R. KOTTNER et al.: IMPROVEMENT OF THE DAMPING PROPERTIES OF CARBON-FIBRE-REINFORCED ... IMPROVEMENT OF THE DAMPING PROPERTIES OF CARBON-FIBRE-REINFORCED LAMINATED PLASTICS USING DAMPING LAYERS IZBOLJ[ANJE DU[ENJA Z OGLJIKOVIMI VLAKNI OJA^ANE LAMINIRANE PLASTIKE Z UPORABO PLASTI ZA DU[ENJE Radek Kottner 1 , Josef Vacík 2 , Robert Zem~ík 3 1 University of West Bohemia, European Centre of Excellence, New Technologies for Information Society, Univerzitní 22, 30614 Plzeò, Czech Republic 2 University of West Bohemia, Department of Machine Design, Univerzitní 22, 30614 Plzeò, Czech Republic 3 University of West Bohemia, Department of Mechanics, Univerzitní 22, 30614 Plzeò, Czech Republic kottner@kme.zcu.cz Prejem rokopisa – received: 2012-09-03; sprejem za objavo – accepted for publication: 2012-10-08 A suitable hybrid composite consisting of carbon-fibre-reinforced plastic and damping layers was investigated in terms of damping and natural frequencies using experiments and numerical simulations. The frequency response and the transient response of cantilever beams were analysed. The damping layers made from rubber or from a cork-rubber composite material were used in the investigated hybrid structure. A laser-measurement device and an accelerometer were used for the measurement of the responses. Pareto optimization was performed using three-dimensional numerical simulations with the aim to maximize the fundamental natural frequency and the damping ratio. Keywords: hybrid, composite, carbon-fibre-reinforced plastic, rubber, damping Sestavljeni kompozit iz plastike, oja~ane z ogljikovimi vlakni in s plastmi za du{enje naravnih frekvenc, je bil preiskovan eksperimentalno in z numeri~no simulacijo. Analiziran je bil frekven~ni odgovor in prehodni odziv konzolnega nosilca. V preiskovani hibridni strukturi je bila plast za du{enje izdelana iz gume ali sestavljena iz gume in plute. Za meritve odgovora je bil uporabljen laserski merilnik in merilnik pospe{ka. Z uporabo tridimenzionalne numeri~ne simulacije je bila izvr{ena Paretova optimizacija za maksimiranje osnovne naravne frekvence in koli~nika du{enja. Klju~ne besede: hibrid, kompozit, z ogljikovimi vlakni oja~ana plastika, guma, du{enje 1 INTRODUCTION Recently, the conventional metallic structures have been replaced with composite structures thanks to their superior dynamic characteristics. For example, a higher specific stiffness of carbon-fibre-reinforced plastics (CFRPs) allows higher natural frequencies of the structu- res. Furthermore, the damping characteristics of CFRPs have higher values and, moreover, can be improved using an integration of the damping layers 1 . The aim of this work was to develop a suitable hybrid structure in terms of damping and natural frequencies. The investigated samples were the cantilever beams, whose damping layers were made from rubber or from the ACM87 cork-rubber composite material. The damp- ing ratio for their fundamental natural frequency was analyzed. 2 THEORY The equation of the motion of a damped system is 2 : Mq Cq Kq f && & () + + = t (1) where q[m], & q[ms –1 ], && q[ms –2 ] are the vectors of the ge- neralized coordinates and their 1 st and 2 nd differenti- ations with respect to time t; f(t)[N] is the vector of the generalized time-dependent applied force; M[kg] is the mass matrix of the system; C[Nsm –1 ] is the damping matrix and K[Nm –1 ] is the stiffness matrix. The motion of the discrete linear systems with a single degree of freedom can be described as: mq cq kq F && & () + + = t (2) In the case of free oscillations, Equation (2) can be consequently rewritten as: && & q q q + + = 2 0 0 zw w 0 2 (3) Materiali in tehnologije / Materials and technology 47 (2013) 2, 189–193 189 UDK 519.61/.64:66.017 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 47(2)189(2013) Figure 1: Response of an underdamped harmonic oscillator Slika 1: Odgovor harmoni~nega nedu{enja