Design for 1:2 Internal Resonances in In-Plane Vibrations of Plates With Hyperelastic Materials

2013 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Strain Energy ◽  
Quadratic Function ◽  
The Body ◽  
Energy Potential ◽  
Internal Resonances ◽  
Element Analysis ◽  
Hyperelastic Materials ◽  
Aerial Vehicle

With advances in technology, hyperelastic materials are seeing increased use in varied applications ranging from microfluidic pumps, artificial muscles to deformable robots. They have also been proposed as materials of choice in the construction of components undergoing dynamic excitation such as the wings of a micro-unmanned aerial vehicle or the body of a serpentine robot. Since the strain energy potentials of various hyperelastic materials are more complex than quadratic, exploration of their nonlinear dynamic response lends itself to some interesting consequences. In this work, a structure made of a Mooney-Rivlin hyperelastic material and undergoing planar vibrations is considered. Since the stresses developed in a Mooney-Rivlin material are at least a quadratic function of strain, a possibility of 1:2 internal resonance is explored. A Finite Element Method (FEM) formulation implemented in Matlab is used to iteratively modify a base structure to get its first two natural frequencies close to the ratio 1:2. Once a topology of the structure is achieved, the linear modes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the hyperelastic structure can be used to develop a nonlinear two-mode model of the structure. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. It is shown that the strain energy potential for the Mooney-Rivlin material makes it possible for internal resonance to occur in such structures.

Design for 1:2 Internal Resonances in In-Plane Vibrations of Plates With Hyperelastic Materials

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Internal Resonance ◽  
Strain Energy ◽  
The Body ◽  
Hyperelastic Material ◽  
Nonlinear Material ◽  
Mode Shapes ◽  
Energy Potential ◽  
Hyperelastic Materials

With advances in technology, hyperelastic materials are seeing use in varied applications ranging from microfluidic pumps, artificial muscles to deformable robots. Development of such complex devices is leading to increased use of hyperelastic materials in the construction of components undergoing dynamic excitation such as the wings of a micro-unmanned aerial vehicle or the body of a serpentine robot made of hyperelastic polymers. Since the strain energy potentials of various hyperelastic material models have nonlinearities present in them, exploration of their nonlinear dynamic response lends itself to some interesting consequences. In this work, a structure made of a Mooney–Rivlin hyperelastic material and undergoing planar vibrations is considered. Since the Mooney–Rivlin material's strain energy potential has quadratic nonlinearities, a possibility of 1:2 internal resonance is explored. A finite element method (FEM) formulation implemented in Matlab is used to iteratively modify a base structure to get its first two natural frequencies close to the 1:2 ratio. Once a topology of the structure is achieved, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete nonlinear Lagrangian formulation of the hyperelastic structure can be used to develop a nonlinear two-mode dynamic model of the structure. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. It is shown that the nonlinear strain energy potential for the Mooney–Rivlin material makes it possible for internal resonance to occur in such structures. The effect of nonlinear material parameters on the dynamic response is investigated.

scholarly journals Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

2012 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Optimization Techniques ◽  
Mode Shapes ◽  
Nonlinear Phenomena ◽  
Mems Devices ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Element Analysis ◽  
Resonant Structures

Nonlinear phenomena such as internal resonances have significant potential applications in Micro Electro Mechanical Systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance as well as are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer’s prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal interactions) computationally. In this work, a preliminary method for computer based synthesis of structures consisting of beams for desired internal resonance is presented. The linear structural design is accompalished by a Finite Element Method (FEM) formulation implemented in Matlab to start with a base structure and iteratively modify it to obtain a structure with the desired properties. Possible design criteria are having the first two natural frequencies of the structure in some required ratio (such as 1:2 or 1:3). Once a topology of the structure is achieved that meets the desired criterion (i.e., the program converges to a definite structure), the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the nonlinear elastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. Many candidate structures are synthesized that meet the desired modal frequency criterion and their nonlinear responses are compared.

Finite Bending and Straightening of Hyperelastic Materials: Analytical Solution and FEM

2019 ◽  
Vol 11 (09) ◽  
pp. 1950084 ◽  
Author(s):  
Sara Sheikhi ◽  
Mohammad Shojaeifard ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Optimization Procedure ◽  
Element Analysis ◽  
Energy Functions ◽  
Hyperelastic Materials ◽  
Finite Bending ◽  
Strain Energy Functions ◽  
Analytical Approaches

In this research, an incompressible, isotropic, nonlinear elastic rectangular block and a circular cylindrical sector are studied under bending and straightening moments, respectively. Analytical approaches are presented on implementing of the left Cauchy–Green tensor and Cauchy stresses. In addition, finite element analysis of both problems is carried out using UHYPER user-defined subroutine in ABAQUS to verify the analytical methods. Four different invariant-based strain energy functions, including neo-Hookean, Mooney–Rivlin, Arruda–Boyce, and recently proposed polynomial Exp-Exp models, are examined, and the results are compared. Material parameters of silicon rubber for the strain energy functions are identified by applying an optimization procedure. Finite element method results confirmed the analytical approach with great compatibility. Results showed that the length of the unbent beam does not affect the stress. Likewise, the initial angle of curved structure does not affect the unbending moment and stresses. Moreover, the Exp-Exp model had a slightly different result rather than other strain energies, which means that this model is more conservative than its counterparts. Furthermore, the Exp-Exp strain energy function is calibrated for tissue-like phantom and is compared with experimental data.

scholarly journals Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Optimization Techniques ◽  
Mode Shapes ◽  
Nonlinear Phenomena ◽  
Mems Devices ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Element Analysis ◽  
Resonant Structures

Nonlinear phenomena such as internal resonances have significant potential applications in micro electro mechanical systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance and that are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer's prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal interactions) computationally. In this work, a preliminary work on computer based synthesis of structures consisting of beams for desired internal resonance is presented. The linear structural design is accomplished by a Finite Element Method (FEM) formulation implemented in Matlab to start with a base structure and iteratively modify it to obtain a structure with the desired properties. Possible design criteria are having the first two natural frequencies of the structure in some required ratio (such as 1:2 or 1:3). Once a topology of the structure is achieved that meets the desired criterion, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the nonlinear elastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. Many candidate structures are synthesized that meet the desired modal frequency criterion and their nonlinear responses are compared.

Finite Element Analysis of some Radial Tire

2012 ◽  
Vol 490-495 ◽  
pp. 2414-2418 ◽  
Author(s):  
Jian Zhang ◽  
Guo Lin Wang ◽  
Nai Ji Fu ◽  
Kui Wang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Energy ◽  
Energy Potential ◽  
Element Analysis ◽  
Radial Tire ◽  
Mechanism Model ◽  
Static Contact ◽  
Shearing Strain ◽  
Critical Regions

Based on some radial tire, Yeoh mechanism model and rebar model are used to simulate rubber and cord. Finite element analysis was used to simulate assembly, shrink, inflated pressure and vertical load case, the process of tire-ground under static contact was analyzed. The computing results were compared with experiments. Mises stress, shearing strain and strain energy potential are used to estimate the critical regions of the tire.

Design for Internal Resonances in Nonlinear Transverse Vibrations of Hyperelastic Plates

2013 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Optimization Techniques ◽  
Mode Shapes ◽  
Nonlinear Phenomenon ◽  
Mems Devices ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Element Analysis ◽  
Nonlinear Properties

Nonlinear phenomenon such as internal resonance have significant potential applications in Micro Electro Mechanical Systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance as well as are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer’s prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal frequencies in certain ratios) computationally. In this work, plate structures which are candidates for internal resonances are obtained using a Finite Element Method (FEM) formulation implemented in Matlab to iteratively modify a base structure to get its first two natural frequencies close to the desired ratio (1:2 or 1:3). Once a structure with desired topology is achieved, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the Hyperelastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes, and the nonlinear response can be obtained by application of perturbation methods such as averaging on the two-mode model.

Rigid-Plastic Finite Element Simulation of Cold Forging and Sheet Metal Forming by Eulerian Meshing Method

2014 ◽  
Vol 970 ◽  
pp. 177-184 ◽  
Author(s):  
Wen Chiet Cheong ◽  
Heng Keong Kam ◽  
Chan Chin Wang ◽  
Ying Pio Lim
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Large Deformation ◽  
Sheet Metal ◽  
Metal Forming ◽  
The Body ◽  
Cold Forging ◽  
Rigid Plastic ◽  
Element Analysis ◽  
Linear Solution

A computational technique of rigid-plastic finite element method by using the Eulerian meshing method was developed to deal with large deformation problem in metal forming by replacing the conventional way of applying complicated remeshing schemes when using the Lagrange’s elements. During metal forming process, a workpiece normally undergoes large deformation and causes severe distortion of elements in finite element analysis. The distorted element may lead to instability in numerical calculation and divergence of non-linear solution in finite element analysis. With Eulerian elements, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. Four types of cold forging and sheet metal clinching were conducted to investigate the effectiveness of the presented method. The proposed method is found to be effective by comparing the results on dimension of the final product, material flow behaviour and punch load versus stroke obtained from simulation and experiment.

An Improved Control Arm Design for a Commercial Vehicle

2021 ◽  
Author(s):  
Sinan Yıldırım ◽  
Ufuk Çoban ◽  
Mehmet Çevik
Keyword(s):  
Finite Element ◽  
Cost Effective ◽  
Element Model ◽  
Tensile Tests ◽  
The Body ◽  
Von Mises Stress ◽  
Driving Safety ◽  
Design Development ◽  
Element Analysis ◽  
Von Mises

Suspension linkages are one of the fundamental structural elements in each vehicle since they connect the wheel carriers i.e. axles to the body of the vehicle. Moreover, the characteristics of suspension linkages within a suspension system can directly affect driving safety, comfort and economics. Beyond these, all these design criteria are bounded to the package space of the vehicle. In last decades, suspension linkages have been focused on in terms of design development and cost reduction. In this study, a control arm of a diesel public bus was taken into account in order to get the most cost-effective design while improving the strength within specified boundary conditions. Due to the change of the supplier, the control arm of a rigid axle was redesigned to find an economical and more durable solution. The new design was analyzed first by the finite element analysis software Ansys and the finite element model of the control arm was validated by physical tensile tests. The outputs of the study demonstrate that the new design geometry reduces the maximum Von Mises stress 15% while being within the elastic region of the material in use and having found an economical solution in terms of supplier’s criteria.

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