As you understand from the title, it will be about permanent vibration. Unfortunately, this problem is being addressed very rarely. There is a minimal amount of car repair specialists who evaluate the performance of the cylinders. Increased vibration of the petrol engines, their users are tolerating well (especially, when changing from the diesel engine car), because these engines subjectively are much less pronounced even by quite a large cylinder disbalance. More often, we hear about increased vibration for the diesel engines (due to the more “sharp” process of burning this fuel can be felt more sharply – with all body), then usually “specialists” get to the gearbox and engine cushions. Yes, such a “solution” method fails essentially. Why?
In the following example, I will describe the performance of 6-cylinders engine. It is, of course, similar to 4-cylinder, 3-cylinder, and other configuration engines, so I will not describe them separately.
In this picture – the correct performance of the engine. Mechanical work (energy) of each cylinder pictured (Y-axis); on the X-axis – time.

Of course, in this picture, the contribution of the cylinders is pictured simplified. Curves of the mechanical energy are not so pretty; for example, for the petrol engines, curves of the developed power are with a more “rounded” peak range, for the diesel engines – with “sharper” peaks. Depending on the engine/type/generation, this mechanical energy for the 6-cylinder engines can slightly overlap. Such overlapping is not possible for 3 and 4-cylinder engines, but for 8-cylinder engines, it is very pronounced. This image (the current/above one and the following) illustrates the principle.
This image shows how the correctly looking mechanical energy (in time) looks if the flywheel is attached to it (curve 1).

Flywheel evens out the pulsations of the mechanical energy. When any of the cylinders is performing a mechanical job, the Increment wheel (flywheel) receives (accumulates) energy, and when (generated) mechanical energy is reduced, it gives accumulated energy it to the load.
In this image, the contribution of the single mass (1 – higher vibrations) and double mass (2 – less vibrations) flywheel is compared.

Single mass flywheel is a Low-pass mechanical filter of the second order, which means – in a range of effective performance, it suppresses pulsations 4 times more effectively by increasing the pulsation frequency by 2 times. Twin mass flywheel creates 3rd or 4th order filter, ensuring a more compelling impression of the cylinder energy.

Let’s calculate the frequency of these pulsations.
At idle, the engine works with around 600 RPM, which means: the rotation frequency of the crankshaft is 600/60=10 turns/second.
Each cylinder performs the combustion cycle on every second turn, so each cylinder performs the job 10/2 = 5 times per second. Accordingly, the 6-cylinder engine cylinders create a combustion cycle of 5*6 = 30 times/per second. So – 30 times per second, any of the cylinders give mechanical energy to the crankshaft.
Pay attention to this number: 30. This frequency is high enough! A human can hear this frequency (a human hears frequencies above 20 Hz) and feels it as a “tingling”, not a pronounced vibration.
The cause of pronounced low vibration is different!

So looks like the engine, whose some of the cylinders work with more considerable mechanical energy.

Possible reasons for such a situation:
a. leaking injector;
b. incorrectly encoded injector;
c. unmeasured or poorly measured injector;

d. other issues which result in unmeasured injectors and/or non-equalized their performance (issues with all possible systems; including chip tuning, etc.).

The cylinder will also create identical problems, whose mechanical efficiency is reduced. Reasons for such problems could be:
a. incorrectly encoded injector;
b. unmeasured or incorrectly measured injector;
c. reduced air amount in the combustion chamber (for the engines equipped with Valvetronic);
d. mechanical problems (increased losses/leaks of the piston group);
e. poor atomization of the injected fuel, incorrect beam (more pronounced in diesel engines, for the petrol engines – in Stratified charge);

f. other issues which result in unmeasured injectors and/or non-equalized their performance (issues with all possible systems; including chip tuning, etc.).

In turn, taking into account the impact of the flywheel, the total mechanical energy developed by the engine (bottom curve) in this problematic case looks as follows:

In the image, we see:
a. 30 times per second (upper curve), one of the cylinders is performing a mechanical job. Frequency of these pulsations – 30 vibrations per second;
b. Increment wheel (bottom curve) also pulsated the lower frequency: 5 times per second, the Increment wheel speeds up and slows down.

Remember some more basic connections of the mechanics:
a. the engine with its mass also creates 2nd order Low-pass mechanical filter;
b. any changes in the turning speed (energy) of the crankshaft are creating precisely the same, opposite changes in the applied force for the engine. The crankshaft turns in one direction, and the engine “tries” to turn in the opposite direction. The same is with changes in the turning/force – these have equal force for the crankshaft and the engine, aimed in the opposite directions.

These low frequencies (in this case: 5 fluctuations per second) humans perceive as vibration. Everything is vibrating – the body of the car, the interior. In addition, these vibrations are not really suppressed by the flywheel. Why? As I already mentioned before, the flywheel creates a Low-pass filter; the efficiency of this filter increases when the frequency of vibration grows. Instead, the lower the vibration frequency, the worst the ability of the flywheel to suppress them. The efficiency of the single-mass flywheel is theoretically decreasing (if frequency of vibrations decreasing 6 times) for around 36 times; the twin-mass flywheel efficiency drops even more dramatically! These vibrations really are not suppressed by the engine itself. Its ability (as a Low-pass filter) as the “accumulator” of the mechanical energy also is swiftly reduced when the frequency of the vibrations is lowered.

Here, one more image – the mechanical efficiency of two (not consecutive) cylinders are different from the ideal.

In this example, the engine’s vibrations will be 3 (6/2) times lower than the “basic frequency” of the cylinder performance, or 30/3 = 10 fluctuations per second. This vibration is “finer” (and also more arithmetic) than in the previous case, but these also are NOT consequences of the correct performance of the engine!
For a long time, both DME and DDE have been evening out the mechanical efficiency of cylinders. A long time ago, such an evening was performed only in idle, but in all driving conditions this feature is available for the last 20+ years. Accordingly – if increased vibration can be felt, the engine cushions are not the ones to replace, but you have to determine which cylinder(s) is/are working with incorrect mechanical efficiency. Obviously, for some reason, DME/DDE has not managed to even out the contribution of all cylinders in the total benefit.