Analysis of Stationary Impact Vibration in Continuous System with Asymmetrical Hysteresis Loop Characteristics(Mechanical Systems)

Abstract

A． na 且 ysis of Stationary Impact Vibration 蓋 n Continuous System with Asymmetr 畫 ca 翌 Hyste 野esis Loop Characteristics Shigeru AOKI ＊ ： i and Yasun 〔 〕ri SAKAI 潤 Dep 乱 rtment Df Mechai 玉icai EngineerinR ， Tokyo Me 亡ropDlitan UolleRe of llldustrial Technc ♪k♪ g｝ ， 1 10 401Jigrashi Ghi， Sllinagawa − k11， Tokyo 、 141〕 一 〔 1〔) 11Japa ロ Th ［ s paper deals with impact vibratiOll ill beam system excited by peri｛｝dic displacement with cosine functien ． The analy し ica］ tnodcl is steady impac 匸 vihration foll a cantilex ・ er l ，eam ． The beam collides elasUcaUy t〔 ＞ clampcd stcel of unsyrnmetri (二 faces at an i ， rbit ． rf i ・ y puint of sl，an ， Tri巳d tQ aiia ！ yze by applying the Fourier series meth (，d for this systeln with ass し lming force of restitution has atriangle hysteresis loop characteristics ． For verification of the analytict ｛］rneth 〔〕 d， experiments are performed ． The analytical results arc 〒 n n fairly g ｛ ｝〔 ，d agreement with the experimental ones ． After that tried to analyze the illfinltesjlll ， al stabilities for the approximate solution b｝ ・ Fourier series method by applying var ｛ ation equatioll ． As the result ， experimenta ［ result appear at the stable s 〔 ⊃ lution region il ／ the analytica ｝solution ． Key rVords ： Nonlinear Vibration， Collision Vib ［ ' ation ， Vibration of Corltilluous S｝s し om ， へTethod of Vibratioil Anaiysis， Stability ， F 〔 ｝ rced Vibration ， Hyst ピr ビ sis Damping ， Approx ［ mate Solution ， Steady − State Respol／se

Nonlinear Vibration Analysis for a Simply Supported Beam Elastically Colliding with Clamped Springs at Arbitrary Locations

“…The nonlinear simultaneous equations derived by harmonic balance were solved by using a Newton-Raphson iteration method, and periodic solutions were calculated. Studies on collision vibrations of continuous systems include analyses by Watanabe [2], Shaw [3], Aoki [4] and Brake [5] of the responses under single harmonic excitation. However, seismic design of chemical plant structures such as piping systems must consider not only single periodic excitation.…”