A time domain model of linear viscoelasticity is developed based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. The anelastic displacement field is used to describe that part of the strain that is not instantaneously proportional to stress. General coupled constitutive equations for (1) the total and (2) the anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. A key feature of the model is the absence of explicit time dependence in the constitutive equations. Apparent time-dependent behavior is described instead by differential equations that govern (1) the motion of mass particles and (2) the relaxation of the anelastic displacement field. These coupled governing equations are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also treated: the anelastic displacement field is effectively an internal field, as it is driven exclusively through coupling to the total displacement, and cannot be directly affected by applied loads. In order to illustrate the use of the method, model parameters for a commonly-used high damping polymer are developed from available complex modulus data.

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This paper explains how piezoelectric devices can be used to control vibrations in a snowboard. Furthermore the details of the approach, testing, design and analysis of a piezoelectric damper applied to a production snowboard are described here. The approach consisted of determining the principal modes of vibration of a snowboard during its operation (on-slope). This information was used to develop a finite element model of the structure. The finite element model was used to find the areas of higher strain energy where a piezoelectric device could be applied and be effective in reducing undesired vibrations. Several prototype piezoelectric dampers were built, applied to snowboards and tested on snow. The proper amount of damping was selected by the test riders, so that a configuration could be selected for production of the 1998 K2 Electra snowboard. The piezoelectric damper selected reduced the snowboard vibration by 75% at the mode to which it was tuned, allowing for a smoother ride and a more precise control of the snowboard in any kind of snow condition.

This paper reports an experimental study on active vibration reduction for automotive shafts with the use of piezoelectric material. The work focuses on an axle of an Audi A2. The demand in the automobile sector for higher comfort in the vehicle is of a great importance alongside the requirements of lighter weight and low fuel consumption. These requirements are typically in conflict with each other. One solution is the use of intelligent materials instead of viscoelastic materials and proof mass absorbers. These solutions are quite heavy especially at low frequencies. Active vibration control and piezoelectric devices are advantageous in this application due to their low mass to performance ratio. Our research study explores the use of such piezoelectric devices for an axle. In conjunction with electronics it will reduce vibrations in the first natural bending mode of the axle. Laboratory tests simulated the condition present in the road. At first a stationary set up was used, then a simulated disturbance was input at the attachment points of the shaft. Finally, a test with rotating shaft was performed. Piezoelectric devices (custom QuickPacks from ACX, a Division of Cymer) were used as sensors and as actuators to properly control the axle during the different operating conditions. The power consumption of each actuator pair was less than 20W. The work described here details the test setup, the control strategy, the hardware implementation as well as the test results obtained

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