VM-WB-MECH-094

VM-WB-MECH-094
Residual Vector in Stand-Alone and Linked Mode-Superposition Harmonic Analysis

Overview

Reference:

Dickens, J. M., Nakagawa, J. M., & Wittbrodt, M. J. (1997). A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Computers & Structures, 62, 985-998.

Solver(s):

Ansys Mechanical

Analysis Type(s):
Modal Analysis
Harmonic Analysis
Element Type(s):
Spring-Damper
Structural Mass

Test Case

A mode-superposition harmonic analysis (stand-alone and linked) with an excitation frequency range of 3-70 Hz and a force load along the X-direction is performed on a spring-mass model, extracting one mode and residual vector. The spring-mass model is represented using Springs and Point Masses. Refer to Mechanical APDL VM149 for more details.

Figure 126: Spring-Mass Model

Spring-Mass Model

Material PropertiesGeometric PropertiesLoading
String stiffness (K) = 1000 N/m
Mass 1 = 1.0 kg
Mass 2 = 0.5 kg
Damping ratio = 2%
Total length = 5 m
Force along X-direction at node 4 = 1 N
Excitation frequency: 3-70 Hz

Analysis Assumptions and Modeling Notes

The spring-mass model is represented using 2-D Spring-Damper and 2-D Structural Mass elements without rotary inertia. The X and Y-axes of the spring model are inverted from the reference model to model it along the global X-axis. The model is fixed at both ends, and the displacement along the Y-direction is constrained on all nodes. In order to obtain four distinct modes, the mass at node 5 is set to half the value of the other three masses defined at nodes 2, 3, and 4. A modal analysis is performed first using the Block Lanczos eigensolver. A mode-superposition harmonic analysis is then performed with an excitation frequency range of 3-70 Hz and a force load along the X-direction at node 4. A damping ratio of 0.02 (2%) is defined in the analysis.

Results Comparison

ResultTargetMechanicalError (%)
Standalone Results
UX_MAX (m)0.0022600.00226110.04870
F_MAX (N)10.0500210.0500700.00050
Frequency @ UX_MAX (Hz)10.1020010.1020000.00000
F_MAX2 (N)4.7292404.72928070.00086
Linked Results
UX_MAX (m)0.0022600.00226110.04870
F_MAX (N)10.0500210.0500700.00050
Frequency @ UX_MAX (Hz)10.1020010.1020000.00000
F_MAX2 (N)4.7292404.72928070.00086