You can, but you have to live with the consequences.
There are several things that can happen: Depending on the vertical gusts ahead, you might not even get close to v$_{NE}$. There is another speed limit for gusty weather called v$_B$ , and exceeding this will run the risk of overstressing the wing structure.
Going above v$_B$ will overstress the wings in a gust of more than 50 ft/s, and more than 25 ft/s
when flying above v$_D$.
The exact values can be found in the flight envelope diagram of the flight manual.
On a calm day, you can fly v$_{NE}$ and even a little faster, but once you fly fast enough, flutter will become very likely.
Note that flutter needs some initial excitation , so you might fly well into the flutter speed range before flutter occurs.
When it does, control surfaces will be ripped from their fittings which will make the aircraft pitch up.
At that point the wings will break off.
The engine on a C 172 is not powerful enough to sustain level flight at v$_{NE}$. You need to dive the aircraft, which requires some altitude.
Maintaining the speed will mean that you dive into the ground, so you need to pull out of the dive in time.
On really fast aircraft the pitch trim will get more nose-heavy when the aircraft approaches the speed of sound.
You don't run that risk in a C 172, but faster aircraft found themselves locked into a dive which they could not end .
aviation.stackexchange.com/users/1961/Peter Kämpf
You can exceed the never exceed speed $V_{NE}$, but doing so will most likely result in damage to the structure.
From FAA handbook of pilot knowledge : $V_{NE}$ —the speed which should never be exceeded.
If flight is attempted above this speed, structural damage or structural failure may result.
aviation.stackexchange.com/users/9731/aeroalias
Because above that airspeed, the airframe is increasingly likely to fail.
Failure would likely start with control surfaces like the ailerons, elevator and flaps, then the wings and tail are likely to separate, resulting in total catastrophic failure.
aviation.stackexchange.com/users/43/abelenky
Think of $V_{NE}$ as the speed at or beyond which the structural integrity of the airframe is not guaranteed.
In other words, parts of the airframe - which is critical for controlled flight cannot be guaranteed to perform as designed.
aviation.stackexchange.com/users/1049/Burhan Khalid
There are both aerodynamic and structural reasons for Vne.
Aircraft controllability is impacted (for specific impacts on a specific make and model, consult with the manufacturer and perhaps they will share their findings from testing) and you may encounter difficulties with control authority (your ability to move control surfaces), airflow (e.g. the Clark-Y airfoil is designed for its lifting capability far more than it is designed for speed), and you may exceed the structural limits of aircraft components (control surfaces, wing spars, windshield, landing gear.)
Operating above Vne now places you in the role of de-facto test pilot and any damage you cause to your aircraft may manifest itself that same flight or many hours later when the results of stresses you induced on the airframe or cables, pulleys etc.
cause a failure of the aircraft structure.
aviation.stackexchange.com/users/33426/Taurus69
The answer depends on how much you exceed V_ne.
I do not have the information for this particular aircraft in front of me, so I can not say what will happen at a specific airspeed.
Cessna spent a lot of money and time on engineering and flight testing to come up with the maximum airspeed (V_ne).
There is a safety factor built in to this calculated and tested speed.
One situation is flying level at a high altitude, then go in to a steep dive.
This may cause an overspeed condition.
One of the first problems as a result of overspeed, will start out as a vibration of control surfaces and controls.
The chance for loss of control by the pilot due to mechanical failure or metal fatigue will increase exponentially, as does the airspeed.
The C172 has airfoil designs meant for low speed.
Depending on the exact plane and loading this could differ slightly, but the stall speed is 49 KIAS.
With its straight, high lift wing structure, the airfoil may actually completely loose its lift at a very high airspeed.
As the airspeed increases, farther above the V_ne, the craft will basically start to tear apart and disintegrate.
aviation.stackexchange.com/users/13886/user13886
As stated in another response the stock engine in a C172 isn't powerful enough to sustain Vne in horizontal flight.
Establishment of the various speeds is part of the aircraft certification process and usually includes a safety margin of 10 to 15 percent and there are many factors that go into determining these numbers.
For example, I have a Beachcraft Baron and one of the important speeds is Vr or V Rotate.
It's not that the aircraft cannot take off at a slower speed
it's just that if you have a critical engine failure at takeoff power and a slower speed you don't have enough control authority to compensate.
There are many factors that go into determining these numbers and structural integrity
is just one of them.
aviation.stackexchange.com/users/13910/ChuckIvie
To add to previous answers, Vne is usually set at near ideal conditions, therefore the 10% - 15% mentioned above really becomes nothing if there are air pockets or other phenomena usually not meaningful, let alone minor fatigue or skin imperfections, hence, as the name implies, never exceed this speed with standard issue airplanes.
aviation.stackexchange.com/users/33419/Daniel Treves
The airspeed indicator has a red marking that means: "never exceed this speed" ($V_{NE}$, around 160 KIAS). Why can't you exceed that speed?
What happens if you exceed the maximum speed on a C172?
aviation.stackexchange.com
<aircraft-performance><airspeed><cessna-172>
aviation.stackexchange.com/questions/25861
aviation.stackexchange.com/users/13197/kepler22b
Although the never exceed speed can be exceeded, it would result in damage to the structure. It would also lead to the aircraft becoming more difficult to control. Exceeding this speed is likely to cause structural damage or even failure of the airframe and may impact the ability to control the aircraft.
Exceeding this speed is likely to cause structural damage or even failure of the airframe.  Exceeding this speed may impact the ability to control the aircraft.