TECHNIQUES by I. Basdogan and E. Dikmen MODELING VISCOELASTIC RESPONSE OF VEHICLE DOOR SEAL A utomotive weatherstrip seals are used in between the doors and vehicle body along the perimeter of the doors. The seals can be held in place through various methods such as intermittent push pins, continuous carriers, and flange mounts. They are mainly used to prevent water and dust entrance to the passenger compartment in all weather conditions and accommodate for the manufacturing variations. The weatherstrip seal affects the door vibrations considerably by changing its stiffness and viscoelastic properties. Hence, accurate representation of the door seals is crucial in the simulation models used for predicting the dynamics of the vehicle. For this purpose, the material properties of the seal must be characterized properly. The weatherstrip seal investigated in this study is made of ethylene propylene diene monomer (EPDM) sponge rubber. The weatherstrip seal is generally in the form of dual extrusion bulbs of sponge and dense rubber. The bulbs can have different shapes generally with a height of approximately 15–30 mm. The wall thickness of the bulb is typically a few millimeters to provide maximum sealing area at a low compression force. 1 The rubber used in the seal can withstand large deformations without permanent deformation and have high damping characteristics. The mechanical properties of the rubber may vary with the amount of deformation, geometrical shape factors, previous load history, temperature, frequency, and amplitude of the motion in the presence of mechanical vibrations. Because these properties are difficult to predict, experimental methods must be often adopted for the dynamic characterization or system identification. 2–4 Several groups have conducted experiments with rubber used in automotive industry to characterize its mechanical properties. In an earlier study, we developed hyperelastic and viscoelastic models of the weatherstrip seal to predict dynamic performance of a vehicle door and its effect on the overall vehicle dynamics. 5 Lin et al. 6 presented a simple experimental method to evaluate frequency dependent stiffness and damping characteristics of a rubber mount. Kren and Vriend 7 used dynamic indentation tests in order to determine viscoelastic properties of rubber. Hummel and Nied developed a procedure for measuring biaxial viscoelastic behavior of thermoplastics. 8 They designed and constructed a heated tensile testing machine to perform large strain deformation testing on polymers at elevated temperatures. They measured the elastic response of the material at elevated temperatures and large deformations. They also developed a numerical procedure to determine the elastic response from the raw viscoelastic data using the Mooney–Rivlin form of the elastic strain energy function. Kulik et al. developed an experimental technique to measure I. Basdogan (ibasdogan@ku.edu.tr) is an assistant professor with the Department of Mechanical Engineering, Koc University, Rumeli Feneri Yolu, Sariyer, Istanbul, Turkey. E. Dikmen is a PhD student with the Department of Mechanical Engineering, University of Twente, Enschede, Netherlands. the dynamic properties of the viscoelastic materials. 9 The method is based on the analysis of forced oscillation of a cylindrical sample loaded with an inertial mass. For the calculation of the properties, a two-dimensional numerical model of cylindrical sample deformation was used. They studied the effect of altering the ratio of load mass to sample mass on the modulus of elasticity and loss tangent curves. Jeong and Singh 10 proposed new analytical methods for modeling vibration isolators and mounts of a vehicle or machinery systems. They used the linear and nonlinear eigenvalue formulations to model the frequency dependency of elastic and dissipative parameters. They developed a nonlinear, frequency domain synthesis method to calculate the forced harmonic response of the overall system, and then validated the method by comparing it with the corresponding time domain method. Richards and Singh 11 proposed new methods to characterize nonlinear stiffness properties of rubber isolators. Their study included experiments investigating the response of single- and multi-degree-of- freedom models of rubber under different types of excitation loads. For analytical characterization of rubber isolators, they used a continuous quasi-linear representation and discrete nonlinear system models. In another study by Park, 12 different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared. Their study showed that despite the widespread notion of the inadequacy of spring-dashpot mechanical models for viscoelastic dampers, the generalized Maxwell or generalized Voigt model, with their expanded degrees of freedom, accurately describes the broad-band rheological behavior of common viscoelastic dampers. Gaillard and Singh 13 developed dynamic lumped parameter models of vehicle clutches using Voigt and Maxwell models, and a dry-friction element based on the Coulomb model. The theoretical predictions were then compared with the experimental data. They observed that the dynamic viscoelastic models with dry-friction component successfully simulate trends observed in the experiments and the dynamic properties depend on excitation frequency and amplitude. Zhang and Richards 14 used a parameter identification method based on constraint optimization for identifying the parameters of a Maxwell solid model having two or more Maxwell elements by fitting the model to measured frequency response spectra. The identification method was validated by several analytical examples. They conducted experiments with three different rubber isolators subjected to both static and dynamic loadings. For all three rubber isolators, they compared the performance of Voigt and Maxwell models and concluded that Maxwell solid having two Maxwell elements can accurately represent the measured static and dynamic characteristics of real elastomeric isolation systems. In a similar study, the same authors studied the dynamic characterization and parameter identification of a single mass elastomeric isolation system represented by a Maxwell–Voigt model. 15 They examined the influences that the stiffness and damping doi: 10.1111/j.1747-1567.2009.00599.x © 2009, Society for Experimental Mechanics May/June 2011 EXPERIMENTAL TECHNIQUES 29