Search

Designing quiet cars has become an important issue in the automotive industry, where passive and active noise control techniques can be employed to improve the acoustic comfort without compromising the vehicle performance. At the design stage of a noise control system, the estimation of the structure-borne sound pressure levels in the car cabin is a challenging problem, as uncertainties in a physical structural-acoustic system have an impact on the vehicle dynamics at high frequencies. Additionally, the response of the system can be affected by nonlinearities in the vibrations transmission path. Therefore, this research has been focused in developing computationally efficient vibro-acoustic models to predict the statistical structural-acoustic response of a system to random inputs, as well as analysing the degree of dependency of the response to nonlinear behaviour in the interface between the excitation and the structure. Key aspects of the impact that a nonlinear transmission path might have in the response of a statistical structural-acoustic system, were investigated from an equivalent damper model of the structural vibrating subsystem, under the assumption of weak acoustic coupling and the infinite plate theory. Numerical data in the time domain were generated from the simplified nonlinear system excited by random inputs with known power spectral density. The effects of nonlinearities were observed and quantified in the power spectral density of the response, as well as in the reduction of coherence between the input and output. Additionally, the Wiener theory in the frequency domain has been explored to estimate the degree of contribution of a nonlinearity of second order to the total response of the system. Finally, an extended hybrid Finite Element-Statistical Energy Analysis (FE-SEA) model was proposed to analyse the response of a deterministic-statistic structural-acoustic system, where the nonlinear transmission path is considered as a deterministic structure. The equations of an existing FE-SEA approach, based on the diffuse field reciprocity, have been generalised to include prescribed displacements as inputs, in addition to external forces. The nonlinear analysis with the FE-SEA approach has been carried out by adopting the concept of equivalent linearisation of the deterministic dynamic stiffness matrix, and the capability of the approach has been validated against experimental data from a physical nonlinear structural-acoustic setup.

This dissertation provides the foundation for an in-depth understanding and significant development of the tail-equivalent linearization method (TELM) to solve different classes of nonlinear random vibration problems. The TELM is a linearization method that uses the first-order reliability method (FORM) to define a tail-equivalent linear system (TELS) and to estimate the tail of the response distribution for nonlinear systems under stochastic inputs. The method was originally developed in the time domain for inelastic systems. It was later extended in the frequency domain for a specific class of nonlinear excitations, while the frequency domain version for inelastic systems is covered in the present work. This dissertation mathematically formalizes and extends TELM analysis with different types of discretization of the input process. A general formulation for discrete representation of a Gaussian band-limited, white-noise process is introduced, which employs the sum of deterministic and orthogonal basis functions weighted by random coefficients. The selection of the basis functions completely defines the two types of discretizations used in the earlier works. Specifically, a train of equally spaced time delta-Dirac functions leads to the current time-domain discretization, while harmonic functions with equally spaced frequencies lead to the current frequency-domain discretization. We show that other types of orthogonal basis functions can be used with advantage to represent a Gaussian band-limited white noise and in particular we employ sinc basis functions, which are at the base of the Whittaker-Shannon interpolation formula. We demonstrate that this representation is suitable for reducing the total number of random variables that are necessary to describe the process, since it decouples the computational-time discretization from the band-limit of the process. Next, the dissertation tackles the problem of a nonlinear system subjected to multi-component excitations by defining an augmented standard normal space composed of all the random variables that define the multiple components of the excitation. The tail-equivalent linearization and definition of the TELS is taken in this new space. Once the augmented TELS is defined, response statistics of interest are determined by linear random vibration analysis by superposition of responses due to each component of the excitation. The method is numerically examined for an asymmetric structure with varying eccentricity and subjected to two statistically independent components of excitation. Several practical problems require analysis for non-stationary excitations. For this important class of problems the original TELM requires linearization for a series of points in time to study the evolution of response statistics. This procedure turns out to be computationally onerous. As an approximate alternative, we propose the evolutionary TELM, ETELM. In particular, we adopt the concepts of the evolutionary process theory, to define an evolutionary TELS, ETELS. The ETELS approximately estimates the continuous time evolution of the design point by only one TELM analysis. This is the essence of its efficiency compared to the standard TELM analysis. Among response statistics of interest, the first-passage probability represents the most important one for this class of problems. This statistic is efficiently computed by using the Au-Beck important sampling algorithm, which requires knowledge of the evolving design points, in conjunction with the ETELS. The method is successfully tested for five types of excitation: (I) uniformly modulated white noise, (II) uniformly modulated broad-band excitation, (III) uniformly modulated narrow-band excitation, (IV) time- and frequency-modulated broad-band excitation, and (V) time- and frequency-modulated narrow-band excitation.