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

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 ...


4

The frequency and ground acceleration and other pertinent data are recorded in a seismic design espectra which is unique for each site and varies with the type of the soil on the side. Usually building department will have that information. For example the following is the link to Los Angeles building department site for design espectra. https://data2.scec....


3

First, can you really actuate white noise? If yes, White noise would probably show many natural frequencies and harmonics. However, make sure the actuation bandwidth is sufficient for your frequency range. If the piezo can be adjusted to your frequencies of interest, a more deterministic approach would be to do a frequency sweep. For that, start from the ...


2

A 3Hz pulsating hum-- noise that is getting louder and softer at 3Hz. Yes, I agree that would be quite annoying. Since this is a residential unit in the US, both the compressor and the fan are run with single phase asynchronous motors. Almost certainly, they are four pole with an 1800 RPM synchronous speed, running about 1750 RPM or so, depending upon ...


2

k=F/d is a linear relationship. If you're doing a non-linear analysis, you shouldn't expect a linear response. For this beam, a geometrically non-linear analysis is appropriate if your deflections are any way significant. This is because a downwards load (if it is big enough) will cause snap-through buckling behaviour, whereas an upwards load will not. ...


2

This is the only place on the internet that I could find that actually gave decent resolution images for tripartite plotting paper. However, it had some limits that affected use in our area: 1) the design earthquakes top out in our area at about 1g and 2) we generally are only concerned with periods between 0.01s and 10s, or 0.1 Hz to 100 Hz. This resulted ...


2

You can try running the following R script which produces the figure below. require(ggplot2) require(data.table) # The constant value grid lines freqs = unique(c(seq(0.1, 0.2, by = 0.05), seq(0.2, 1.0, by = 0.1), seq(1.0, 2.0, by = 0.50), seq(2.0, 10.0, by = 1.0), seq(10.0, 20.0, by = 5.0), seq(20.0, 100.0, by = 10.0), seq(100.0, 200.0, ...


2

The most basic purpose of the measurements is system identification - i.e. to determine the modal frequencies, mode shapes, and damping factors for the modes in some frequency range. You can use that information for many different purposes. If you measure it in sufficient detail, you can construct a mathematical model of the structure that can be used in ...


2

Typically you are not doing modal analysis for its own sake. Typically you have a problem and you are using modal analysis as a tool to solve that problem. The goal of the modal analysis will depend on what exactly your problem is. Here are some examples 1) You have a part which is exposed to vibration, and is failing (cracking) due to high cycle fatigue. ...


2

"Multiplicity" usually refers to several different modes with the same natural frequency. For example, ignoring any fault conditions and tolerances, if there are several identical planet gears, each one will have the same mode shapes and frequencies. If you are measuring the vibration response, you may not be able to distinguish these modes - you will ...


2

It depends on what your data looks like. I recently got some accelerometer data that looked like this after running it through Python's Scipy fft function: The results are pretty straightforward- natural frequency at about 5.5 Hz. In that particular case, the analysis was basically trivial- 20 lines of python, most of which was importing and plotting. If ...


2

Regarding the different state space formulations. First, M might not be invertible. In many cases it will be invertible, but sometimes it will not be. In your specific case, this would correspond to a gear with zero mass. Obviously that never happens in the real world as all gears would have some finite mass. But there are situations, where the modeling ...


2

For any sinusoidal motion, the $\mathbf{q}$ really represents the motion $\Re(\mathbf{q}\,e^{i \omega t})$ in the time domain. $\mathbf{q}$ is complex because in general, the different elements of the eigenvector have different phase angles. This will be the case for your problem since your first equation seems to contain a gyroscopic term - if the ...


2

If your structure was literally hung on a piece of (plastic covered) wire then it was constrained vertically, at that point, by the wire. A better method is to hang it from a soft bungee cord, so its natural frequency of vibration as a "mass on a spring" moving vertically is a factor of 10 (or more) lower than the frequencies you are interested in measuring....


2

You can't make much use of just one FRF, especially if none of the peak responses line up between the model and the test. Fix the accelerometer at the position of one of your model DOFs and then impact the model at all 12 DOF positions (in the correct directions, of course). Move the accelerometer to the other DOF positions in turn, and repeat. You ...


2

I assume you will be doing this in a software, matlab or Abaqus for example, it’s not particularly easy thing to do with your given info, but. Perhaps this example method will help Abaqus Infos at csiamerica Matlab function I am unsure how directly your data types will fit, but these are some links to get you started


1

The gain and phase margins of a system are characteristics that can be obtained by studying one of the following well-known plots: Nyquist Plot, Bode Plot, Nichols Chart, Disk Margin which gives details in a different way (may be others that I'm not aware of). I will address the issue of your question by using the bode plot tool. When looking into a bode ...


1

Natural frequencies depend upon stiffness and mass. These two properties depend on the material characteristics and geometric configurations. In general: Increasing stiffness, the natural frequencies are increased Increasing mass, the natural frequencies are reduced With geometry things are a bit different. Because it will depend how you distribute mass ...


1

We know for undamped harmonic vibration $\omega= angular velocity \space, L=length of brick \ , m=mass \ , \\ I= \text{second moment of area of the brick section } \ , \ h= \text{the height of the brick section} $ $ \omega = \sqrt {k/m }$ And $ k=I/L $ $ I =bh^3/12$ So everything else being equal the thicker brick will have larger " I " hence larger ...


1

In response spectrum analysis of MDOF structures, the most common methods of modal combination are: absolute sum (assume the peak response of all modes occurs simultaneously) SRSS (square root of the sum of the squares) CQC (complete quadratic combination) If what you're aiming for is a pencil-and-paper check of the software output, the first two methods ...


1

The code in your OP seems to be for a 2 DOF system not a 24 DOF system. You could check that by printing the "frequencies" variable from your eigensolution. The reason you are not getting anti-resonances is because you are taking the absolute values in the wrong place. You should be calculating $$X(\omega) = \left|\sum_n \frac{F/M}{\omega_n^2 - \omega^2}\...


1

You basically want to solve for the homogeneous solutions of the system $$ \textbf{M}\, \ddot{\textbf{q}} + \textbf{D}\, \dot{\textbf{q}} + \textbf{K}\, \textbf{q} = \textbf{0}. $$ It can be shown that each solution will be of the form $$ \textbf{q}_i(t) = \textbf{u}_i\,e^{\mu_i\,t}, $$ where $\textbf{u}_i$ is a vector of the same dimension as $\textbf{q}...


1

Some large buildings have a transformer attached to them for the mains supply for all apartments. The vibrations are probably being transmitted via harmonic resonance due to acoustic amplification. This may have been why previous owners sold the property. Human body operates at 25Hz which means harmonic octave frequencies are more noticeable to us. It may ...


1

You said you applied a constant displacement to the base. In that situation, if the structure doesn't have any modes that can are excited at a particular frequency, the response is going to be approximately the same as a rigid body being moved with a fixed amplitude, which is what your plot shows. Note that if you apply a fixed displacement, the excitation ...


1

If a MIMO plant is upper or lower triangular then one can't create an interaction loop which might make the system unstable. So using stabilizing SISO feedback control for each diagonal term should stabilize the system. Therefore from a stability standpoint decoupling would not be necessary. That being said, if reference is not the equilibrium point then ...


1

I'm unsure about the magnitude of the change, but providing tension by preloading an object definitely alters the natural frequency. It is commonly adopted to avoid resonance from external disruptions. I have seen the idea adopted with shafts, but in a single lap joint like your example I can't imagine the affect is very big, as you observed. When ...


1

Are you looking for a single number for one particular beam, or a closed form solution for any possible combination of dimensions? If the former, the easiest will be ANSYS (or Abaqus or NASTRAN or any other commercial FEA software). Model the two different beams as shell elements. With shell elements you can use a single layer for each sub-beam. With ...


1

This question is rather confused, but I'll take it as "Can AC power be produced from DC power without mechanically moving parts". Of course. That's what devices called "inverters" do. Most inverters are designed to work at a single frequency, but they certainly don't have to be. Think of class D amplifiers as examples. Clearly they can produce a wide ...


1

I've done this before. I had to be pretty careful to generate the FRF. It helped me to know the input (force vs. time) and the output (acceleration vs. time). I have done it without knowing the input. I typically plot the FFT using a logarithmic scale. When you know the input, you divide the output by the input (in the frequency domain) and the peaks ...


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