Transverse Vibrations Of Shear-deformable Beams Using A General Higher Order Theory

✍ Scribed by J.B. Kosmatka

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 557 KB
• Volume: 160
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1993.1022

✦ Synopsis

A new one-dimensional theory is presented for studying the static and vibration behavior of cylindrical or prismatic beam-type structures. This general higher order theory, which is developed for beams having an arbitrary cross-section, accurately accounts for transverse shear deformation out of the cross-sectional plane and anticlastic-type deformation within the cross-sectional plane. The two equations of motion are derived using Hamilton's principle along with the full three-dimensional constitutive relations. The resulting equations correctly predict the stress-free conditions on the beam cylindrical surface. A simplified form of the general higher order theory is also presented that accounts for transverse sheardependent deformation out of the cross-sectional plane, but assumes that the stresses within the cross-section are zero. Both approaches are shown exactly to reduce to existing first and higher order theories for beams with thin rectangular cross-sections. Numerical results show that including in-plane cross-sectional deformations will slightly increase the bendingdominant frequency and greatly reduce the shear-dominant frequency for extremely short wavelengths. Furthermore, the cross-section aspect ratio has only a minimal effect on the bending-dominated frequency, even for short wavelengths, but the effect on the sheardominated frequency can be significant for long slender beams with either rectangular or an elliptical cross-section.