PSI - Issue 77

Job S. Silva et al. / Procedia Structural Integrity 77 (2026) 550–558 Author name / Structural Integrity Procedia 00 (2026) 000–000

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approximately, 450,000 elements with reduced integration. The wagon platforms and its reinforcements, Fig. 4-a, were modelled with two-dimensional shell elements, while the axle boxes and bogie frames, Fig. 4-b, were modelled with three-dimensional solid elements The primary suspension elements are represented by linear spring elements with an elastic constant = 1,930 N / m , and a mass = 4.5 g , while the wheel axels are modelled with beam elements. Transmission of force is accounted for with spiders of pseudo-rigid (RBE3) elements. A summary of the number and types of elements used in the model is given in Table 1.

a)

b)

Fig. 4. Finite Element model of the scaled wagon: (a) overall structure; (b) bogie detail.

Table 1. Mesh properties of the Finite Element Model.

Element type

Number of elements

1D: Beam, Rigid and Spring elements 402 2D: Shell elements 51,162 3D: Solid elements 406,371

The materials of the components were modelled as linear isotropic with the properties depicted in Table 2. As for contact modelling, some interactions were simplified using tied interfaces which constraints the nodes of the surfaces to be perfectly bonded. For interactions where friction is relevant, contact with a static friction coefficient of = 0.6 was modelled, this simulates dry contact behaviour. Table 2. Mechanical properties of the materials used in the model. Density, ρ , [ m 3 ⁄ ] Young’s Modulus, E, [MPa] 193,000 Poisson’s Ratio, υ 0.3 0.33 In order to estimate the dynamic properties of the modelled structure, a constrained modal analysis was performed with natural frequency extraction up to a maximum of 1000 . A fixed constraint was modelled in the areas of fixation of the structure, and the displacement of the spring elements was restricted to its longitudinal axis only. 3.3. Experimental Setup Experimental modal tests were carried out using two triaxial ICP® accelerometers (Model 356A17, PCB Piezotronics) mounted on the two wagon platforms. These sensors, have a sensitivity of 500 mV/g and an operational frequency range up to 3 kHz, allowing accurate measurement of acceleration in three orthogonal directions. Excitation was applied at multiple locations using a rubber hammer to ensure a sufficiently broad excitation throughout the structure. The data acquisition system consisted of a National Instruments cDAQ-9191 chassis equipped with NI 9232 modules, operated via SignalExpress software. The sampling frequency was set to 2048 Hz to capture all relevant vibration 8,000 2,700 71,000 Steel – AISI316 Aluminium – 6061T4

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