彭凡 王樑 肖健
摘 要:研究質(zhì)量時(shí)變系統(tǒng)的動(dòng)態(tài)載荷識(shí)別技術(shù),引入廣義模態(tài)概念,在初瞬時(shí)的模態(tài)空間中利用模態(tài)疊加法得到部分解耦的動(dòng)力學(xué)方程,結(jié)合考慮質(zhì)量變化效應(yīng)的虛擬變形法和Duhamel積分,構(gòu)建反演動(dòng)態(tài)力的2種分析途徑.一種是基于加速度反演的連鎖遞推格式,另一種是基于位移和加速度反演的正則化求解格式.分析2個(gè)動(dòng)載荷作用下的變質(zhì)量多自由度系統(tǒng),利用Euler中點(diǎn)辛差分方法求得系統(tǒng)的響應(yīng),將其疊加隨機(jī)噪聲以模擬測(cè)點(diǎn)響應(yīng),然后,應(yīng)用2種模態(tài)力反求格式反演動(dòng)載荷.研究結(jié)果表明,連鎖遞推格式計(jì)算效率高,但對(duì)加速度測(cè)量噪聲敏感;正則化求解格式的穩(wěn)健性較高.
關(guān)鍵詞:變質(zhì)量;動(dòng)態(tài)載荷;反問(wèn)題;遞歸計(jì)算;正則化
中圖分類號(hào):O326;O347.1 文獻(xiàn)標(biāo)識(shí)碼:A
Abstract:The technique of the load identification of mass variable system was studied. The generalized modal concept applied on time-varying system was introduced, and the method of modal superposition was used to give dynamic equations with partially decoupled in initial modal space defined at initial instant. Based on both virtual distortion method (VDM) accounting for the effect of mass change and the Duhamel integration in initial modal space, two approaches to identify modal forces were constructed: one is the recursive calculation pattern formulated on the basis of modal acceleration, and the other is the regularized solution by the direct discretization of Duhamel integration with modal displacement and acceleration. A mass variable system with 16 degrees of freedom subjected to two external loads was analyzed. The responses were calculated by applying Euler midpoint symplectic difference method and added with random noise to simulate measured signals. Two dynamic loads were identified by two inversion approaches of modal forces. The comparison of results has indicated that regularized solution format has a higher numerical robust than the recursive calculation pattern, but the latter is sensitive to the noise of measurement.
Key words:time-varying mass;dynamic loads;inverse problems; recursive calculation; regularization
許多工程領(lǐng)域存在質(zhì)量等振動(dòng)參數(shù)隨時(shí)間發(fā)生變化的動(dòng)力學(xué)問(wèn)題 [1-5].質(zhì)量時(shí)變系統(tǒng)的動(dòng)力學(xué)響應(yīng)分析方法主要包括2類,一類是直接積分法,包括Newmark法和各類差分算法[6];另一類是基于短時(shí)時(shí)不變假設(shè)的模態(tài)疊加法[7-8].與動(dòng)力響應(yīng)分析相對(duì)應(yīng)的是質(zhì)量時(shí)變振動(dòng)系統(tǒng)的載荷反求,如考慮質(zhì)量快速減少的運(yùn)載工具的脈動(dòng)推力反求,這在工程上也是非常有意義的課題.針對(duì)時(shí)不變結(jié)構(gòu)的動(dòng)態(tài)載荷識(shí)別,已經(jīng)發(fā)展了較為豐富的方法與技術(shù)[9].然而,關(guān)于時(shí)變結(jié)構(gòu)的動(dòng)態(tài)載荷識(shí)別方法的研究還較少,張青霞等[10]將車橋系統(tǒng)視為質(zhì)量時(shí)變系統(tǒng),移動(dòng)荷載的反求轉(zhuǎn)化為移動(dòng)質(zhì)量的識(shí)別,基于虛擬變形法識(shí)別移動(dòng)質(zhì)量.
本文研究質(zhì)量時(shí)變系統(tǒng)載荷識(shí)別方法,在初始模態(tài)空間中,結(jié)合模態(tài)疊加和虛擬變形技術(shù),構(gòu)造模態(tài)力反求格式,經(jīng)模態(tài)轉(zhuǎn)換得到相應(yīng)的物理量.分析變質(zhì)量多自由度系統(tǒng),首先由差分法計(jì)算受激振動(dòng)響應(yīng),將其疊加噪聲以模擬測(cè)量信號(hào),然后,反求模態(tài)力得到動(dòng)載荷,比較2種反求格式的有效性及優(yōu)劣.
1 初始模態(tài)空間中的模態(tài)力計(jì)算格式
1.1 基于初始模態(tài)求解時(shí)變質(zhì)量系統(tǒng)的動(dòng)力學(xué)方程
3 結(jié) 論
在初始模態(tài)空間中建立變質(zhì)量系統(tǒng)動(dòng)載荷識(shí)別途徑.以變質(zhì)量多自由度系統(tǒng)的動(dòng)態(tài)激勵(lì)反演為算例,考察所構(gòu)造的2種模態(tài)力反求格式的穩(wěn)健性和耐噪性.1)利用離散Duhamel積分構(gòu)造的模態(tài)力連鎖遞推計(jì)算僅需加速度測(cè)量信號(hào),且計(jì)算量小,但容易產(chǎn)生誤差累積導(dǎo)致反演結(jié)果對(duì)初值敏感.2)利用位移的Duhamel積分離散進(jìn)行模態(tài)力的正則化求解格式需要位移、加速度測(cè)量信號(hào),穩(wěn)健性較第1種方法強(qiáng),計(jì)算量較大.
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