Nonsmooth modal analysis of complex mechanical structures

复杂机械结构的非光滑模态分析

• 批准号: RGPIN-2018-04497
• 负责人: Legrand, Mathias
• 金额: $ 2.84万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=687399
• 关键词: Nonsmooth; modal; analysis; complex; mechanical

In structural dynamics, sustained vibration occurrences may lead to fatigue mechanisms and component failures. The vibration analysis of systems involving nonlinear terms that are smooth functions of the unknowns (displacement and velocity) has recently made convincing advances. However, this is far from being true for systems undergoing unilateral contact conditions on their boundary. The objective of this research program is to provide improved modeling, understanding, and prediction of the vibratory responses of complex mechanical structures prone to unilateral contact conditions. In the framework of continuum mechanics, such analysis is currently unavailable or incomplete as the appropriate numerical tools are missing. This is explained by the fact that solutions are expected to take the form of travelling shock waves which are challenging to capture numerically.******The proposed research program will be accomplished by developing innovative numerical methods capable of efficiently tackling the ever-growing complexities in the dynamic responses of nonsmooth mechanical systems. It is designed to address vibration, fatigue and failure issues by systematically identifying potential vibratory resonance occurrences in a unified framework called "Nonsmooth Modal Analysis". This method searches for continuous families of periodic solutions of conservative autonomous nonsmooth mechanical systems in the vicinity of which vibratory resonances commonly arise. To this end, the proposed Discovery Grant application will focus on two major items:***1) Simplified one-dimensional systems in space will be considered such as (1) a simple bar with one end in contact with a rigid foundation, (2) two contacting bars sharing a common unilateral contact interface, and (3) one bar with large distortion terms combining polynomial and nonsmooth nonlinearities within the formulation.***2) Nonsmooth Modal Analysis will be developed to tackle mechanical systems in three dimensions with the assumption of linear elasticity. The numerical implementation will be grounded on a higher-dimensional version of the Time-Domain Boundary Element Method and Finite Volumes schemes which enjoy highly appealing features when progressive waves are targeted. A chattering-free and energy-preserving Finite Element technique will also be developed.******The long-term goal of this research program is to provide efficient numerical solution methods able to help engineers in their endeavour to design always more efficient and safer mechanical systems operating in possibly hostile unilateral and nonsmooth conditions. Aerospace industrial systems will serve as preferred applications. A very important example is the design of blades inevitably prone to contact occurrences with surrounding casings in modern turbomachines. Such blades should safely function away from nonlinear vibratory resonance conditions.

在结构动力学中，持续的振动可能会导致疲劳机制和部件故障。涉及非线性项（未知数（位移和速度）的平滑函数）的系统振动分析最近取得了令人信服的进展。然而，对于边界上经历单侧接触条件的系统来说，情况远非如此。该研究项目的目标是改进对容易出现单侧接触条件的复杂机械结构的振动响应的建模、理解和预测。在连续介质力学的框架中，由于缺少适当的数值工具，这种分析目前不可用或不完整。这是因为解决方案预计采用行进冲击波的形式，而行进冲击波的数值捕获具有挑战性。******所提出的研究计划将通过开发创新的数值方法来完成，该方法能够有效地解决非光滑机械系统动态响应中日益增长的复杂性。它旨在通过在称为“非平滑模态分析”的统一框架中系统地识别潜在的振动共振发生来解决振动、疲劳和故障问题。该方法搜索保守自主非光滑机械系统的连续周期解族，在该系统附近通常会出现振动共振。为此，拟议的发现补助金申请将重点关注两个主要项目：***1）将考虑空间中的简化一维系统，例如（1）一端与刚性基础接触的简单杆，（2）共享公共单边接触界面的两个接触杆，以及（3）一个具有大畸变项的杆，结合了公式中的多项式和非平滑非线性。***2）非平滑模态分析将是 开发用于在线性弹性假设的情况下处理三维机械系统。数值实现将基于时域边界元法和有限体积方案的高维版本，当针对行进波时，这些方案具有非常吸引人的功能。还将开发一种无颤振且节能的有限元技术。******该研究计划的长期目标是提供有效的数值求解方法，能够帮助工程师努力设计在可能不利的单边和非光滑条件下运行的更高效、更安全的机械系统。航空航天工业系统将作为首选应用。一个非常重要的例子是现代涡轮机中叶片的设计不可避免地容易与周围的壳体发生接触。此类叶片应在远离非线性振动共振条件的情况下安全运行。