Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

2021 ◽  
pp. 1-24
Author(s):  
Liguo Jin ◽  
Liting Du ◽  
Haiyan Wang
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Half Space ◽  
Strong Interaction ◽  
Rigid Foundation ◽  
Structural Stiffness ◽  
Sh Waves ◽  
Closed Form Analytical Solution ◽  
Flexible Foundation ◽  
Plane Sh Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

An Improved Analytical Model for Deflections of a Circular Multi-Layer Piezoelectric Actuator

2005 ◽  
Author(s):  
Mandar Deshpande ◽  
Laxman Saggere
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Piezoelectric Actuator ◽  
Plate Theory ◽  
Analytical Models ◽  
Sensors And Actuators ◽  
Closed Form Solutions ◽  
Design And Optimization ◽  
Closed Form Analytical Solution ◽  
Model Correlation

Models for simple closed-form analytical solutions for accurately predicting static deflections of circular thin-film piezoelectric microactuators are very useful in design and optimization of a variety of MEMS sensors and actuators utilizing piezoelectric actuators. While closed-form solutions treating actuators with simple geometries such as cantilevers and beams are available, simple analytical models treating circular bending-type actuators commonly used in MEMS applications are generally lacking. This paper presents a closed-form analytical solution for accurately estimating the deflections and the volume displacements of a circular multi-layer piezoelectric actuator under combined voltage and pressure loading. The model for the analytical solution presented in this paper, which is based on classical laminated plate theory, allows for inclusion of multiple layers and non-uniform diameters of various layers in the actuator including bonding and electrode layers, unlike other models previously reported in the literature. The analytical solution presented is validated experimentally as well as through a finite element solution and excellent experiment-model correlation within 1% variation is demonstrated. General guidelines for optimization of circular piezoelectric actuator are also discussed. The utility of the model for design optimization of a multi-layered piezoelectric actuator is demonstrated through a numerical example wherein the dimensions of a test actuator are optimized to improve the displaced volume by three-fold under combined voltage and resisting pressure loads.

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