相关实验视频
Updated: Jun 21, 2025

08:12
Experimental Methods to Study Human Postural Control
Published on: September 11, 2019
9.4K
在参数共振下非线性机械系统的模型还原的非自主光谱次元组
Thomas Thurnher1, George Haller1, Shobhit Jain2
1Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland.
Chaos (Woodbury, N.Y.)
|July 12, 2024
概括
频谱次元组 (SSM) 简化了非线性机械系统的缩小. 这项工作开发了复杂刺激的高级SSM参数化和减少动态,使得高效的共振分析和响应计算成为可能.
科学领域:
- 非线性动力学是一种非线性动力学.
- 机械系统工程 机械系统工程
- 计算力学是计算力学.
背景情况:
- 模型缩小对于分析复杂的非线性机械系统至关重要.
- 参数和外部激发在系统动态中带来了重大挑战.
- 频谱次数组 (SSM) 为模型缩小提供了一个有前途的理论框架.
研究的目的:
- 为非线性机械系统的模型还原扩展光谱次元组 (SSM) 理论.
- 为周期性和准周期性激发下的系统开发更高阶的非自主术语和减少的动态.
- 为分析共振现象和计算强制反应提供实用方法.
主要方法:
- 频谱亚多元 (SSM) 理论应用于一级和二级机械系统.
- 开发基于多指数的参数化,以优化计算效率.
- 在二维SSM中制定用于稳态响应计算的显式表达式.
- 使用SSM提取共振舌头并分析强制反应.
主要成果:
- 在SSM参数化和降低动态中获得更高阶非自主项的表达式.
- 介绍了第二阶动态系统中SSM参数化的理论简化.
- 在SSM上减少的动态有效地提取了共振舌头和强制反应.
- 为具有外部和参数激发的系统实现了稳定状态响应的并行计算.
结论:
- 扩展的SSM理论为复杂的非线性机械系统的模型缩小和分析提供了一个强大的工具.
- 开发的方法可以有效地提取像共振舌头这样的关键动态特征.
- 开源的SSMTool促进了这些先进的模型缩减技术的实际应用.
相关概念视频
Linear Approximation in Time Domain
81
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
81
Linear Approximation in Frequency Domain
89
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
89
Mechanical Systems
190
Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically...
190
One-Degree-of-Freedom System
481
In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
481
Forced Oscillations
6.5K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.5K
Damped Oscillations
5.7K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
5.7K

