11

It really depends on the problem and what you want to capture. Usually, in classes, it may be beneficial for the students at an initial stage to disregard gravity alltogether in order to simplify the equations of motion. Below are a few scenarios, starting from the most trivial. Horizontal Case In the following mass spring system: There is no point in ...


9

In a more general sense, the electrical concepts of inductance, capacitance and resistance are equivalent to mass, spring constant and friction in the mechanical world. Voltage becomes force and current becomes velocity. For example, the suspension in a vehicle is a carefully-tuned low-pass filter that uses the mass of the frame and body, the springs on the ...


8

Yes, for sound specifically there is a term called "acoustic impedance" that, just like electrical impedance, is frequency dependent. Acoustic impedance results from the acoustic wave equation, which takes the same form as the electromagnetic wave equation. So any solid has an acoustic impedance just like every conductor has an electric impedance. Acoustic ...


7

Stiffness is a murky term frequently used ambiguously in engineering. However, the most common definition of stiffness is the product of a beam's Young's Modulus $E$ (which is a function of its material) and its moment of inertia $I$ (which is a function of its cross-section). So $\text{Stiffness} = EI$. Loading has nothing to do with stiffness according ...


6

But I'm thinking it may be better (more efficient maybe? less vibration maybe?) to run it in three-phase mode, with the load balanced among the three hot terminals. Correct. Figure 1. The load is constant through the generator cycle. Source: T. Davies - website not found. My thinking, based on my coarse understanding of generators, is that in three ...


5

Take the Fourier Transform of the time varying driving force, this will give the frequency content of the driving force. Multiple modes of vibration can be driven at once, and will superpose with each other, but time varying driving forces with a frequency content that are high at frequencies near a particular resonant frequency will mainly drive the ...


5

This may be only a partial answer since I don't have any idea what to do for the Young's modulus of the fluid. Consider the paper Dynamic Pressures on Accelerated Fluid Containers by G. W. Housner. This is referenced by ASCE 4-98 Seismic Analysis of Safety-Related Nuclear Structures, Commentary Section C3.1, for analysis of hydrodynamic loads on tanks. In ...


5

There are analogs to filters in lots of mechanical systems. In fluid systems prone to pressure spikes perhaps because they use a fixed displacement pump, an accumulator will be used to filter out those spikes to prevent damaging other parts of the system. A vibration isolator acts in much the same way. Sometimes they're used as is. Other times, for more ...


5

The ESA has a page on compressor blades. They give a good dimensioned diagram of an approximate shape; here are some basic dimensions: Length: 300 mm Width: 30 mm Height: 70 mm Thickness: 5 mm I can't find any complete open source designs (i.e. high-quality, technical engineering drawings), but this is a good approximation.


5

Double nutting can be an easy option for this. I was about to describe it myself, but these folks do a great job. This image, from the article, models the forces that do the job. Take note of the contact surfaces between the threading of the bolt, in the top vs. bottom nut:


5

To obtain the modes shapes and resonant frequencies, you start from your equation of motion with no externally applied forces, which is indeed as you've stated. $$\mathbf M \mathbf{\ddot q} + \mathbf K \mathbf q = \mathbf 0 \qquad (1)$$ For brevity, I've let $\mathbf K = \mathbf K_b + \mathbf K_m$. Currently, $\mathbf q(t)$ is a function of time. If the ...


5

You won't get much resonance because the phase the thing is being driven with keeps changing. The resonant thing will act like a notch filter, so you are left with the frequencies near its resonance. However, for resonant energy to build up, the system has to get pumped for a while. While a short segment of the filtered white noise could resonate the ...


5

Consider a small piece cut out of a structure that has non-zero internal stress. To maintain equilibrium, there must be some forces applied to the boundary of the piece. (Of course when it was part of the complete structure, those forces came from the stress in the adjacent parts of the structure.) When you deform the piece further, those external forces ...


5

According to the wiki, these are called Stockbridge dampers. The design is tuned for a specific length and one might also expect a specific mass/material. The weights are mounted on flexible arms, typically a length of stiff cable, which allow the assembly to absorb energy that might otherwise be imparted to the longer power lines, or more accurately, that ...


4

When I have received fragile content in the past it has always come with a Shockwatch label attached to the side. I'm not 100% sure, but I believe there is some sort of guarantee by the shipper to keep the forces below the level registered by the label (a guarantee which most certainly comes at added cost). Looking up the specs in the link above, these ...


4

Build two tables. The outer table will have a hole in the middle and only hold the glass plate. There should be about 10 cm of free space between the tables. The train will be placed on the inner table: ================== <-- glass plate || ______ || || || || || <-- train platform || || || || This way people won't bump the ...


4

Mathematically, an eigenvalue analysis assumes the modal displacements are infinitesimally small, so the change in stiffness in the cable caused by the vibration is a second order effect which can be ignored. This very-small-amplitude vibration is a good place to start understanding the behaviour of the structure - for example, look at how the frequency ...


4

RPM = revolutions per minute. In the context of vibration monitoring, 1 x rpm means a vibration frequency that is the same as the rotation speed (one vibration oscillation per revolution of the rotor), 2 x rpm means a frequency 2 x the rpm (two oscillations per revolution), etc. Because of nonlinear effects in the mechanical system, vibrations can be ...


4

An accelerometer is the correct choice, but the smartphone accelerometer gets its readouts smoothed out in software before being made accessible to userspace. It won't pick up such fine vibrations. You'll need a microcontroller (for up to ~1khz frequencies) or a DSP (higher), preferably on a development board, to perform the sampling. (note you should have ...


4

An o-ring usually (but not always) has a round section and is made of a compressible material such as rubber, neoprene, silicon etc. A washer tends to have a square or rectangular section and is usually made of a harder material brass, copper, aluminium, steel etc. It is not about advantages or disadvantages, but which is used will depend on the ...


3

While the acoustic analysis idea may* work, I think the accellerometer data would be much easier to analyze. If you are looking for something that can give you better rates of data, try looking into other accellerometers. This one from Adafruit has a maximum rate of 800 Hz(datasheet). According to your calculations, this should be enough. You could log this ...


3

Unless the blade is made of a ceramic material, there is very little chance of this working. The idea you have in mind, I think, is something like the shattering of a wine glass by exciting one of it's resonance frequencies. This works because the $Q$ of the resonance (the ratio of amplitude of the motion to excitation amplitude) is very high so that a ...


3

This certainly isn't an answer, but more of a guidance on how to approach the problem. The analysis that you choose to do depends entirely on why you are collecting the data in the first place. For example, the structure may have been designed and constructed to behave a certain way, and you are collecting data to determine whether it is behaving to spec. ...


3

Section 2.1.14 of the Abaqus Example Problems Manual is 'Water sloshing in a baffled tank', which might be useful (even if you don't use Abaqus at your own institution, the manuals are hosted by many institutions that allow public access). The Abaqus water model uses an equation of state (EOS). If you download the input file from the manual, you can cut ...


3

UPS has, or at least had when I was transit testing packaged products, a specific packaging test standard based on ISTA standards and ASTM D4169. There's also a MIL-STD, 810 something, but I don't remember the exact number. Typically, for a parcel carrier, the test, regardless of standard, consists of environmental conditioning, a "10 pt" drop test and a ...


3

The body of your question (the title is somewhat different) asks about computing the frequency response function (FRF) between a multi-input, multi-output (MIMO) system. First off, the numerical transfer function/FRF between two time domain signals is usually calculated by calculating the cross power spectrum between the two signals and dividing it by the ...


3

It's not just about selecting a level of vibration. There's a lot more that goes into developing a vibration test program that does what you're talking about. There's probably not any one vibration test that will address everything you're looking to do. First, you need to understand the vibration environment that your product will see. Are you only ...


3

Karlo mentioned to use the state space of $[q,\dot{q}]^T$ this allows you to write the system as a first order differential equation of state space. If $X$ were the state space, you could write $\dot{X} = f(X)$. As far as the work you need to do, you write that $$ X = \begin{bmatrix} q\\ \dot{q}\end{bmatrix} $$ the derivative of $\frac{dq}{dt}=\dot{q}$ ...


3

If the gear is not balanced then the center of mass will oscillate as it spins which will induce additional load on the shaft and create vibrations. This effect greatly depends on the speed of the imbalanced gear. If the gear is perfectly balanced then there will be no oscillations. However at extremely high speeds you will need to ensure that the tensile ...


3

This depends greatly on the context. Here is a counter-example, a situation in which the spin velocity of the gear is relevant to the dynamics of the overall system, even if that velocity is constant. That situation is high speed gears on aircraft (e.g. in the engines). At sufficiently high speed, the gear will exhibit the gyroscopic effect. Then when the ...


Only top voted, non community-wiki answers of a minimum length are eligible