stjorthotic Chapter 14 Multiscale Perturbation Method
Chapter 14 Multiscale Perturbation Method
Newton released his grip, took a step back, and lingered his gaze on Lu Feng's face for a few seconds.
"Friend, I don't know your name yet."
"Lufeng".
Newton nodded slightly, as if savoring the two syllables.
He then stood up straight, one hand behind his back, in a very formal posture.
"Isaac Newton, it's a pleasure to meet you, Lu Feng."
This self-introduction struck Lu Feng as somewhat absurd.
All of humanity knows you; you don't need to introduce yourself.
Newton turned and walked back to the lab bench, pushing the lenses and mercury trough aside to clear a blank space on the table.
He spread out the draft paper filled with formulas, smoothed out the wrinkles with his palm, then leaned against the edge of the table, looking at Lu Feng.
"I don't know what's going on with this space, and I can sense that there's another being in this space who's no less powerful than me."
He spoke calmly, without any confusion or fear in his tone.
"The fact that I am here means that I have a reason to exist here."
Lu Feng didn't respond, waiting for him to continue.
Newton looked up, his gaze piercing through the white void, as if looking at something distant.
"Everyone who comes into this world carries their own mission. Some people's mission is to plant a tree, some people's mission is to build a bridge, and some people's mission is to light a lamp so that those who come after them will not have to walk in the dark."
He turned his gaze back to Lu Feng.
"I've accomplished most of my mission, but this one part remains."
He tapped the draft paper on the table with his finger.
"It means walking alongside you and progressing together."
Let's make progress together.
When Newton uttered those four words, they carried a weight so heavy they could shatter the floor.
Lu Feng clenched his fist, and that surge of heat in his chest rose again.
Standing before him now is the brightest star in the history of human science.
"Then let's work together." Lu Feng's voice wasn't loud, but it was steady.
Newton smiled.
This was the first time Lu Feng had seen him smile, not the kind of polite social smile, but a genuine smile from the heart.
"No problem. You're welcome to come see me anytime. We can talk anytime, right?"
After he finished speaking, he picked up another apple from the fruit plate, and this time he didn't throw it away, but took a bite himself.
Lu Feng remembered that the system notification mentioned that the "external chat" mode allowed for both text and voice communication.
In other words, he doesn't need to enter this inner space every time; he can just send a message if he has any questions.
If you need to conduct experiments or have problems that can't be solved by chatting, you can come in and find Newton.
"Then I'll head back now, Sir."
Newton waved his hand, still chewing on an apple, and mumbled something, probably meaning "Go."
Lu Feng silently told himself to quit.
The white space quickly faded, and the library's bookshelves, fluorescent lights, and the darkening sky outside the window came back into view.
He is back.
The draft paper on the table was still lying there, the pen was still between his fingers, and everything around him remained unchanged.
Lu Feng let out a long breath and leaned back in his chair.
Cool.
That's fucking awesome.
This feeling isn't about how much money you've earned or what promotion you've received.
It's a sense of security, like standing on the shoulders of giants.
Before he could think about it, the system's chat interface popped up automatically.
A new message.
Sender: Isaac Newton.
Lu Feng clicked on it.
It's an emoji.
A cartoon version of Newton sits under an apple tree, getting hit on the head by an apple, with the caption: "Time to get to work."
Lu Feng was completely stunned.
Emojis?
Would Newton use emojis?
He stared at the cartoon version of Newton for three seconds, his lips twitching uncontrollably.
Is this system for real?
He replied with an emoji and a thumbs-up.
He himself thought it was outrageous after posting it.
A scientific giant from over 300 years ago exchanging emojis with him in a chat interface—if this scene were included in a history textbook, it would send physics teachers all over the world packing.
And that's enough for Lu Feng to brag about for a lifetime.
The system notification sounded the instant he closed the chat window.
[Congratulations, host, on gaining the approval of a powerful figure!]
[Gain exclusive ability: Newton's Observational Skills]
[Ability Effect: Careful observation of anything will reveal its profound mysteries. It greatly enhances insight into physical phenomena, mechanical structures, and mathematical relationships.]
Lu Feng's fingers tightened slightly.
He had previously seen in the system description that if he gained the approval or guidance of a powerful figure, he could acquire exclusive abilities belonging to that figure.
Just now in the inner space, he helped Newton break through the barrier of wave-particle duality, and Newton gave him sincere thanks and recognition.
This recognition has been transformed into a permanent skill.
Observational skills.
The ability to see what others cannot is the true core competitiveness.
Lu Feng took a deep breath and opened the system panel.
Current learning value: 1050
Current mood score: 50
Summoning Newton cost 10,000 learning points and 1,000 emotion points, leaving just over 1,000 learning points remaining.
1050.
It costs 1000 to exchange for a high-tech blueprint.
enough.
Lu Feng didn't hesitate and directly opened the store.
[High-Tech Blueprint Exchange (1000 Learning Points/time)]
[Confirm redemption after consuming 1000 learning points?]
confirm.
The learning value jumped from 1050 to 50. Golden light shone again in the center of the panel, and a semi-transparent blue-background drawing emerged from the light.
This drawing is smaller than the previous one, about A4 size, but the content is denser.
The moment the title appeared in his eyes, Lu Feng paused for a moment.
[Multi-scale perturbation solution method for nonlinear structural dynamics and its engineering application in complex mechanical systems]
Multi-scale perturbation method.
I know Lufeng very well.
When encountering complex nonlinear vibration problems, this method is almost always the way to go.
However, the perturbation method has a very high mathematical threshold. It requires expanding the original equation into multiple levels according to small parameters, with each level corresponding to a different time scale, and then solving the secular term layer by layer.
He had studied it on his own in his previous life, but he was always stuck on the step of "eliminating duration terms".
Every time I push it to that point, it gets burnt. I don't know how to choose the right slow time scale.
The first part directly presents a general framework for multi-scale expansion, a standardized process that can handle any N-degree-of-freedom nonlinear system.
The second part is the core, which uses matrix perturbation theory to systematize the process of eliminating secular terms and provides a criterion that can directly determine how many slow time scales should be introduced and what the equations at each scale should look like.
The third part is an engineering application example, which applies this method to a gear and bearing coupled system with clearance and dry friction, and solves for the steady-state response and bifurcation characteristics of the system.
The fourth part is the interface design with the finite element method, which provides a hybrid solution strategy that injects the analytical solution of the perturbation method as the initial value into the numerical simulation.
Lu Feng became more and more excited as he looked at it.
This drawing is completely complementary to the previous one.
The previous paper solved the constitutive equation problem at the material level, and this paper solves the dynamic response problem at the structural level.
The two drawings, when put together, cover almost everything from materials to structure.
More importantly, the example of the gear-bearing coupling system in Part Three is a perfect match for the multi-stage gear transmission system studied in Li Hongde's project.