On measuring the elastic and damping constants of orthotropic sheet materials

Abstract

Many common sheet materials, ranging from natural materials such as wood to modern composites, possess approximately orthotropic symmetry. Within the approximations of thin-plate bending theory, the linear vibrational properties of such sheets are governed by four elastic constants and four damping constants (at any given frequency). A simple procedure is presented whereby all four elastic constants may be determined, quickly and with reasonable accuracy, from measurements of the resonant frequencies of low-frequency modes of thin rectangular plates with free edges. Also, at least three of the four damping constants may be determined by measuring the damping factors of the same modes-it turns out that the fourth damping constant does not usually have sufficient influence on the low-frequency modes for a reliable value to be found by this approach. The procedure is illustrated with measurements on a range of different sheet materials: wooden plates cut at different angles from the solid timber, plywood, and two very different fibre-reinforced composites. The discussion of these experimental results suggests that this simple procedure could form a valuable part of any programme of quality control, material selection or non-destructive testing involving orthotropic sheet materials.

Physical and Biological Characterization of Ferromagnetic Fiber Networks: Effect of Fibrin Deposition on Short-Term In Vitro Responses of Human Osteoblasts

“…Using thin-plate bending theory, 47 the measured mode frequencies, together with the plate dimensions and density, were used to estimate the constants D 1 , D 2 , D 3 , and D 4 of the plate (D 1 and D 3 are associated with bending of the plate middle surface, D 2 with Poisson's ratio coupling between the in-plane directions, and D 4 with out-of-plane twisting of the middle surface). After using an iterative process 47 to improve the accuracy of these constants, the in-plane elastic constants were determined using the following relationships:…”

“…The resonant frequencies for the first three mode shapes (Table 2), obtained using a rectangular plate, lead to first estimates of D 1 , D 3 , and D 4 . To estimate D 2 , the square plate (with adjusted aspect ratio 47 ) was used to observe the ''X'' and ''O'' (ring) vibration mode frequencies (mode Nos. 4 and 5 in Table 2).…”

“…4 and 5 in Table 2). The accuracy of these first estimates of D 1 , D 2 , D 3 , and D 4 was improved using an iterative method, 47 employing numerical calculations of plate frequencies based on the Rayleigh-Ritz method. Since there should be no preferred in-plane direction in the fiber network material, this iterative process was carried out assuming in-plane transverse isotropy.…”

Radiation damping, efficiency, and directivity for violin normal modes below 4 kHz

“…In practice it is quite troublesome to determine "pure" internal damping because ζ int is dependent on mode shape. 9 Approximate functional forms 5 such as ζ int ∝ 1/√f, while useful for general behaviors, disregard specific mode-to-mode variations in internal damping. Total damping (%crit) vs. corpus mode frequency is shown in Fig.…”

Measurement of relevant elastic and damping material properties in sandwich thick plates

“…The problem of estimating elasticity and damping parameters of homogeneous materials by using point measurements [22][23][24][25] has retained some attention in a thin-plate context. In a thick-plate context, methods involving full-field measurements are currently available [26][27][28], but they are very time-consuming or need sophisticated equipment.…”