scholarly journals Application of a Novel Picard-Type Time-Integration Technique to the Linear and Non-Linear Dynamics of Mechanical Structures: An Exemplary Study

2021 ◽  
Vol 11 (9) ◽  
pp. 3742
Author(s):  
Evgenii Oborin ◽  
Hans Irschik
Keyword(s):  
Time Integration ◽  
Harmonic Excitation ◽  
Free Vibrations ◽  
Observation Time ◽  
Double Pendulum ◽  
Integration Technique ◽  
Linear Dynamics ◽  
Non Linear ◽  
Linear Vibrations ◽  
Numerical Time Integration

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods.

Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

2005 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Implicit Time ◽  
Linear Elastic ◽  
Time Integration Method ◽  
Thermal Fields ◽  
Non Linear ◽  
Linear Vibrations ◽  
The Time Domain ◽  
Constitutive Material

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

Random Wave Response of Double Pendulum Articulated Off-Shore Tower

2003 ◽  
Author(s):  
Nazrul Islam ◽  
Suhail Ahmad
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Time Integration ◽  
Power Spectra ◽  
Integration Scheme ◽  
Random Wave ◽  
Double Pendulum ◽  
Non Linear ◽  
Time Histories ◽  
Time Integration Scheme

Present study investigates the non-linear dynamic behavior of Double Hinged Articulated Tower (DHAT) under long crested random Sea and directional random sea. The non-linearities due to time wise variation of submergence, buoyancy, added mass, instantaneous tower orientation and resulting hydrodynamic loading have been taken into account for modeling the forcing functions of equation of motion which is derived by Largrangian approach. A long crested random sea has been modeled by Monte-Carlo Simulation using P-M spectrum. The non-linear equations of motion are solved by an iterative time integration scheme using Newmark’s β integration scheme. Various important parameters such as heel angles, deck displacements, base share for double hinged articulated tower under long and short crested random sea are compared and presented in the form of time-histories and their respective PSDFs. Statistical studies of random time histories have been carried out and important characteristics like mean, maxima, minima, standard deviations etc. have been analyzed. The dynamic behaviors have been investigated in detail in terms of various parametric combinations. Effect of current, and significant wave height are also studied. Sub and super harmonic excitations are highlighted through power spectra. A multi-hinged articulated tower is found to be economical and suitable for various offshore activities in adverse environmental and deep sea conditions.

Optimal Semi-active Control and Non-linear Dynamic Response of Variable Stiffness Structures

2005 ◽  
Vol 11 (10) ◽  
pp. 1253-1289 ◽  
Author(s):  
Emanuele Renzi ◽  
Maurizio De Angelis
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Initial Conditions ◽  
Variable Stiffness ◽  
Free Vibrations ◽  
Controlled System ◽  
Linear Dynamics ◽  
Control Approach ◽  
Non Linear ◽  
Non Linear System

In this paper we study the semi-active control of structural systems by means of variable stiffness devices, and the resulting non-linear dynamics of the controlled system. In particular, the study is applied to base-excited single-degree-of-freedom systems, controlled by variable ON–OFF elastic devices and subjected to simple motion conditions: free vibrations following initial conditions and stationary response to harmonic input. A performance index, which, in the case of base-excited structures, assumes an original dual formulation following the relative or absolute approaches, has been proposed for instantaneous optimal control. The study includes both the optimal control design and the observation of the resulting non-linear dynamics of the controlled system. The dynamic behavior of the controlled non-linear system is studied with respect to the parameters which characterize the algorithms, the control device, and the input. In this way, also by means of significant (and original) analytical solutions of the equations of motion, the optimal formulation of the algorithms, some particular behaviors of the controlled systems, and the performances of the control approach are shown and explained for the different control strategies.

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