Vibrations in engineering structures can lead to severe instabilities, especially under low-frequency excitations that traditional linear isolators cannot effectively suppress. To address this, quasi-zero stiffness (QZS) vibration isolators, known for their high-static-low-dynamic stiffness properties, have gained increasing attention. This report investigates the reflection and absorption characteristics of a nonlinear string with a QZS mechanism applied as a boundary condition. The model is considered, and the governing equations are derived and nondimensionalized. Using regular perturbation methods and the method of multiple time scales, analytical solutions are obtained and evaluated. The analysis distinguishes between cases where the oblique springs are extended or compressed. It is found that with compressed springs, when the vertical damping coefficient is below unity, the system is counterintuitively stable. Furthermore, the inclusion of oblique dampers leads to unphysical energy growth. These phenomena are attributed to the singular nature of the system’s dynamics and the limitations of the chosen multiple time scale method. The results indicate that the current model does not fully capture the effects of the oblique springs and dampers, underscoring the need for further investigation into the system’s asymptotic expansions. Moreover, exploring second-order dynamics and external forcing could provide a deeper understanding of the system’s complex behaviour.

Janus particles are colloidal particles for which one half of the surface has different attributes than the other half. One property of a spherical dielectric particle with half of its surface covered by a layer of another dielectric or metal is that it has a non-uniform scattering pattern when exposed to light. However, the angle with which the light is shone on the particle has a large effect on the scattering pattern produced. Thus it is important that we are able to orient these Janus particles. The orientation can be controlled if we apply an electric field to the particle for example. The movement of colloidal particles with an electric field is widely studied and this field is called dielectrophoresis. For a Janus particle, the calculations for the force and torque become complicated. The movement and rotation of these particles have been studied, however, no analytic solution has been found. In this report, we derive a semi-analytic description of the force and torque due to an external electric field on a spherical Janus particle. For this, first the potential due to an external electric field is determined and then the force and torque are calculated with two methods: the dipole approximation and the Maxwell Stress Tensor method. In the dipole approximation, there is no force on the Janus particle. But, there is a torque on the particle in the dipole approximation. Due to this torque, the Janus particle will orient itself such that its cap points in the direction perpendicular to the applied field. For the torque calculated with the Maxwell Stress Tensor, we get a similar result as in the dipole approximation. On the other hand, according to the calculations with the stress tensor, there is a relatively small force on the particle.