Exact solutions for free longitudinal vibration of bars with non-uniform Cross-sections

• Autorzy: Li Q. S.
• Języki publikacji: EN

Abstrakty

EN

Using appropriate transformations, the differential equations of free longitudinal vibration of bars with variably distributed mass and axial stiffness are reduced to Bessel?s equations or ordinary differential equations with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of mass and axial stiffness. Exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived and used to obtain the general solution and the frequency equation of a multi-step non-uniform bar with various boundary conditions, including non-classical cases. This approach which combines the transfer matrix method and closed form solutions of one step bars leads to a single frequency equation for any number of steps.

Słowa kluczowe

EN

longitudinal vibration; exact solutions; non-uniform bars; natural frequency; mode shape

PL

mechanika

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: Applied Mechanics and Engineering
• Rocznik: 2000
• Tom: Vol. 5, no 3
• Strony: 521--541
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Li Q. S.

• City University of Hong Kong, Department of Building and Construction, Tat Chee Avenue, Kowloon, HONG KONG,