developed from my blog, Mechanics Corner, here on the ME Forum has been the opportunity to correspond directly with a modest number of readers. This has included both young men and young women scattered across In

DrD

DrD

 

#17 -- MDOF Vibrations / Part IV

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 17     © Machinery Dynamics Research, 2015   Vibrations -- Part IV Multiple Degrees of Freedom Introduction     The first three parts of this series have involved only a single mass moving in a single direction. Such a system constitutes a single degree of freedom. In this part, a second mass is added which changes the required approach considerably. The new system is shown in Figure 1.            Fig. 1  Two Degr

DrD

DrD

 

#16 -- Vibration Part III/Effects of Damping

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 16     © Machinery Dynamics Research, 2015 Vibrations -- Part III Effects of Damping Introduction     In the previous discussions of the simple, displacement driven mechanical oscillator, damping has been explicitly omitted. In this part, viscous damping is taken into account. Viscous damping is the effect of forces that (1) always oppose existing relative motion, and (2) are proportional to the relative velocity

DrD

DrD

 

#15 -- SDOF Near & At Resonance, Part II

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 15     © Machinery Dynamics Research, 2015 Introduction & Review     In Part I of this discussion, the single degree of freedom oscillator was introduced with displacement excitation. The system is shown in Figure 1.            The impressed support motion is s(t) and the response of the mass is measured by x(t). As shown in the upper figure, s(0)=0, x(0)=0, and there is no strain in the spring. The elongation (

DrD

DrD

 

#14 -- SDOF Vibrations Part I

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 14     © Machinery Dynamics Research, LLC, 2015      SDOF Vibrations -- Part I Undamped System With Non-Resonant Conditions      Introduction     The undamped single degree of freedom oscillator is a suitable model for countless physical systems. It might represent a wheel on a vehicle (without shock absorbers), a machine on an elastic foundation, a sensitive instrument mounted on a shaky support, or any number of

DrD

DrD

 

#13 -- Numerical Methods/Roots & Solutions of Equations

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, #13     © Machinery Dynamics Research, LLC, 2015     Numerical Methods Roots & Solutions of Equations   Introduction       When we write a mathematical expression of the form y=f(x), a value of x for which y=0 is called a root of the equation. The root is a value of x at which the ordinate is zero and the curve passes through the x-axis.     Further, we are often called upon to consider two equations of th

DrD

DrD

 

#12 -- Numerical Solution of Ordinary Differential Equations

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #12 © Machinery Dynamics Research, LLC, 2015     Numerical Solution of Ordinary Differential Equations   Introduction   When we take the mathematics course titled Differential Equations, we learn a bag of tricks for the solution of many different types of differential equations. We also learn that every different type seems to require a completely new approach. There is no general approach to differential equations

DrD

DrD

 

#11 -- Eksergian's Equation of Motion for SDOF

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, # 11 © Machinery Dynamics Research, LLC, 2015     Eksergian's Equation of Motion for SDOF       Introduction   In undergraduate engineering education, when someone says "equation of motion," it is almost reflexive to think "Newton's Second Law of motion." Recall that Newton's Second Law says   ∑F=m a   where both the left and right sides of the equation are vector expressions. Vector are very powerful, but t

DrD

DrD

 

An Integrity Problem

The article referenced below points to a serious integrity problem, one that should be a matter of concern to all engineers. Is their no honor among these people? Is this how India expects to advance? By fraud? It involves blatant cheating on exams. Most of us do not enjoy taking exams, but we recognize that they are necessary to evaluate who is competent and who is not. The determination of who is competent to practice any profession, be it law, medicine, engineering, etc., is a matter of

DrD

DrD

 

Verbal Description of a Doonesbury Cartoon

The following is a verbal description of a Doonesbury cartoon of unknown date by Garry Trudeau. Doonesbury has long been one of America’s major cartoon strips, with a very dry wit and a decidedly left-of-center outlook. I found this today in going through some old files. SCENE: A college classroom, the teacher lecturing in a rather absent minded fashion, the students silently bent over, taking notes and keeping their heads down. TEACHER: Of course, in his deliberations on American capi

DrD

DrD

 

#10 -- Virtual Work / Part II (Revised)

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #10 © Machinery Dynamics Research, LLC, 2015     Virtual Work -- Part II (Revised)   Introduction   The main ideas related to virtual displacements and virtual work were introduced in a previous article titled Virtual Work -- Part I; understanding of that article is essential background for this article. Everything that is really necessary to be said about virtual work has be

DrD

DrD

 

#9 -- Virtual Work / Part I

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #9 © Machinery Dynamics Research, LLC, 2015     Virtual Work -- Part I   Introduction   The whole topic of virtual work is one that is usually not well handled at the undergraduate level (and frequently not well done at the graduate level, either!). It is, however, a very powerful concept, and critical to the application of many of the most powerful tools available for both statics and dynamics. The term virtual is

DrD

DrD

 

#8 -- Kinematics Part V / Rolling Constraints

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, # 8 © Machinery Dynamics Research, LLC, 2015     Rolling Constraints       Introduction   The previous discussion of Constraints, Part IV, dealt mostly with holonomic constraints representing a rigid link between two points in a mechanism. That is a very useful concept, but it neglects another important constraint type, the rolling constraint. This article will deal with the latter. Rather than make a very formal

DrD

DrD

 

Engineering Philosophy

  Engineering Philosophy   You have probably heard of Engineering Econ, Engineering Management, etc., but what about Engineering Philosophy?   Most of the time, in engineering discussions we talk about “hard information,” that is, facts, ideas, and methods for doing various engineering activities. But behind all that, guiding it, there needs to be a correct philosop

DrD

DrD

 

#7 -- Kinematics Part IV / Degrees of Freedom & Constraints

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, # 7 © Machinery Dynamics Research, LLC, 2015 Degrees of Freedom &  Constraints Introduction   The term "Degrees of Freedom" (often abbreviated as DOF) has been carefully avoided for the most part in these presentations up to this point, although it has crept in unavoidably a time or two. In this article, we attempted to face the matter squarely and deal with it fully. It is an importan

DrD

DrD

 

#6 -- AC Power in Real Variables Only

Mechanics Corner A Journal of Applied Mechanics & Mathematics by DrD, #6 © Machinery Dynamics Research, LLC, 2015 AC Power in Real Variables Only   Most mechanical engineers get a pretty good understanding of DC circuits, and this carries over fairly well into single phase AC circuits. The difficulties come when we get into industry and discover that almost everything is powered by three phase AC circuits. This is where it starts getting sticky! In the dis

DrD

DrD

 

Puzzled (A Poll)

The response here at Mechanical Engineering Forums, or should I say, the lack of response, has left me puzzled. There was a modest response (as indicated by comments) to my first post, but the number of comments has dropped to almost nothing since then. I am only aware of one person who has actually worked on one of the challenge problems that I have posed (but I hope that there are more who have). In the previous poll, there have been a good number of views, but an extremely small number of peo

DrD

DrD

 

#5 -- Kinematics Part III / Accelerations

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, # 5 © Machinery Dynamics Research, LLC, 2015     Vector Loop Kinematics -- Part III Acceleration Analysis Introduction In the first article in this series, titled "Vector Loop Kinematics - Part I/Position Analysis" the idea of using closed vector loops for the position analysis of mechanisms and machines was introduced. A second article, "Vector Loop Kinematics - Part II/Velocity

DrD

DrD

 

#4 -- Kinematics Part II / Velocity Analysis

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, # 4 © Machinery Dynamics Research, LLC, 2015     Vector Loop Kinematics -- Part II Velocity Analysis   Introduction In the previous article in this series, titled "Vector Loop Kinematics - Part I/Position Analysis" the idea of using closed vector loops for the position analysis of mechanisms and machines was introduced. This is an extremely powerful method; I have never found

DrD

DrD

 

How Do You Compute?? -- A Poll

The use of desktop, laptop, tablet, and other computers has become routine these days for engineering work. Along with this, there has been an ever-increasing number of software options for engineering calculations. It would be interesting to know just what software the readership here uses in their daily work and/or study.

DrD

DrD

 

#3 -- Kinematics Part I / Position Analysis

Position Analysis Introduction Many years ago, when I first began to study mechanics, the "conventional wisdom," expressed by both teachers and fellow students, was this: "Statics is easy, Dynamics is hard, and Kinematics -- who bothers to actually study kinematics? Kinematic relations, when needed, simply drop from the sky like rain, but nobody seriously studies kinematics." I eventually found the truth to be a bit more subtle: Statics of structures is generally easy, while the s

DrD

DrD

 

#2 -- Box Tipping

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, No. 2 © Machinery Dynamics Research, LLC, 2015 It is a common practice for manufacturers to ship their products in packing crates that are strapped down on pallets for handling. There is often concern about the stability of this package as it is handled in transit to the purchaser. For this problem, we understand that the manufacturer wants to perform a simple test on each package shipped to assure that it wil

DrD

DrD

 

#1 -- Introductions

Welcome to the first installment of Mechanics Corner, a feature that we hope will become a regular blog item on Mechanical Engineering Forum. The intent is that every week we will have a new article on some aspect of Applied Mechanics and Mathematics, things of broad interest to mechanical engineers. Some of these articles will be fairly elementary, while others will be considerably more advanced, but the idea is to have something for everyone. We will hope to amuse, entertain, and most importan

DrD

DrD



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