When products are subjected to dynamic loads where energy and motion controls are required use is made of thermoplastic elastomer (TPE) components. These products involve buildings (Fig. 2.11), bridges, highways, sporting goods, home appliances, automobiles, boats, aircraft, and spacecraft.

Schematic of a building isolator


Steel FMnforcing Plain \


Steel FMnforcing Plain \

Elattam Layan

Elattam Layan

In a building, TPE controls vibration and noise from motors and engines that is generated to the building itself. For rapid transit TPE supports the rail and the vehicle reducing noise and vibration to adjacent buildings. For ships TPE absorb their berthing energies used in vibration units that are as large as 3 m (9.9 ft.) high and weighing up to 19 tons. For all these and other applications, TPEs are used either in shear, compression, tension, torsion, buckling, or a combination of two or more load conditions depending on the needs of the specific application. The particular application will dictate which would be best.

When berthing a vessel the structure has to be designed to withstand the energy developed by the vessel. The more rigid the system, the higher the reactive forces must be to absorb the vessel's kinetic energy. The area under the structure's load as against its deflection response curve is typical to that shown in Fig. 2.12.

Load-deflection energy absorbed behavior in these type isolators

Maximum Lateral Reaction Force

Maximum Lateral Reaction Force

Energy Absorbed

Lateral Deflection

that could be obtained compared to an ideal hydraulic system with 100% energy efficiency.

In Fig. 2.13 the energy capacity is approximately 50% efficient, requiring 100% more deflection or load, if the deflection or load of a 100% efficient curve is required. Fig. 2.14 shows an energy capacity approximately 35% efficient, requiring 300% higher deflection or a 350% higher load if the deflection or load of a 100% efficient curve is required. The energy capacity shown in Fig. 2.15 is approximately 75% efficient, requiring a 25% higher deflection or a 20% higher load if the deflection or load of a 100% efficient curve is required.

The buckling column was selected because it produces the lowest reaction load and the lowest deflection (deflection controls the projection of the berthing system out from the structure).When designing to support structures and allow the horizontal input of an earthquake or to allow the structural movement needed on a structure such as a bridge pier, the vertical and horizontal stiffnesses must be calculated, then a system can be designed. Take, for example, a rectangular elastomeric section with a length of 762 cm, a width of 508 cm, and a thickness of 508 cm (305 x 203 x 203 in.). Table 2.3 lists the formulas used to calculate the respective compression and shear stiffnesses for these data. For the elastomeric section of the example use the following formula:

508 =762kcEc

508 = 762ksGs

Data required for formulas.


Compression (KJ

Shear (KJ


Variable k Variable LA Variable £c Variable Gs Variable t

Factor of geometry Load area

Compression modulus Elastomer thickness

Factor of geometry Load area

Elastomer thickness

The calculations for kc and ks adjust for such design parameters as strain, bulk compression, and bending by the elastomer section, as developed over many years of sample testing. A way to forego the pain of getting there is to let ks = 0.98 and kc = 1.0, using a 0.69 MPa shear-modulus elastomer as follows:

Kc= 762fcand Ks= 747GS.

For compression, the shape factor (SF), which is the projected load area of the product divided by the elastomer area that is free to move (known in the industry as the bulge area, or BA), is the major design parameter. For this example the shape factor is calculated thus:

Load area/Bulge area = (726)(508)/(762 + 508)(2)(508) = 0.3 (2-14)

Using SF = 0.3 and a Gs= 0.69MPa, and Ec+ = 2.42-MPa is obtained, Therefore Kc = 1. 8-MN/m and Ks= 0.5-MN/m.

Applying a 20% maximum compression strain to the product results in a maximum compression deflection of 102 cm (41 in.). This allows a maximum compression load of only 19 kg (42 lb.), hardly sufficient to support a building or a bridge.

Given that shear stiffness Ks cannot change, the sole remaining option is to change the compression stiffness, by adjusting the shape factor. Designing the product as two units each 762 x 508 x 254 cm (305 x 203 x 102 in.) thick will not change the shear characteristic, but it does change the shape factor to 0.060. In this instance, Ec = 3.03 MPa and Kc becomes 4.6 MN/m per section. With two sections in series the spring rate is 2.3 MN/m, which now allows for 24.3 kg of compression load. Dividing each of these sections into a total of four sections each 762 x 508 x 127 cm (305 x 203 x 51 in.) thick yields a shape factor of 1.2 and an Ec equal to 151.7 MPa. An individual section Kc will be 46 MN/m, with a series of four being 115 MN/m, allowing a compression load of about 120 kg. It always maintains a shear spring rate of about 0.5 MN/m. This is the basic design philosophy for obtaining high-compression loads while maintaining the soft shear stiffness needed for seismic considerations or for thermal expansion and contraction. Continued thinning of the individual elastomer sections will drive the compression load-carrying capacity upward.

In the rapid transit industry, wherever there is an elevated structure or subway tunnel, noise and vibration caused by the vehicles can generate unrest among those living along the route. There are three areas that can be adjusted to reduce annoying frequencies: the vehicles' suspension system; the trackbed, including the tie-to-rail interface and the floating slab; and various acoustic barriers. For the vehicle suspension system and trackbed techniques, good elastomeric product design and application are generally sufficient. The product design requires including the design considerations mentioned previously of the compression and shear curve and shape factor, but also introduces new combinations of compression and shear. These occur either by shear and compression in planes 90 degrees to each other or shear with compression, as in seismic and thermo designs, only installed at angles to the horizontal.

We have now looked at the more common types of single-axis load-deflection characteristics possible with elastomeric products, as well as various methods to change die stiffness in one direction while maintaining an initial stiffness in a plane that is 90 degrees from the reference plane. The angular considerations in different directions can now yield an unlimited number of design-configuration options.

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