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Kinematics and Inverse Dynamics
Published in Parviz E. Nikravesh, Planar Multibody Dynamics, 2018
The equations of motion for a mechanical system represent the relationship between the forces that act on the system and its motion. If a specified motion of a mechanical system is sought and some of the applied forces and moments are known, it could be possible to determine the remaining forces and moments that cause that particular motion. When the desired motion is known and the objective is to find the unknown forces and torques, the process is referred to as inverse dynamic analysis. Inverse dynamics is an extension of kinematic analysis in which the reaction forces and the unknown forces or torques associated with the driver constraints are determined. The fundamental process for inverse dynamic analysis is the same, regardless of the method used to formulate a problem.
Stress analysis and thermoelastic instability of an annular functionally graded rotating disk
Published in Journal of Thermal Stresses, 2022
Hassan Bahaloo, Hamid Nayeb-Hashemi
The aim of this study is to realize the effects of thermal loading on the vibration and stability characteristics of clamped-free FG rotating disks with a constant thickness. For the transverse vibration of disk, we first use a semi-analytical method to find the radial and hoop stresses in a centrally clamped and peripherally free FG annular rotating disk based on linearized strains. The out of plane equations of motion of the FG rotating disk are developed by exploiting solution periodicity to transform the time dependent partial differential equation of motion into an ordinary differential equation in space. A finite difference scheme is then used to find the natural frequencies and mode shapes. The first critical speed is also obtained by constructing the Campbell Diagram. The stability margins are trace by real parts of the eigen values.
An index 0 differential-algebraic equation formulation for multibody dynamics: Nonholonomic constraints
Published in Mechanics Based Design of Structures and Machines, 2018
The paper is organized as follows. Tangent space parameterizations of configuration and velocity spaces are presented in Section 2, satisfying both holonomic and nonholonomic constraints. A system of index 0 DAE is derived in Section 3 that includes (i) first-order kinematic equations in configuration generalized coordinates and (ii) first-order kinetic equations of motion in velocity generalized coordinates. A numerical algorithm is presented in Section 4 for integrating the equations of motion using explicit numerical integration algorithms. Derivatives required for implicit numerical integration of the index 0 DAE are presented in Section 5. Trapezoidal and singly diagonal Runge–Kutta (SDIRK) implicit algorithms for numerical solution are presented in Section 6. Three examples are presented in Sections 7–9, a planar two chassis articulated vehicle with wheels that roll without slip and two spatial systems, including roll without slip of a disk on a horizontal surface and a three-wheel motorcycle whose wheels roll without slip. Conclusions are presented in Section 10. Euler parameter identities used in the paper are summarized in Appendix B of the companion paper (Haug, 2016).
Vibration analysis of a porous hollow conical rotor with circumferentially distributed piezoceramic strips
Published in Mechanics Based Design of Structures and Machines, 2022
Mohammad Jafari Niasar, Mohammad Javad Babaei, Ali Asghar Jafari, Mohsen Irani Rahaghi
The kinetic and potential energies are calculated for the porous rotor and each piezoceramic, separately, considering Coriolis and centrifugal effects. Afterwards, acquired energies are discretizes by means of displacement field which is made up of double mixed series. In this order the governing equations of motion are obtained using the Lagrange method in form of ordinary differential equation. To compute the forward and backward natural frequencies, the equations are converted to special state-space form, then eigenvalue problem is solved. Also, the accuracy of modeling and obtained equations is investigated by comparing the results of this study with other research. Finally, the most influential parameters on natural frequency such as piezoceramic angular pitch and thickness, porosity coefficient and different porosity patterns, and rotor’s angular velocity in various circumferential and longitudinal modes are studied and analyzed. According to above explanations, the major purpose of this article, which distinguishes it from other studies, is to investigate the effect of piezoceramic patches and porosity of the rotor with three different patterns on the vibrational behavior of the system. Generally, the novelties include the following:Modeling of a porous hollow conical rotor with sensor and actuator in the form of ODEInvestigating the effect of sensors and actuators strip on porous hollow conical rotorObtaining the mode shapes of the systemComputing the natural frequencies based on the special state-space model