Polymer Testing 22 (2003) 343–351 www.elsevier.com/locate/polytest Product Performance Testing of nonlinear interaction effects of sinusoidal and noise excitation on rubber isolator stiffness M. Sjo ¨berg a,b,* , L. Kari a a The Marcus Wallenberg Laboratory for Sound and Vibration Research, Department of Vehicle Engineering, KTH, 100 44 Stockholm, Sweden b Scania CV AB, Group of Vehicle Dynamics, 151 87 So ¨derta ¨lje, Sweden Received 21 June 2002; accepted 16 August 2002 Abstract The nonlinear excitation effects on dynamic stiffness and damping of a ﬁlled rubber isolator are investigated through measurements. For a single harmonic excitation they are found to exhibit a strong amplitude dependence, following the well-known Payne effect where stiffness is high for small excitation amplitudes and low for large amplitudes while damping displays a maximum at intermediate amplitudes. However, expanding the measurements to a multiple harmonic excitation, the commonly applied superimposition principle of single harmonic responses due to this excitation is shown to be non-valid. On the contrary, it is found that reference stiffness at a small excitation amplitude and high frequency is reduced and damping increased while superimposing a large amplitude low frequency excitation component. Superim- position of low frequency noise signals displays essentially the same inﬂuence on the reference characteristics. As a rule of thumb, the largest excitation amplitude over the isolator normally determines the stiffness at the reference frequency while the inﬂuence of envelope amplitude is increased as its frequency approaches that of the component of interest.  2002 Elsevier Science Ltd. All rights reserved. Keywords: Rubber isolator; Measurement; Dynamic stiffness; Damping; Nonlinear; Payne effect 1. Introduction Ever since it was found that a material with unique mechanical properties is produced from heated natural gum mixed with sulphur, it has found an indisputable role in many mechanical applications. One of the main reasons is that it is generally soft and withstands defor- mation up to several hundred percent while resuming its original shape after stress release. This elastic property facilitates its wide use as a ﬂexible coupling between stiff components in various constructions. Vibration iso- * Corresponding author. Tel.: +46-8-790-79-01; fax: +46-8- 790-61-22. E-mail addresses: mattiass@fkt.kth.se (M. Sjo ¨berg); leifk@fkt.kth.se (L. Kari). 0142-9418/02/$ - see front matter  2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0142-9418(02)00110-1 lators, suspensions and ﬂexible joints are examples of such machine elements. Engineering knowledge of rub- ber material properties is often rather poor, despite it being so commonly used. This is probably due to its complex behavior where mechanical properties, e.g. dynamic hardness and damping, are dependent not only on additives in the material but also on temperature, fre- quency and amplitude of the motion. This knowledge is essential when elements composed of rubber are included in dynamic systems. Component nonlinearities, due to either material properties or geometric inﬂuences, are often present as discussed by Harris and Stevenson [1]. The rubber compound frequently has carbon black ﬁllers added, consisting of very small carbon particles (20 nm–50 μm), which are not chemically joined with the elastomer but are rather forming agglomerates within the rubber material. Inclusion of ﬁllers increases material