Nonlinear dynamic analysis of a four-bar mechanism having revolute joint with clearance

In general, joints are assumed without clearance in the dynamic analysis of multi-body echanical systems. When joint clearance is considered, the mechanism obtains two uncontrollable degrees of freedom and hence the dynamic response considerably changes. The joints’ clearances are the main sources of vibrations and noise due to the impact of the coupling parts in the joints. Therefore, the system responses lead to chaotic and unpredictable behaviors instead of being periodic and regular. In this paper, nonlinear dynamic behavior of a four-bar linkage with clearance at the joint between the coupler and the rocker is studied. The system response is performed by using a nonlinear continuous contact force model proposed by Lankarani and Nikravesh [1] and the friction effect is considered by a modified Coulomb friction law [2]. By using the Poincaré portrait, it is proven that either strange attractors or chaos exist in the system response. Numerical simulations display both periodic and chaotic motions in the system behavior. Therefore, bifurcation analysis is carried out with a change in the size of the clearance corresponding to different values of crank rotational velocities. Fast Fourier Transformation is applied to analyze the frequency spectrum of the system response

Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance

The impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made from a hyperelastic material, providing large deformation under small excitation amplitude. A nonlinear strain energy function is proposed to capture the elastic energy stored in the flexible component of the device. The tip–sample interaction is modeled based on the van der Waals non-contact force. The nonlinear equation governing the AFM’s dynamics is established using the extended Hamilton’s principle, obeying the Euler–Bernoulli beam theory. As a result, the vibration behavior of the system is introduced by a nonlinear equation having a time-dependent boundary condition. To capture the steady-state numerical response of the system, a developed Galerkin method is utilized to discretize the partial differential equation to a set of nonlinear ordinary differential equations (ODE) that are solved by the combination of shooting and arc-length continuation method. The output reveals that while the resonator is set to be operating near twice the fundamental natural frequency, the response amplitude undergoes a significant drop to the trivial stable branch as the sample’s profile experiences depression in the order of the picometer. According to the performed sensitivity analysis, the proposed working principle based on principal parametric resonance is recommended to design AFMs with ultra-high detection resolution for surface profile scanning

Built-In Packaging for Single Terminal Devices

An alternative packaging method, termed built-in packaging, is proposed for single terminal devices, and demonstrated with an actuator application. Built-in packaging removes the requirements of wire bonding, chip carrier, PCB, probe station, interconnection elements, and even wires to drive single terminal devices. Reducing these needs simplifies operation and eliminates possible noise sources. A micro resonator device is fabricated and built-in packaged for demonstration with electrostatic actuation and optical measurement. Identical actuation performances are achieved with the most conventional packaging method, wire bonding. The proposed method offers a compact and cheap packaging for industrial and academic applications

Soliton Frequency Combs in Elastomer Membrane-Cavity Optomechanics

Solitons, arising from nonlinear wave-matter interactions, stand out for their intrinsic stability during wave propagation and exceptional spectral characteristics. Their applications span diverse physical systems, including telecommunications, atomic clocks, and precise measurements. In recent years, significant strides have been made in developing cavity-optomechanics based approaches to generate optical frequency combs (FCs). In this study, we present an innovative approach, never explored before, that leverages elastomer membrane (EM)-cavity optomechanics to achieve the generation of soliton FCs, a highly sought-after phenomenon in the realm of nonlinear wave-matter interactions. Our method represents a significant breakthrough due to its streamlined simplicity, relying on a single continuous-wave (CW) laser pump and an externally applied acoustic wave exciting an EM-cavity, which gives rise to phonons, quantized vibrational energy states intrinsic to the elastomer's crystalline lattice structure. The mechanical resonator and electromagnetic cavity resonance are parametrically coupled within the microwave frequency range, collectively orchestrate the process of soliton FCs formation with remarkable efficiency. Numerical simulations and experimental observations demonstrate the emergence of multiple stable localized opto-mechanical wave packets, characterized by a narrow pulses time-domain response. Crucially, by setting the acoustic wave frequency to match the natural frequency of the EM resonator, the solitons' teeth are precisely spaced, and the EM's motion is significantly amplified, giving rise to a Kerr medium. The successful realization of optomechanical stable solitons represents a monumental advancement with transformative potential across various fields, including quantum computing and spectroscopy