Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Simulation of Differentials in Four-Wheel Drive Vehicles Using Multibody Dynamics

The dynamic performance of vehicle drivetrains is significantly influenced by differentials which are subjected to complex phenomena. In this paper, detailed models of TORSEN differentials are presented using a flexible multibody simulation approach, based on the nonlinear finite element method. A central and a front TORSEN differential have been studied and the numerical results have been compared with experimental data obtained on test bench. The models are composed of several rigid and flexible bodies mainly constrainted by flexible gear pair joints and contact conditions. The three differentials of a four wheel drive vehicle have been assembled in a full drivetrain in a simplified vehicle model with modeling of driveshafts and tires. These simulations enable to observe the four working modes of the differentials with a good accuracy.

On the Application of the Lu-Gre Model to Simulate Joint Friction in Multi-Body Systems

Advances in the application of multi-body simulation technology to real world problems have led to an ever increasing demand for higher fidelity modeling techniques. Of these, accurate modeling of friction is of strategic interest in applications such as control system design, automotive suspension analysis, robotics etc. Joints (sometimes referred to as constraints) play an important role in defining the dynamics of a multi-body system. Hence, it is imperative to accurately account for friction forces arising at these joints due to the underlying interface dynamics. In this paper, we discuss the application of LuGre, a dynamic friction model to simulate joint friction. We choose the LuGre model due to its ability to capture important effects such as the Stribeck effect and the Dahl effect. The native 1-d LuGre model is extended to formulate friction computations for non-trivial joint geometries and dynamics in 2 and 3 dimensions. It is also extended to work in the quasi-static regime. Specific applications to revolute, cylindrical and spherical joints in multi-body systems are discussed. Finally, an engineering case study on the effects of joint friction in automotive suspension analysis is presented.

Trajectory Tracking of Underactuated Multibody Systems

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Subharmonic Resonance Cascades in a Class of Coupled Resonators

We consider a chain of N nonlinear resonators with natural frequency ratios of approximately 2:1 along the chain and weak nonlinear coupling of a form that allows energy to flow between resonators. Specifically, the coupling is such that the response of one resonator parametrically excites the next resonator in the chain, and also creates a resonant backaction on the previous resonator in the chain. This class of systems, which is being proposed for micro-electro-mechanical frequency dividers, is shown to have rich dynamical behavior. Of particular interest is the case when the high frequency end of the chain is resonantly excited, and coupling results in the potential for a cascade of sub-harmonic bifurcations down the chain. When the entire chain is activated, that is, when all N resonators have non-zero amplitudes, if the input frequency on the first resonator is Ω, then the terminal resonator responds with frequency Ω/2N. The details of the activation depend on the strength and frequency of the input, the level of resonator dissipation, and the mistuning in the chain. In this paper we present analytical results, based on perturbation methods, which provide useful predictions about these responses in terms of system and input parameters. Parameter conditions for activation of the entire chain are derived, along with results about other phenomena, such as bistability and partial activation of the chain. We demonstrate the utility of the predictive results by direct comparison with simulations of the equations of motion, and we also present samples of mechanical and electromechanical systems that realize the desired properties. These results will be useful for the design and operation of mechanical frequency dividers based on subharmonic resonances.

Advanced System Identification of Plates Using a Higher-Order-Spectral Approach: Theory and Experiment

A nonlinear system identification technique exploiting the dynamic response features of fully nonlinear physics-based plate models extracted by Higher-Order Spectral (HOS) analysis tools is developed. The changes induced by an imperfection in the dynamics through the structural nonlinearities are used as key detection mechanism. The differences in dynamic response of a baseline and a modified/imperfect structure are enhanced by the local nonlinearities induced by the structural modification which thus represent the specific objective of identification. The validation of the procedure and the developed algorithms is carried out through extensive experimental testing employing various plates, including isotropic and composite lay-ups, and excitation sources, including White Gaussian Noise and a train of impulses.

A Model for Highly Strained DNA in a Cavity

A single DNA molecule is a long and flexible biopolymer that contains the genetic code. Building upon the discovery of the iconic double helix over 50 years ago, subsequent studies have emphasized how its biological function is related to the mechanical properties of the molecule. A remarkable system which high-lights the role of DNA bending and twisting is the packing and ejection of DNA into and from viral capsids. A recent 3D reconstruction of bacteriophage φ29 reveals a novel toroidal structure thought to be 30–40 bp of highly bent/twisted DNA contained in a small cavity below the capsid. Here, we extend an elastic rod model for DNA to enable simulation of the toroid as it is compacted and subsequently ejected from a small volume. We compute biologically-realistic forces required to form the toroid and predict ejection times of several nanoseconds.

Kinematics and Dynamics of a Sliding/Bouncing Two Mass System

This paper presents the solution of the impact problem for a sliding/bouncing baton on flat and inclined planes subject to surface friction. The baton is assumed to have unilaterally constrained motion, which means one end slides on the ground while the other end collides with the ground. We use the impulse momentum approach and incorporate the impulse correlation ratio (ICR) hypothesis to solve the ground impact problem when the system has unilaterally constrained dynamics. Parametric investigations were carried out to examine the effect of the baton’s length and the inclined wall slope angle on the impulse correlation ratio. Numerical simulation and experiments were carried out to validate the model.

Multibody Dynamics in Generalized Divide and Conquer Algorithm (GDCA) Scheme

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Fast Electrostatic Force and Moment Calculations in Multibody-Based Simulations of Coarse-Grained Biopolymers

In molecular simulations, the dominant portion of the computational cost is associated with force field calculations. Herein, we extend the approach used to approximate long range gravitational force and the associated moment in spacecraft dynamics to the coulomb forces present in coarse grained biopolymer simulations. We approximate the resultant force and moment for long-range particle-body and body-body interactions due to the electrostatic force field. The resultant moment approximated here is due to the fact that the net force does not necessarily act through the center of mass of the body (pseudoatom). This moment is considered in multibody-based coarse grain simulations while neglected in bead models which use particle dynamics to address the dynamics of the system. A novel binary divide and conquer algorithm (BDCA) is presented to implement the force field approximation. The proposed algorithm is implemented by considering each rigid/flexible domain as a node of the leaf level of the binary tree. This substructuring strategy is well suited to coarse grain simulations of chain biopolymers using an articulated multibody approach.