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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.

A finite element for planar beams with active constrained layer (ACL) damping treatments is presented. Features of this non-shear locking element include a time-domain viscoelastic material model, and the ability to readily accommodate segmented (i.e. non-continuous) constraining layers. These features are potentially important in active control applications: the frequency-dependent stiffness and damping of the viscoelastic material directly affects system modal frequencies and damping; the high local damping of the viscoelastic layer can result in complex vibration modes and differences in the relative phase of vibration between points; and segmentation, an effective means of increasing passive damping in long-wavelength vibration modes, affords multiple control inputs and improved performance in an active constrained layer application. The anelastic displacement fields (ADF) method is used to implement the viscoelastic material model, enabling the straightforward development of time-domain finite elements. The performance of the finite element is verified through several sample modal analyses, including proportional-derivative control based on discrete strain sensing. Because of phasing associated with mode shapes, control using a single continuous ACL can be destabilizing. A segmented ACL is more robust than the continuous treatment, in that the damping of modes at least up to the number of independent patches is increased by control action.

An electromechanical coupling coefficient is a measure of the effectiveness with which a piezoelectric material (or a device employing such a material) converts the energy in an imposed electrical signal to mechanical energy, or vice versa. There are different kinds of material and device coupling coefficients, corresponding to different modes of excitation and response. Device coupling coefficients are properties of the device and, although related to the material coupling coefficients, are generally different from them. It is commonly held that a device coupling coefficient cannot be greater than some corresponding coupling coefficient of the active material used in the device. A class of devices was recently identified in which the apparent coupling coefficient can, in principle, approach 1.0, which corresponds to the limit of perfect electromechanical energy conversion. The key feature of this class of devices is the use of destabilizing mechanical pre-loads to counter inherent stiffness. The approach is illustrated for a symmetric piezoelectric bimorph device: theory predicts a smooth increase of the apparent coupling coefficient with pre-load, approaching 1.0 at the buckling load. An experiment verified the trend of increasing coupling with pre-load: a load corresponding to 50% of the buckling load increased the bimorph coupling coefficient by more than 40%. This approach provides a way to simultaneously increase both the operating displacement and force of a piezoelectric device, distinguishing it from alternatives such as motion amplification. and may allow transducer designers to achieve substantial performance gains for some actuator and sensor devices.