The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear...The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.展开更多
BACKGROUND: Auditory steady-state evoked response (ASSR) is one of the new objective electrophysiological methods to test hearing in infants. It can provide a reliable and complete audiogram with specific frequency to...BACKGROUND: Auditory steady-state evoked response (ASSR) is one of the new objective electrophysiological methods to test hearing in infants. It can provide a reliable and complete audiogram with specific frequency to help the hearing diagnosis and rehabilitation of hearing and languaging following auditory screening. OBJECTIVE: To compare the response threshold of ASSR with auditory threshold of visual reinforcement audiometry (VRA) in infants failed in the hearing screening for investigating their hearing loss. DESIGN: A comparative observation. SETTINGS: Maternal and child health care hospitals of Guangdong province, Shunde city, Nanhai city and Huadu district. PARTICIPANTS: Totally 321 infants of 0-3 years undergoing ASSR test were selected from the Hearing Center of Guangdong Maternal and Child Health Care Hospital from January 2002 to December 2004. Informed consents were obtained from their guardians. There were 193 cases (60.2%) of 0-6 months, 31 cases (9.7%) of 7-12 months, 17 cases (5.3%) of 13-18 months, 14 cases (4.4%) of 19-24 months, 33 cases of 25-30 months, and 33 cases (10.2%) of 31-36 months. METHODS: ① The 321 infants failed in the hearing screening were tested under sleeping status, the ranges of response threshold distribution in ASSR of different frequencies were analyzed in each age group. ② The infants above 2 years old were also tested with VRA, and their response thresholds were compared between VRA and ASSR. ③ Evaluative standards: The response threshold was < 30 dB for normal hearing, 31-50 dB for mild hearing loss, 51-70 dB for moderate hearing loss, 71-90 dB for severe hearing loss, and > 91 dB for extremely severe hearing loss. MAIN OUTCOME MEASURES: ① ASSR results of the infants failed in the screening; ② Proportion of cases of each response threshold in each age group; ③ Comparison of ASSR response thresholds and VRA auditory thresholds in the infants of 2-3 years old. RESULTS: ①The response threshold was < 30 dB in 47.4% of the 321 infants failed in the initial hearing screening and secondary screening after 42 days. ② Severe to extremely severe hearing loss was detected in only 16 cases (8.3%) of the 193 infants of 0-6 months, in 9 cases (27.3%) of the 33 infants of 25-30 months, and 13 cases (39.4%) of the 33 infants of 31-36 months. Of the 193 infants of 0-6 months old who failed in the initial screening and the second screening after 42 days, the ASSR auditory threshold was < 30 dB in 97 cases (50.26%), 31-50 dB in 63 cases (32.6%), 51-70 dB in 17 cases (8.8%), 71-90 dB in 7 cases (3.6%), and > 91 dB in 9 cases (4.7%). ③ Among the 321 infants failed in the screening, the auditory threshold in the 6 age groups was < 30 dB in 47.4%, 31-50 dB in 27.1%, 51-70 dB in 8.4%, 71-90 dB in 6.2%, and > 91 dB in 10.9%. ④ The difference between ASSR response threshold and VRA auditory thresholds was 6-18 dB in the normal hearing group, mild and moderate hearing loss groups, and there was high correlation between them. The difference of ASSR and VRA thresholds was less than 5 dB between extremely severe and severe hearing loss groups, 5-13 dB between extremely severe and moderate-to-severe hearing loss groups (P < 0.05), and there was no significant differences between severe and moderate-to-severe hearing loss groups (P > 0.05). CONCLUSION: ① The hearing was normal in about half of the infants, although they failed in the primary screening and secondary screening. ② The proportion of the severity of hearing loss was increased along with aging. ③ Mild and moderate hearing losses are dominant in infants. ④ ASSR is reliable to evaluate the hearing of infants.展开更多
文摘The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
基金a grant from Medical Scientific Research Foundation of G uangdong Bureau of Hygiene,No.W STJJ2001111044082219581224001
文摘BACKGROUND: Auditory steady-state evoked response (ASSR) is one of the new objective electrophysiological methods to test hearing in infants. It can provide a reliable and complete audiogram with specific frequency to help the hearing diagnosis and rehabilitation of hearing and languaging following auditory screening. OBJECTIVE: To compare the response threshold of ASSR with auditory threshold of visual reinforcement audiometry (VRA) in infants failed in the hearing screening for investigating their hearing loss. DESIGN: A comparative observation. SETTINGS: Maternal and child health care hospitals of Guangdong province, Shunde city, Nanhai city and Huadu district. PARTICIPANTS: Totally 321 infants of 0-3 years undergoing ASSR test were selected from the Hearing Center of Guangdong Maternal and Child Health Care Hospital from January 2002 to December 2004. Informed consents were obtained from their guardians. There were 193 cases (60.2%) of 0-6 months, 31 cases (9.7%) of 7-12 months, 17 cases (5.3%) of 13-18 months, 14 cases (4.4%) of 19-24 months, 33 cases of 25-30 months, and 33 cases (10.2%) of 31-36 months. METHODS: ① The 321 infants failed in the hearing screening were tested under sleeping status, the ranges of response threshold distribution in ASSR of different frequencies were analyzed in each age group. ② The infants above 2 years old were also tested with VRA, and their response thresholds were compared between VRA and ASSR. ③ Evaluative standards: The response threshold was < 30 dB for normal hearing, 31-50 dB for mild hearing loss, 51-70 dB for moderate hearing loss, 71-90 dB for severe hearing loss, and > 91 dB for extremely severe hearing loss. MAIN OUTCOME MEASURES: ① ASSR results of the infants failed in the screening; ② Proportion of cases of each response threshold in each age group; ③ Comparison of ASSR response thresholds and VRA auditory thresholds in the infants of 2-3 years old. RESULTS: ①The response threshold was < 30 dB in 47.4% of the 321 infants failed in the initial hearing screening and secondary screening after 42 days. ② Severe to extremely severe hearing loss was detected in only 16 cases (8.3%) of the 193 infants of 0-6 months, in 9 cases (27.3%) of the 33 infants of 25-30 months, and 13 cases (39.4%) of the 33 infants of 31-36 months. Of the 193 infants of 0-6 months old who failed in the initial screening and the second screening after 42 days, the ASSR auditory threshold was < 30 dB in 97 cases (50.26%), 31-50 dB in 63 cases (32.6%), 51-70 dB in 17 cases (8.8%), 71-90 dB in 7 cases (3.6%), and > 91 dB in 9 cases (4.7%). ③ Among the 321 infants failed in the screening, the auditory threshold in the 6 age groups was < 30 dB in 47.4%, 31-50 dB in 27.1%, 51-70 dB in 8.4%, 71-90 dB in 6.2%, and > 91 dB in 10.9%. ④ The difference between ASSR response threshold and VRA auditory thresholds was 6-18 dB in the normal hearing group, mild and moderate hearing loss groups, and there was high correlation between them. The difference of ASSR and VRA thresholds was less than 5 dB between extremely severe and severe hearing loss groups, 5-13 dB between extremely severe and moderate-to-severe hearing loss groups (P < 0.05), and there was no significant differences between severe and moderate-to-severe hearing loss groups (P > 0.05). CONCLUSION: ① The hearing was normal in about half of the infants, although they failed in the primary screening and secondary screening. ② The proportion of the severity of hearing loss was increased along with aging. ③ Mild and moderate hearing losses are dominant in infants. ④ ASSR is reliable to evaluate the hearing of infants.
