International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:12 No:04 76 I J E N S IJENS © August 2012 IJENS - IJMME - 5959 - 129304 Vibration Analysis of Hyper Composite Material Beam Utilizing Shear Deformation and Rotary Inertia Effects Dr. Luay S. Al-Ansari , Muhannad Al-Waily and Ali M. H. Yusif Abstract-- This paper presents an analytical and numerical vibration analysis of hyper composite material beam utilizing shear deformation and rotary inertia. The hyper composite material used in this research is consists of long reinforcement fiber and composite matrix which is components are resin with short fiber. The vibration analysis of this hybrid composite material beam using development theory for the beam which the effect of transverse shear deformation and rotary inertia included. Where the results are the natural frequency and general equation of motion. Also the effect of volume fraction and types of short, long fiber and resin material on the natural frequency are investigated. The results shows the natural frequency of the hyper composite material beam increases with increase of the strength of fiber and with the increases of volume ratio of the long fiber (when uses short fiber and long fiber of the same kind). Index Term-- Vibration of Beam, Composite Materials, Vibration of Composite Materials, Hyper Composite Materials Properties, Vibration of Beam with Rotary Effect. لخاصة: ا ΔيΩΪ وعΔيϠيϠ تحΔاسέΩ ϡΪ يقΚحΒا الά هίاΰΘيل اهϠحΘ ل اتيά الέالقصو القص وϩ تشوϦيϤπΘ بΔΒاكήΘϣ Ωواϣ ΔΒΘ ع اي.ϧاέوΪ لϦϣ Δϧكوϣ ΔΒΘعϠ لΔϧكوϤ الΔΒاكήΘϤ الΩواϤ الΩواϣ ΙاΛ , ألΔوليρ ألياف( قΘϣ يافΩΩήΘ الΔاسέΩ تϤ.ت)Δابطέ ΓΩاϣ, وΔ طع ΔΒΘعϠعي ليΒ الطϤ الΘ ή اΒ كΔ ήيΛ تأΩ وإيجاΔΒسϧ ,Δف الطوليأليا اϢ حج اή الΓΩاϤ, والΔقطعΘϤف الأليا اعييΒ الطΩΩήΘ الέاΪقϣ ىϠ عΔ بط ΔΒΘعϠ ل. Κ حي في اΔϨيΒϤئج الاΘϨ العييΒ الطΩΩήΘ الϥ باϦيΒ تΚحΒ ل ΔΒΘعϠ لΩاΩΰ وتΔΒكήϤ الΓΩاϤϠ لΔقويϤ الΓΩاϤϠ لΔϣقاوϤ الΓΩياΰ بΩاΩΰ ي أليافϡاΪΨΘ اسΔفي حال( Δف الطولي لألياΔيϤ الحجΔΒسϨ الΓΩياΰ ب .)Δف الطوليألياوع اϧ فسϧ Ϧϣ ΔقطعΘϣ I. INTRODUCTION In the recent decades the applications of composite structures has been increased especially the composite beam applications. Applications such as mechanical, civil, electrical, robotics, aerospace and many other applications. So the vibration of composite beam had the attention of many researchers. Abarcar[2] in 1972 studied the vibration Dr. Luay S. Al-Ansari is Lecturer in University of Kufa Muhannad Al-Waily is Ass. Lecturer in College of Engineering Muhannad_al_waily@yahoo.com Ali M. H. Yusif is Ass. Lecturer in Mechanical Engineering department of cantilever composite beam. In 1979 Mansfield and Sobey[4] presents a study of the behavior of composite helicopter blade. Also in 1979 Teh and Haung[6] presents a finite element approach as a study of vibration of generally orthotropic beams. Kapani and Raciti[7] in 1989 studied the nonlinear vibration of unsymmetricaly laminated composite beam. Then in 1990 the vibration of symmetric composite beam was studied by Chandrashekhara and Krishanamurthy[8] . Abramovitch[10] in 1992 studied the effect of shear deformation and rotary inertia on vibration of composite beam. Marur and Kant[11] in 1996 used a higher order theories and Finite element method modeling to investigate the vibration of composite beam. In 1999 Yilidirim[12] and et al presents a comparison of in plane natural frequencies of symmetric cross ply laminated beams based on the Bernolli-Eueller and Temoshenko beam theories. Erol[13] and et al in 2004 study the lateral vibration of composite beam. In 2007 Kaya[14] investigated flexural-torsional-coupled vibration analysis of axially loaded composite beam. In 2009 Su[15] investigated the effects of shape memory alloy on the dynamical properties of a composite beam. Mirtalaie and Hajabasi[16] in 2011 give an analytical approach to study the coupled lateral- torsional vibrations of laminated composite beams. Also in 2011 Hasan and Atlihan[17] study the effect of delamination length and orientation angle on the natural frequency of symmetric composite beams numerically and analytically. Considering the above, the scope of this research is to present a vibration analysis of hyper composite material beam utilizing shear deformation and rotary inertia effect. Also study the effect of the volume fraction of short, long fiber, and resin material on the natural frequency of hyper composite material beam. In addition the effect of type of short fiber on the natural frequency. DYNAMIC ANALYTICAL STUDY A theory of free vibration for moderately Hybrid composite material beams of rectangular cross-section is treated; this will include the effects of transverse shear deformation and rotator inertia. In order to derive the equations of motion, apply Hamilton's principle in conjunction with the ReissnerVariational Theorem. It will be remembered that Hamilion's principle is nothing but a variational statement of Newton's Laws of motion. Thus, we may state that the motion of the beam of Fig. 1. will be such as to minimize the integral,      2 1 . t t dt T   (1)