Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part 1: Nonlinear Anisotropic Piezothermoelastic Shell Laminates

1997 ◽  
Vol 119 (3) ◽  
pp. 374-381 ◽  
Author(s):  
H. S. Tzou ◽  
Y. Bao
Keyword(s):  
Geometric Nonlinearity ◽  
Large Deformations ◽  
Geometrical Nonlinearity ◽  
Dynamic Control ◽  
Temperature Fields ◽  
Nonlinear Characteristics ◽  
Temperature Variations ◽  
Laminated Circular Plate ◽  
Lamination Theory ◽  
Nonlinear Components

Nonlinear characteristics, either material or geometrical nonlinearity, and temperature variations can significantly influence the performance and reliability of piezoelectric sensors, actuators, structures, and systems. This paper is intended to examine the nonlinear piezothermoelastic characteristics and temperature effects of piezoelectric laminated systems, and it is divided into two parts. Part 1 is concerned with a mathematical modeling of nonlinear anisotropic piezothermoelastic shell laminates and Part 2 is a study of static and dynamic control of a nonlinear piezoelectric laminated circular plate subjected to mechanical, electric, and temperature excitations. Geometric nonlinearity induced by large deformations is considered in both parts. A generic nonlinear piezothermoelastic shell lamination theory is proposed and its nonlinear thermo-electromechanical equations are derived based on Hamilton’s principle. Thermo-electromechanical couplings among the elastic, electric, and temperature fields are discussed, and nonlinear components identified. Applications of the nonlinear theory to other materials, continua, sensors, actuators, and linear systems are discussed.

On Free Vibrations at Temperature-Dependent Material Properties and Transient Temperature Fields

1972 ◽  
Vol 39 (3) ◽  
pp. 723-726 ◽  
Author(s):  
U. Olsson
Keyword(s):  
Temperature Dependence ◽  
Analytical Solutions ◽  
Material Properties ◽  
Free Vibrations ◽  
Temperature Fields ◽  
Transient Temperature ◽  
Material Damping ◽  
Temperature Dependent ◽  
Temperature Variations ◽  
Damping Parameter

The influence of the temperature-dependence of the material properties on the free vibrations of transiently heated structures is investigated. Analytical solutions are given for linear, exponential, and harmonic temperature variations when the material damping parameter, Poisson’s ratio, and Young’s modulus depend on the temperature.

scholarly journals Multistable Morphing Mechanisms of Nonlinear Springs

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Chrysoula Aza ◽  
Alberto Pirrera ◽  
Mark Schenk
Keyword(s):  
Design Space ◽  
Large Deformations ◽  
Compliant Mechanisms ◽  
Helical Structures ◽  
Nonlinear Springs ◽  
Structural Assembly ◽  
Stiffness Characteristics ◽  
Nonlinear Components ◽  
Type Of Behavior ◽  
Initial Geometry

Compliant mechanisms find use in numerous applications in both microscale and macroscale devices. Most of the current compliant mechanisms base their behavior on beam flexures. Their range of motion is thus limited by the stresses developed upon deflection. Conversely, the proposed mechanism relies on elastically nonlinear components to achieve large deformations. These nonlinear elements are composite morphing double-helical structures that are able to extend and coil like springs, yet, with nonlinear stiffness characteristics. A mechanism consisting of such structures, assembled in a simple truss configuration, is explored. A variety of behaviors is unveiled that could be exploited to expand the design space of current compliant mechanisms. The type of behavior is found to depend on the initial geometry of the structural assembly, the lay-up, and other characteristics specific of the composite components.

Prediction of Periodic Response of Flexible Mechanical Systems With Nonlinear Characteristics

1990 ◽  
Vol 112 (4) ◽  
pp. 501-507 ◽  
Author(s):  
Ting-Nung Shiau ◽  
An-Nan Jean
Keyword(s):  
Nonlinear Differential Equations ◽  
System Response ◽  
Algebraic Equations ◽  
Nonlinear Characteristics ◽  
Periodic Response ◽  
Rotor Systems ◽  
Nonlinear Algebraic Equations ◽  
Numerical Analytical Method ◽  
Harmonic Components ◽  
Nonlinear Components

A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotordynamic systems is addressed. Using this method, the set of nonlinear differential equations governing the motion of the rotor systems is transformed to a set of nonlinear algebraic equations. A condensation technique is proposed to reduce the nonlinear algebraic equations to those only related to the physical coordinates associated with nonlinear components. The method allows for the inclusion of searching for sub, super, ultra-sub and ultra-super harmonic components of the system response. Furthermore it can be used to locate limit cycles of an autonomous system. Three examples are employed to demonstrate the accuracy and the efficiency of the present method.

scholarly journals GEOMETRICAL NONLINEARITY ANALYSIS OF THE STEEL NETWORK ARCH BRIDGES / PLIENINŲ TINKLINIŲ ARKINIŲ TILTŲ GEOMETRINIO NETIESIŠKUMO VERTINIMAS

2016 ◽  
Vol 8 (5) ◽  
pp. 490-494
Author(s):  
Sigutė Žilėnaitė
Keyword(s):  
Geometric Nonlinearity ◽  
Geometrical Nonlinearity ◽  
Compressive Force ◽  
Work Conditions ◽  
Geometrical Factor ◽  
Principal Behavior ◽  
New Construction ◽  
Arch Bridges ◽  
The Individual ◽  
The City

Arch bridges are one of the popular, oldest and graceful bridges which are being built in zones of the city and out of the city. However arches becomes especially sensitive to their buckling response due to dominated compressive force in the arch. In order to ensure stability conditions of the individual arch and arch bridges, it is estimated not just geometrical factor of arch, residual stress, work conditions, geometric imperfections but geometrical nonlinearity too. Geometric nonlinearity especially dominates in many times static indeterminable systems such as network arch bridges. However there are a few represents of estimation of geometric nonlinearity of the new construction form of the arch bridges created in a middle of 20th century. This paper represents estimation of geometric nonlinearity with numerical method of the steel arch bridges with vertical hangers and network arch bridges. There are determined stress-strain law and principal behavior of the steel network arch bridges under symmetric and asymmetric pedestrian loadings. Arkiniai tiltai – vieni populiariausių, seniausių ir grakščiausių tiltų, statomų miesto ir užmiesčio zonose. Tačiau dėl dominuojančios ašinės gniuždymo jėgos arkos tampa ypač jautrios stabilumo praradimui. Siekiant užtikrinti pavienių arkų ir arkinių tiltų pastovumo sąlygas, vertinami ne tik arkos geometriniai rodikliai, darbo stadijos, pradiniai įtempiai, geometriniai netobulumai, bet ir netiesinė konstrukcijos elgsena. Geometrinis netiesiškumas ypač dominuoja daug kartų statiškai neišsprendžiamose sistemose, tokiose kaip tinkliniai arkiniai tiltai. Tačiau šios XX a. viduryje atsiradusios naujos arkinių tiltų konstrukcinės formos geometrinio netiesiškumo vertinimas pateiktas minimaliai. Straipsnyje pateikiamas plieninių arkinių tiltų su vertikaliomis pakabomis ir tinklinių arkinių tiltų geometrinio netiesiškumo vertinimas skaitiniais metodais. Nustatomas plieninių tinklinių arkinių tiltų įtempių-deformacijų būvis ir esminiai elgsenos ypatumai, veikiant simetrine ir asimetrine pėsčiųjų apkrovomis.

Geometrically Nonlinear Calculation of Trailing rod designs. Part 1. Calculation of flexible threads

10.12737/335 ◽  
2013 ◽  
Vol 1 (1) ◽  
pp. 7-17
Author(s):  
Андрей Свентиков
Keyword(s):  
Linear Model ◽  
Geometric Nonlinearity ◽  
Geometrical Nonlinearity ◽  
Constant Load ◽  
Geometrically Nonlinear ◽  
Flexible Rods ◽  
Nonlinear Matrix ◽  
Current Value ◽  
Special Case ◽  
Matrix Calculation

Is treated geometrically nonlinear matrix calculation core construction with the use of flexible threads. The first part is devoted to the study the major calculation dependencies of flexible threads. It is established that the geometric nonlinearity of flexible rods depends on the cube of the ratio of the calculation in a zero-offsets end stabilize relations to its current value. Also found that the constructive nonlinearity is a special case of geometrical nonlinearity and depends on the degree of impact on the VDS of flexible thread load on its own weight. It is found that the preliminary adjustment of the length of flexible rods leads to the increase of the share of the stresses of constant load and, accordingly, to the approximation of the nature of the work of these elements into a linear model.

Nonlinear Transient Analysis of Large Rotordynamic Systems

1991 ◽  
Vol 58 (2) ◽  
pp. 596-598 ◽  
Author(s):  
T. N. Shiau ◽  
A. N. Jean
Keyword(s):  
Degrees Of Freedom ◽  
Substantial Reduction ◽  
Computational Time ◽  
Solution Technique ◽  
Flexible Rotor ◽  
Nonlinear Characteristics ◽  
Rotor Systems ◽  
Nonlinear Transient ◽  
Nonlinear Components ◽  
Flexible Rotor Systems

A solution technique based on implicit numerical integration combined with a condensation technique is presented to predict the transient response of large flexible rotor systems with nonlinear characteristics. The analysis directly tackles the nonlinear second-order differential equations which describe the system motion. The condensation technique can lead to a reduced model in which only the coordinates associated with nonlinear components of the system are considered. Thus, a substantial reduction of computation can be expected if the nonlinear components of system are sparse. A flexible rotor system is studied to illustrate the merits of the procedures. The results show that, if the system is of a small number of coordinates associated with nonlinear components compared to that of entire system degrees-of-freedom, the computational time can be considerably reduced using this technique.

scholarly journals MODELING THE BEHAVIOR OF THE PHYSICAL AND GEOMETRIC NON-LINEAR FUNCTIONAL HETEROGENEOUS MATERIALS

2021 ◽  
Vol 1 (45) ◽  
pp. 82
Author(s):  
K. Domichev
Keyword(s):  
Geometric Nonlinearity ◽  
Large Deformations ◽  
Heterogeneous Materials ◽  
Spline Functions ◽  
Large Strains ◽  
Strain Rates ◽  
Inhomogeneous Materials ◽  
Physical Relationship ◽  
Small Deformations ◽  
Cauchy Relations

The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions

The Nonlinear Dynamics of Long, Slender Cylinders

1984 ◽  
Vol 106 (2) ◽  
pp. 250-256 ◽  
Author(s):  
Y. C. Kim ◽  
M. S. Triantafyllou
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Geometric Nonlinearity ◽  
Linear Problem ◽  
Large Deformations ◽  
Nonlinear Ordinary Differential Equations ◽  
Wkb Method ◽  
Fluid Drag ◽  
Nonlinear Fluid

The nonlinear dynamics of long, slender cylinders for moderately large deformations are studied by projecting the solution along the set of eigenmodes of the linear problem. The resulting set of nonlinear ordinary differential equations is truncated on the basis of bandlimited response. The efficiency of the method is due to the derivation of asymptotic solutions for the linear problem in its general form, by using the WKB method. Applications for the dynamics of risers, including the effects of nonlinear fluid drag and geometric nonlinearity demonstrate the features of the method.

scholarly journals Effect of Geometric Nonlinearity on Membrane Roof Stability in Air Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Weiju Song ◽  
Jun Xu ◽  
Xiaowei Wang ◽  
Changjiang Liu
Keyword(s):  
Geometric Nonlinearity ◽  
Geometrical Nonlinearity ◽  
Reference Value ◽  
Single Mode ◽  
Small Mass ◽  
Wind Load ◽  
Strong Wind ◽  
Membrane Structures ◽  
Open Structures ◽  
High Flexibility

Membrane materials are widely used in construction engineering with small mass and high flexibility, which presents strong geometric nonlinearity in vibration. In this paper, an improved multiscale perturbation method is used to solve the aerostatics stability of membrane roofs on closed and open structures by quantifying the effect of geometric nonlinearity on the single-mode aeroelastic instability wind velocity. Results show that the critical wind velocities of two models are smaller when the geometrical nonlinearity of the membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of the membrane on the aerodynamic stability of the roof can be neglected. However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of the membrane roof. The results obtained in this paper have an important theoretical reference value for the design membrane structures.

Analytic Models for Temperature Distribution Near a Nanoantenna

2013 ◽  
Author(s):  
Casey N. Brock ◽  
Greg Walker ◽  
Zack Coppens
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Temperature Fields ◽  
Analytic Model ◽  
Superposition Model ◽  
Metallic Structures ◽  
Temperature Variations ◽  
Temperature Distributions ◽  
Analytic Models

Thermoplasmonic structures produce highly localized temperature fields. For simplicity, researchers often use a superposition of representative spheres to model the temperature in the non-conductive region (presumably a substrate) near the metallic structures deposited on the substrate. The superposition model provides reasonable solutions, but direct comparison to experiments is difficult because local temperature variations at the nanoscale are not accessible. Moreover, the model requires several approximations. Therefore, we compare this model to other analytic models to determine the efficacy of the superposition approach in capturing temperature distributions close to the surface of the substrate and to capture realistic boundary conditions. Results indicate that a 3D analytic model can relax approximations required for the superposition model and show that the superposition model consistently over-predicts the surface temperature.

Sign in / Sign up

Export Citation Format

Share Document