Non-contact experimental methods to characterise the response of a hyper-elastic membrane

Abstract

Background: Membranes often feature in dynamic structures. The design of such structures generally includes the evaluation of their dynamic characteristics, such as natural frequecies and mode shapes. Methods: The quasi-statics ad dyamic responses of thin rubber sheeting were investigated through non-contact experimental techniques. The rubber sheeting was modelled as a membrane structure and the material was assumed to be hyper-elastic, isotopic and incompressible. Two hyper-elastic material models were considered, namely the Mooney-Rivlin model and the Neo-Hookean model. The natural frequencies and mode shapes of the hyprt-elastic membrane were anatically and numerically calculated by assuming small linear vibrations and an equi-bi-axial stress state in the membrane. To validate the mathematical analyses, experimental modal analysis was performed where the vibration response was measured with a laser Doppler vibrometer. Results and conclusions:The analytical model, shows that the natural frequencies of the membrane depend on the initial stretch. Mathematical and experimental results agree well at the lower modes. However, measurement resolution is found to be a vital factor which limits the extraction of closely spaced modes due to difficulties with the accurate identification of nodal line in a purely experimental approach.

An electromechanically driven dielectric elastomer based tunable reflector

“…Measurements are acquired using a custom-designed experimental setup, shown in figure 4(b). The main component of the system is the laser doppler vibrometer which functions as a non-contact measurement device and can be suitably employed for the measurement of hyperelastic systems [49]. The user terminal is used to generate the input electrical signal.…”

Archives of Acoustics

“…Theoretical studies, though numerous, are often complex and therefore limited to the simplest cases (Kwak, Kim, 1991;Amabili et al, 1996;Lee, Singh, 1994;Rdzanek et al, 2003; Consequently, experimental methods of analysis are widely accepted due to obvious shortcomings and limitations of the theoretical methods. The results of both theoretical and experimental investigations are often used in different practical applications such as active control of noise and vibrations (Leniowska, 2006 Kamper, Bekker, 2017). The discretisation technique has been used to investigate the sound radiation inside a layer bounded by two walls (Díaz-Cereceda et al, 2012).…”

“…p(z) = A(k) sin[k(z +l/2)]+B(k) cos[k(z +l/2)] (25). Inserting this solution to the boundary conditions yields immediatelyA(k) cos(kl/2) − iβ sin(kl/2) + B(k) sin(kl/2) + iβ cos(kl/2) = 0,(26)A(k) cos(kl/2) − B(k) sin(kl/2) = +i 0 cv 0 .…”