Vibration Analysis of Magnetostrictive Composite Cantilever Resonators with Nonlocal Effects

Orcun Szemela^*
*Correspondence: Orcun Szemela, Department of Engineering Sciences, Izmir Katip Celebi University, Cigli, Izmir, Turkey, Izmir Katip Celebi University, Turkey, Email:

Introduction

Magnetostrictive materials exhibit unique properties that make them highly suitable for applications involving sensors, actuators, and energy harvesting devices. These materials can change their shape or dimensions in response to an applied magnetic field, making them attractive for use in composite structures, where the mechanical and magnetic responses can be precisely controlled. One area of interest in magnetostrictive materials is their application in cantilever resonators, which are widely used in various engineering fields, including vibration sensing, force measurement, and micro-electromechanical systems (MEMS). The vibration characteristics of magnetostrictive composite cantilever resonators have been extensively studied; however, many existing models fail to account for the nonlocal effects, which can significantly influence the resonator's behavior, especially at the micro- and nano-scales. In the traditional theory of elasticity, the material is assumed to have a local response to external forces, meaning that the stress at any point within the material is influenced only by the strain at that same point. However, recent studies have shown that this assumption does not always hold true, especially when dealing with materials at smaller scales, where long-range interactions between particles or atoms can no longer be neglected. The nonlocal elasticity theory, which accounts for these long-range interactions, has gained prominence as a more accurate representation of the material behavior at micro- and nanoscales.

Description

In the context of magnetostrictive composite cantilever resonators, nonlocal effects can have a profound impact on the vibration characteristics of the system. Nonlocal elasticity modifies the classical equations of motion by introducing a higher-order term, which reflects the influence of distant points in the material on the local stress-strain relationship. This results in changes to the resonant frequencies, mode shapes, and damping characteristics of the cantilever resonator. The study of vibration behavior in such systems, considering nonlocal effects, is crucial for optimizing the design and performance of magnetostrictive devices in precision applications. The behavior of magnetostrictive composite cantilever resonators can be analyzed using a combination of theoretical models and numerical methods. To study the vibration characteristics, the governing equations must be formulated based on the principles of magnetostrictive materials, which couple the mechanical deformation with the magnetic field. These equations typically involve the magnetostrictive strain tensor, which represents the strain generated in the material due to changes in the magnetic field. In addition, the equations must also account for the elastic properties of the composite material, including both the matrix and the embedded magnetostrictive phase [1]. When considering nonlocal effects, the classical elasticity theory must be modified to include a nonlocal stress-strain relationship. In this framework, the stress at a given point is not only dependent on the strain at that point but also on the strain at surrounding points within the material. This nonlocal influence is typically modeled using a length scale parameter, which quantifies the extent of the nonlocal interaction. The governing equations for the vibration analysis of magnetostrictive composite cantilever resonators must therefore include both the local elastic properties of the material and the nonlocal interactions, leading to a more complex set of differential equations. The vibration analysis of these resonators is typically performed using Finite Element Analysis (FEA) or other numerical techniques, which can solve the complex differential equations that govern the system's behavior. These methods allow for the prediction of resonant frequencies, vibration modes, and the effects of various parameters, such as the nonlocal length scale, the material properties of the composite, and the external magnetic field. The finite element model can be implemented to simulate the behavior of the resonator under various conditions, and the results can be compared with experimental data to validate the theoretical predictions [2]. The introduction of nonlocal effects into the vibration analysis of magnetostrictive composite cantilever resonators significantly alters the results when compared to classical models. For example, the resonant frequencies of the system are typically reduced when nonlocal effects are included, particularly for smaller length scales. This reduction in frequency is due to the increased influence of distant points within the material, which leads to a redistribution of the strain and stress within the resonator. Similarly, the mode shapes of the resonator can also be modified by nonlocal effects, with changes in the deformation patterns observed at higher modes. These changes are particularly noticeable in composite materials, where the coupling between the magnetostrictive phase and the matrix phase can amplify the effects of nonlocal interactions. One of the key challenges in studying the vibration characteristics of magnetostrictive composite cantilever resonators with nonlocal effects is the determination of the appropriate length scale parameter for the nonlocal elasticity theory. This parameter depends on the material properties and the scale of the resonator and must be determined experimentally or through calibration with more detailed molecular or atomicscale models. The length scale plays a critical role in governing the magnitude of the nonlocal interactions, with larger length scales leading to stronger effects on the material's behavior. For most practical applications, the length scale is relatively small, but for micro- and nano-scale resonators, these effects can become significant and must be carefully accounted for in the design process In addition to nonlocal effects, other factors can influence the vibration characteristics of magnetostrictive composite cantilever resonators. These include the geometry of the cantilever, the composition of the composite material, and the intensity and direction of the applied magnetic field. For instance, the shape and size of the cantilever can have a significant impact on the resonant frequencies, with longer cantilevers typically exhibiting lower resonant frequencies. Similarly, the magnetic properties of the composite, including the magnetostriction constant and the coupling between the magnetostrictive phase and the matrix phase, can influence the vibration behavior. The applied magnetic field itself can also induce additional strains within the material, leading to changes in the resonant frequencies and mode shapes. Experimental studies have been conducted to validate the theoretical models and numerical simulations of magnetostrictive composite cantilever resonators with nonlocal effects. These experiments typically involve measuring the resonant frequencies and mode shapes of the resonator under varying magnetic fields and geometries. The results can be used to determine the material properties, including the magnetostrictive coefficients and the nonlocal length scale, and to assess the accuracy of the theoretical predictions. In some cases, these experiments have revealed significant discrepancies between classical and nonlocal models, further highlighting the importance of accounting for nonlocal effects in the design of magnetostrictive devices.

Conclusion

The inclusion of nonlocal effects in the vibration analysis of magnetostrictive composite cantilever resonators also has implications for their practical applications. For instance, in the design of sensors and actuators, the nonlocal behavior of the resonator must be carefully considered to ensure accurate and reliable performance. The sensitivity of the resonator to external magnetic fields, temperature variations, and mechanical stresses can be influenced by the nonlocal interactions, and these factors must be accounted for in the design process. In addition, nonlocal effects can also play a role in the performance of energy harvesting devices, where the resonant frequency of the cantilever must be matched to the frequency of the external vibrations for optimal energy conversion. In conclusion, the vibration analysis of magnetostrictive composite cantilever resonators with nonlocal effects represents a significant advancement in the study of these materials and their applications. By incorporating nonlocal elasticity into the models, a more accurate representation of the resonator's behavior at small scales is obtained, leading to improved design and performance of magnetostrictive devices. The inclusion of nonlocal effects alters the resonant frequencies, mode shapes, and damping characteristics of the resonator, and must be carefully considered in the design process to optimize the performance of sensors, actuators, and energy harvesting devices. As research in this area continues to advance, it is expected that the role of nonlocal effects in magnetostrictive composites will become increasingly important in the development of next-generation microand nano-scale devices.

References

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